Masoud Rostami's research focuses on Earth and planetary atmospheric dynamics, geophysical fluid dynamics, and Earth System Modeling. Notably, he leads the development of Aeolus 2.0, a state-of-the-art tool designed to serve as the atmospheric component of the Potsdam Earth Model (POEM). The dynamical core of Aeolus 2.0 is a pseudo-spectral multi-layer moist-convective Thermal Rotating Shallow Water (mcTRSW) atmosphere model. With a PhD from Sorbonne University (formerly UPMC), Laboratoire de Météorologie Dynamique (LMD), he continues to serve as a visiting scientist at LMD.
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14412 Potsdam
ORCID
https://orcid.org/0000-0003-1730-5145 Some highlighted scientific activities, publications, and innovations include:
1. New Theory for MJO’s Dynamics: He introduced a novel theory explaining the genesis and behavior of the Madden-Julian Oscillation (MJO). The MJO is distinguished by a large-scale atmospheric circulation pattern coupled with convective activity that moves eastward along the equator. This phenomenon stands as the most prominent source of intraseasonal variability within the tropics, exerting profound influence over global weather patterns and climate dynamics.
According to the proposed theory by Rostami et al. (2022), an eastward-propagating MJO-like structure can be generated in a self-sustained and self-propelled manner due to nonlinear relaxation (adjustment) of a large-scale positive buoyancy anomaly, depressed anomaly, or a combination of these, as soon as this anomaly reaches a critical threshold in the presence of moist convection at the Equator. This anomaly, when reaching a critical threshold in the presence of moist convection at the Equator, leads to the formation of a convectively coupled "hybrid structure" with a "quasi-equatorial modon" and a convectively coupled baroclinic Kelvin wave (BKW). Interaction of the BKW with a new large-scale buoyancy anomaly contributes to the recurrent generation of the next cycle of MJO-like structure.
Rostami, M., Zhao, B., Petri, S., On the genesis and dynamics of Madden-Julian oscillation-like structure formed by equatorial adjustment of localized heating, Quarterly Journal of the Royal Meteorological Society, 2022, 148 (749), 3788-3813, https://doi.org/10.1002/qj.4388.
Rostami, M. and Zeitlin, V., Can geostrophic adjustment of baroclinic disturbances in tropical atmosphere explain MJO events?, Quarterly Journal of the Royal Meteorological Society, 2020, 146: 3998– 4013, https://doi.org/10.1002/qj.3884.
2. Adjusted Equatorial Modons: His research on eastward propagating structures led to the discovery of coherent, non-linear Equatorial Modons—steady, long-living, slowly eastward-moving, large-scale twin cyclones in the equatorial beta-plane. This discovery offers new insights into the large-scale dynamics of the tropical atmosphere, particularly the dynamical backbone of the Madden-Julian Oscillation (MJO). The findings suggest that vorticity, rather than divergence, plays a dominant role in the MJO.
Rostami, M., and Zeitlin, V., Eastward-moving convection-enhanced modons in shallow water in the equatorial tangent plane, Physics of Fluids, 2019, 31, 021701, https://doi.org/10.1063/1.5080415.
Rostami, M., and Zeitlin, V., Eastward-moving equatorial modons in shallow-water models of the tropical atmosphere, Geophysical & Astrophysical Fluid Dynamics, 2020, 115:3, 345-367, https://doi.org/10.1080/03091929.2020.1805448.
3. Aeolus 2.0: A New Generation of Atmospheric Model: The development of the Aeolus 2.0 atmospheric model marks a significant leap forward in the field of atmospheric science. The model's dynamic core is built upon a novel multi-layer pseudo-spectral moist-convective Thermal Rotating Shallow Water (mcTRSW) model, enabling the consistent incorporation of horizontal variations in material properties. In contrast to classical shallow-water models, which assume a homogeneous, incompressible fluid under hydrostatic balance, Aeolus 2.0's inhomogeneous layers allow for variations in mean temperature and density gradients. Recently, the conceptual multi-layer version of the model has been employed to propose a novel theory for the genesis and dynamics of the Madden-Julian Oscillation (MJO), a prominent atmospheric phenomenon.
The link to the ZENODO repository for the open-source stand-alone version of the Atmospheric Model Aeolus 2.0 is provided below: [ZENODO Link]
To explore and gain further insights into the applications of Aeolus 2.0, its legacy models, and moist convection in the RSW model, please visit the following link: [link].
Rostami, M., Petri, S., Fallah, B., Fazel-Rastgar, F., Aeolus 2.0's thermal rotating shallow water model: A new paradigm for simulating extreme heatwaves, westerly jet intensification, and more. Physics of Fluids, 2025, 37 (1), 016604. https://doi.org/10.1063/5.0244908. [PDF]
4. Improved Moist Convective Rotating Shallow Water Model (imcRSW): This output presents an updated version of the idealized moist convective RSW model, referred to as the imcRSW model. This model incorporates various diabatic effects through appropriate parameterizations, including surface evaporation, condensation, latent heat release, tracer fields, precipitable water, and vaporization and entrainment. The imcRSW model has demonstrated successful applications in simulating tropical cyclones and polar vortices on both Earth and Mars. It is a robust and efficient model that maintains simplicity while accounting for diabatic effects. The model employs well-balanced numerical schemes and is capable of resolving fronts and capturing shocks. This feature enables researchers to explore fundamental characteristics of moist-convectively coupled synoptic-scale structures on Earth and other planets within a relatively short computational timeframe. The imcRSW model has been utilized to investigate the impact of moist convection on the instability of barotropic large-scale cyclonic and anticyclonic vortices on various planetary planes, including the f -plane, gamma-plane, and beta-plane.
Rostami, M., and Zeitlin, V., An improved moist-convective rotating shallow water model and its application to instabilities of hurricane-like vortices, Quarterly Journal of the Royal Meteorological Society, 2018, 1-13, https://doi.org/10.1002/qj.3292.
5. Dynamical Nature of Saturn’s North Polar Hexagon: “On the dynamical nature of Saturn’s North Polar hexagon” is another research that has garnered scientific and public attention. In this research an innovative method is proposed to explain hexagon’s instability and to reproduce its structure, which is one of the enigmatic structures in the universe and has raised many open questions for more than three decades. Stability of the hexagonal shape for a few decades, its dependency on Saturn’s North polar vortex, and lack of a similar pattern on the Saturn’s South Pole are explained in this article. All dynamical variables of the large scale Saturn’s atmosphere are nondimensionalized by just one single parameter of Rossby deformation radius. Reproduction of hexagon by barotropic model, for the first time, and clarifying its dynamics help scientists to better understand the atmospheric circulation of Saturn and spatial distribution of passive tracers. Applying the same methodology on other planets is straight forward.
Rostami, M., and Zeitlin, V., and Spiga, A., On the dynamical nature of Saturn’s North Polar hexagon, Icarus, 2017, 297, 59-70, https://doi.org/10.1016/j.icarus.2017.06.006.
6. Dynamics of Jupiter’s Equatorial zone: Instability Analysis and a Mechanism for Y-shaped Structures: This study investigates the dynamics of Jupiter's Equatorial Zone (EZ) by analyzing the stability of equatorial jets and exploring the role of moist convection in shaping atmospheric structures. Using linear stability analysis and nonlinear simulations, the research highlights how zonal wind strength influences instability modes and examines the nonlinear evolution of moist-convective flows. The findings reveal mechanisms for vortex amplification and suppression near zonal jets, and propose a novel explanation for the formation of Y-shaped cloud structures, attributing them to hybrid dipolar modons coupled with baroclinic Kelvin waves driven by localized heating in a diabatic environment.
Rostami M., Fallah B., Fazel-Rastgar F., Dynamics of Jupiter’s equatorial zone: Instability analysis and a mechanism for Y-shaped structures, Icarus, 429, 2025, 116414,
https://doi.org/10.1016/j.icarus.2024.116414.
7. Spatially Inhomogeneous CO2 Deposition in Mars’ Atmosphere: In this study, a new mechanism for explaining spatially inhomogeneous diabatic effects in the atmosphere of Mars has been proposed. Specifically, it involves the inhomogeneous deposition of CO2 through a gas-solid phase transition. This mechanism suggests that aerosol nuclei could trigger CO2 ice nucleation, leading to the formation of high potential vorticity blobs within Mars’ annular polar vortex. This study also introduces a parameterization to replicate and elucidate the generation of these vortices.
Rostami, M., and Zeitlin, V., Montabone, L., On the role of spatially inhomogeneous diabatic effects
upon the evolution of Mars’ annular polar vortex, Icarus, 2018, 314, 376-388, https://doi.org/10.1016/j.icarus.2018.05.026.
8. Equatorial Modon Genesis & Non-Universality of the Gill’s Mechanism: An innovative method has been initiated to generate the recently discovered Equatorial Modon (item 2) by adjusting the equatorial moist convective environment. This study offers new perspectives on the generation and dynamics of large-scale equatorial excited systems during equatorial adjustment over the warm pool.
The non-universality of the Gill mechanism is a significant breakthrough in understanding tropical circulation. The classical Gill theory, explaining the generation of Rossby and Kelvin waves due to a localized heating, was widely accepted as a universal mechanism. However, our recent studies have shown that the emergence of the "Equatorial Modon" can occur through geostrophic adjustment of a large-scale depression-type disturbance on the equatorial beta-plane. This finding provides new insights into equatorial excited systems and offers avenues for further research on tropical circulation.
Rostami, M., and Zeitlin, V., Geostrophic adjustment on the equatorial beta-plane revisited, Physics of Fluids, 2019, 31, 081702, https://doi.org/10.1063/1.5110441.
9. Numerical Model for Modern Human Dispersal by Environmental, Cultural, and Societal Drivers: The development of two new human mobility/dispersal models, in collaboration with the interdisciplinary CRC806 project, represents a significant advancement in our understanding of the environmental, cultural, and societal drivers of human migration. These models, the Constrained Random Walk (CRW) models, have been applied to a range of time periods, from Heinrich events to the Holocene, and have been used to analyze the dispersal patterns of different technocomplexes. By taking into account both environmental factors and cultural/social influences, these models provide a more comprehensive understanding of the drivers of human migration and offer insights into how these factors have shaped human societies throughout history. The CRC806 project’s interdisciplinary approach highlights the importance of collaboration across fields in advancing our knowledge of complex societal issues. Indeed, this research aimed to simulate the interstadial and stadial periods of climate oscillations, specifically the Heinrich and Dansgaard-Oeschger (DO) events, which are believed to be caused by episodic discharge of massive numbers of icebergs from the Hudson Strait region into the North Atlantic Ocean. The study uses the CCSM4 climate model to better understand the potential for human existence during the early and late phases of the Aurignacian technocomplex, which occurred during these periods.
Shao, Y., Limberg, H., Klein, K., Wegener, C., Schmidt, I., Weniger, G. C., Hense, A., Rostami, M., Human-existence probability of the aurignacian techno-complex under extreme climate conditions,
Quaternary Science Reviews, 2021, 263, 106995, https://doi.org/10.1016/j.quascirev.2021.106995.
Klein, K., Wegener, C., Schmidt, I., Rostami, M., Ludwig, P., Ulbrich, S., Weniger,G. C., Shao, Y., Human existence potential during the last glacial maximum, Quaternary International, , 2020, https://doi.org/10.1016/j.quaint.2020.07.046.
10. Analyzing Hurricane-like Vortices: Insights from Barotropic and Baroclinic Linear Stability Analysis: This study delves into the dynamics of hurricane-like vortices and conducts barotropic and baroclinic linear stability analysis using Chebyshev grid points. The investigation spans one- and two-layer shallow water models, with a particular focus on various atmospheric phenomena including Saturn’s north polar vortex, the hexagonal circumpolar jet on Saturn, Mars’ annular polar vortex, Earth cyclonic structures, and the African Easterly Jet. The research undertaken sheds light on the evolution of hurricane-like vortices and their trajectories, including their interactions with diverse topographies such as elliptical islands, zonal and meridional mountainous ridges on the beta-plane.
Rostami, M. and Zeitlin, V., Evolution of double-eye wall hurricanes and emergence of complex tripolar end states in moist-convective rotating shallow water model, Physics of Fluids, 2022, 32, 066602, https://doi.org/10.1063/5.0096554.
Rostami, M., and Zeitlin, V., Evolution, propagation, and interactions with topography of hurricane-
like vortices in moist-convective rotating shallow-water model, Journal of Fluid Mechanics, 2020, 902, A24, https://dx.doi.org/10.1017/jfm.2020.567.
Rostami, M., and Zeitlin, V., Influence of condensation and latent heat release upon barotropic
and baroclinic instabilities of vortices in a rotating shallow water f-plane model, Geophysical &
Astrophysical Fluid Dynamics, 2017, 111 (1), 1–31, https://doi.org/10.1080/03091929.2016.1269897.
11. Natural versus anthropogenic pollution sources of insoluble precipitation residues: This set of studies has focused on the distribution, concentration, and isotopic composition of insoluble precipitation residues, trace elements such as Sr, Nd, and Pb, as well as atmospheric deposition and contamination of heavy metal elements in glacier depositions in the northeastern Tibetan Plateau region.
Jiao, X., Dong, Z., Kang, S., Li, Y., Jiang, C., & Rostami, M., New insights into heavy metal
elements deposition in the snowpacks of mountain glaciers in the eastern Tibetan Plateau,
Ecotoxicology and Environmental Safety, 2021, 207, 111228, https://doi.org/10.1016/j.ecoenv.2020.111228.
Wei, T., Kang, S., Dong, Z., Qin, X., Zong, C., Shao, Y., & Rostami, M., Natural versus
anthropogenic sources and seasonal variability of insoluble precipitation residues at Laohugou
Glacier in northeastern Tibetan Plateau, Environmental Pollution, 2020, 261, 114114, https://doi.org/10.1016/j.envpol.2020.114114.
Wei, T., Dong, Z., Kang, S., Rostami, M., Ulbrich, S., & Shao, Y., Hf-Nd-Sr isotopic fingerprinting for aeolian dust deposited on glaciers in the northeastern Tibetan Plateau region, Global and Planetary Change, 2019, 177, 69-80, https://doi.org/10.1016/j.gloplacha.2019.03.015.
Wei, T., Dong, Z., Kang, S., Zong, C., Rostami, M., & Shao, Y., Atmospheric deposition and contamination of trace elements in snowpacks of mountain glaciers in the northeastern Tibetan Plateau, Science of The Total Environment, 2019, https://doi.org/10.1016/j.scitotenv.2019.06.455.
12. Dynamics of extreme heatwaves in the mid-latitude atmosphere: This study examines the influence of large-scale localized temperature anomalies in mid-latitude regions on condensation patterns and corresponding circulation in various environments. The research reveals that these anomalies give rise to distinct circulation patterns and heat fluxes. Depending on the perturbation’s characteristics, they can induce atmospheric instability, leading to precipitation systems such as rain bands and distinctive cloud patterns. The study also demonstrates the initiation of an anticyclonic high-pressure rotation in the upper troposphere, resulting in an anisotropic northeast-southwest tilted circulation of heat flux.
Rostami, M., Severino, L., Petri, S., Hariri, S., Dynamics of localized extreme heatwaves in the
mid-latitude atmosphere: A Conceptual examination, Atmospheric Science Letters, 2023, 25 (1),
e1188, https://doi.org/10.1002/asl.1188.
13. Climate Change Impacts in Central Asia: These studies explore the repercussions of recent global warming on extreme weather events in Central Asia (CA). By comparing observational and hypothetical climate scenarios, the analysis reveals a notable increase in both the frequency and intensity of extreme temperature and precipitation events attributed to global warming. Particularly noteworthy is the observed surge in heatwave occurrences, coupled with a heightened sensitivity of dry and wet events to changes in precipitation and temperature. Additionally, high-resolution climate models highlight shifts in Tundra climate zones within the Alps and Tibetan Plateau, revealing significant and irreversible impacts on global ecosystems.
Fallah, B. and Rostami, M., Exploring the impact of the recent global warming on extreme
weather events in Central Asia using the counterfactual climate data ATTRICI v1.1, Climate
Change & Policy , 2024, 177, 80, https://doi.org/10.1007/s10584-024-03743-0.
Fallah, B., Didovets, I., Rostami, M., Hamidi, M., Climate change impacts on central Asia: trends, extremes, and future projections, International Journal of Climatology, 2024, 1–23. https://doi.org/10.1002/joc.8519
, , , & High-resolution CMIP6 analysis highlights emerging climate challenges in alpine and Tibetan Tundra zones. Meteorological Applications, 2024, 31(5), e70001. https://doi.org/10.1002/met.70001
Fallah, B., Rostami, M., Russo, E., Harder, P., Menz, C., Hoffmann, P., Didovets, I. and Hattermann, F. F., Climate model downscaling in central Asia: a dynamical and a neural network approach, Geoscientific Model Development, 2025, 18, 161-180. https://gmd.copernicus.org/articles/18/161/2025/
14. Case Studies of Extreme Events: This series of studies focuses on analyzing observational and reanalysis data to understand the dynamics behind major extreme events, such as extreme rainfall, heatwaves, droughts, and air quality issues.
Fazel-Rastgar, F., Sivakumar, V., Rostami, M., & Fallah, B. H., Unveiling meteorological synergies in the coupling of an abnormal easterly wave and cutoff low in South Africa's February 2023 rainfall. Meteorological Applications, 2025, 32(1): e70027. doi:10.1002/met.70027.
Fazel-Rastgar, F., Sivakumar, V., Rostami, M., & Fallah, B. H. Study on associated effects of extreme drought and heatwave on air quality in South Africa during October 2022. Bulletin of Atmospheric Science & Technology, 2025, 6(1): 14. doi:10.1007/s42865-025-00101-5.
Fazel-Rastgar, F., Rostami, M., Fallah, B. H., & Sivakumar, V. Torrential rainfall with severe flooding associated with a baroclinic disturbance on November 17, 2023, United Arab Emirates (UAE). International Journal of River Basin Management, 2025. doi:10.1080/15715124.2025.2462575.
This page explores the applications of Aeolus 2.0, as well as the chronological advancements and applications of its predecessors, in relation to published peer-reviewed studies on the barotropic and baroclinic versions of the moist-convective (Thermal) Rotating Shallow Water (mc(T)RSW) models. It also discusses other numerical schemes that incorporate the same physics as the mc(T)RSW models. Aeolus 2.0 integrates advancements in moist convection, precipitation dynamics, insolation, and topographic effects, building on the theoretical and numerical foundations of the RSW model. This page traces the evolution and applications of these developments, highlighting key milestones that have transformed Aeolus 2.0’s dynamical core into a versatile framework for advancing research in atmospheric and climate processes.
Since the rotating shallow water magnetohydrodynamics (MHD) equations can also be implemented within the developed schemes of the (T)RSW model, we have extended both the numerical schemes and theoretical foundations to include the thermal rotating shallow water magnetohydrodynamics (MHD) equations. In the following chronological advancements, you will observe the influence of MHD as well.
2009: Foundations of Moist Dynamics
The theoretical groundwork for incorporating moisture transport, precipitation, and convection effects into the one-layer Rotating Shallow Water (RSW) model began in 2009 (Bouchut et al., 2009). This model integrates the hydrodynamic nonlinearity of the standard shallow-water model with additional nonlinearity arising from the precipitation threshold. It supports both a theoretical approach via the method of characteristics and efficient numerical solutions through shock-capturing finite-volume schemes. When linearized in the dynamical sector, the model accurately replicated the propagation of precipitation region boundaries—termed "precipitation fronts"—as observed in earlier studies. Numerical experiments on simple wave interactions with a moisture front aligned well with analytical findings, underscoring the role of precipitating zones as dissipative reflectors. The study also examined how disturbances propagate in uniformly saturated areas, deriving criteria for the formation of precipitation fronts. Finally, this model simulated wave breaking as an inherently nonlinear phenomenon, demonstrating how moisture effects alter the classical shock formation scenario.
Reference: Bouchut, F., Lambaerts, J., Lapeyre, G., & Zeitlin, V. (2009). Fronts and nonlinear waves in a simplified shallow-water model of the atmosphere with moisture and convection. Physics of Fluids, 21(11), 116604. https://doi.org/10.1063/1.3265970
2011: Two-Layer Moist Dynamics
In 2011, Lambaerts et al. (2011a) derived a two-layer Rotating Shallow Water (RSW) model for a moist atmosphere, incorporating water vapor condensation and related diabatic heating. Moist convection is represented by additional mass exchanges between the layers, determined based on the principle of moist enthalpy conservation, which is linked to precipitation. The model accommodates various boundary conditions at both the lower and upper boundaries. The authors demonstrated that the model, under appropriate limits, reproduces key simplified models previously used in the literature for describing large-scale moist-convective dynamics and precipitation fronts. These include linear two-layer baroclinic models, nonlinear two-layer quasigeostrophic models, and nonlinear one-layer moist-convective rotating shallow-water models. They examined the properties of the model equations, with special attention to the hyperbolicity loss inherent in multilayer RSW models and the dynamics of front propagation. Numerical illustrations of these properties were provided using a recently proposed high-resolution finite-volume numerical scheme that incorporates precipitation sources and sinks.
Lambaerts et al. (2011b) then applied the two-layer moist-convective RSW model to study the dynamical influence of moist convection on the development of barotropic instability in the RSW model. They performed an exhaustive linear "dry" stability analysis of the Bickley jet, using the most unstable mode identified to initialize simulations for comparing the development and saturation of the instability in dry and moist configurations. They showed that moist effects influence both the balanced and unbalanced components of the flow. The most significant differences between dry and moist evolution include: (1) the efficiency of the moist-convective instability, which manifests as an increase in the growth rate at the onset of precipitation and a stronger deviation of the end state from the initial state, measured with various norms; (2) a pronounced cyclone-anticyclone asymmetry during the nonlinear evolution of the moist-convective instability, leading to additional geostrophic adjustment compared to the dry case and a modification of the end state; and (3) ageostrophic activity in both precipitation zones and non-precipitating areas due to secondary geostrophic adjustment.
References:
Lambaerts, J., Lapeyre, G., & Zeitlin, V. (2011). Moist versus dry barotropic instability in a shallow-water model of the atmosphere with moist convection. Journal of Atmospheric Sciences, 68(6), 1234–1252. https://doi.org/10.1175/2011JAS3540.1
Lambaerts, J., Lapeyre, G., Zeitlin, V., & Bouchut, F. (2011). Simplified two-layer models of a precipitating atmosphere and their properties. Physics of Fluids, 23(4), 046603. https://doi.org/10.1063/1.3582356
2012: Baroclinic Instability in Moist Conditions
Lambaerts et al. (2012) applied the two-layer moist-convective Rotating Shallow Water (2mcRSW) model to analyze the effects of water vapor condensation and latent heat release on the evolution of baroclinic instability. This model represents a two-layer RSW system where moisture dynamically couples with mass exchanges between layers due to condensation and precipitation processes, incorporating all known models of this type in the literature as specific limiting cases. It is fully nonlinear and ageostrophic, with a baroclinic Bickley jet as the reference state. The study begins with a "dry" linear stability analysis of the jet, identifying the most unstable mode, which then serves as the initial condition for high-resolution numerical simulations of the instability's life cycle in both non-precipitating (where moisture acts as a passive tracer) and precipitating cases. A new-generation well-balanced finite-volume scheme is used for these simulations. In the non-precipitating case, the model reproduces the typical cyclonic wave-breaking life cycle of baroclinic instability with high accuracy. In the precipitating case, condensation at the initial stages significantly accelerates the growth rate of baroclinic instability by producing additional available potential energy through latent heat release. Condensation occurs in frontal regions and wraps around the cyclone, aligning well with both moist cyclogenesis theory and observational data. This process introduces a distinct cyclone–anticyclone asymmetry, which the authors explain in detail, highlighting its impact on the flow equilibration in the later stages of instability saturation. Despite the considerable differences in the evolution, only minor differences in various norms of the perturbations persist between the precipitating and non-precipitating cases by the end of the saturation process.
Reference: Lambaerts, J., Lapeyre, G., & Zeitlin, V. (2012). Moist versus dry baroclinic instability in a simplified two-layer atmospheric model with condensation and latent heat release. Journal of Atmospheric Sciences, 69, 1405–1426. https://doi.org/10.1175/JAS-D-11-0205.1
2016: Instabilities in Hurricane-Like Vortices
Lahaye and Zeitlin (2016) investigated the instabilities of hurricane-like vortices using a one-layer mcRSW model. Their linear stability analysis revealed that the dominant unstable modes are mixed Rossby-inertia-gravity waves. Depending on the specifics of the vorticity profile, the instability may exhibit wavenumber selection, resulting in either a single mode with a distinct maximum growth rate or multiple modes with similar growth rates. Consistent with earlier findings, the study confirmed the axisymmetrization of vorticity during instability development, impacting hurricane intensity. In "dry" simulations, wind intensification occurs only within the radius of maximum wind, while the peak wind speed decreases. Conversely, "moist precipitating" simulations, both with and without evaporation, show a net increase in wind speeds, including at the radius of maximum wind. The study quantified the significant dynamical effects of moisture on vortex reorganization and the efficiency of inertia-gravity wave emission. It also identified periodic bursts of wave emission associated with the development of unstable modes within the vortex and the emergence of convectively coupled waves in moist simulations with evaporation.
Reference: Lahaye, N., & Zeitlin, V. (2016). Understanding instabilities of tropical cyclones and their evolution with a moist-convective rotating shallow-water model. J. Atmos. Sci., 73, 505–523. https://doi.org/10.1175/JAS-D-15-0115.1
2017 (a): Moist Effects on Vortex Instabilities
Rostami and Zeitlin (2017) utilized the mcRW model to examine how condensation and latent heat release affect the development of barotropic and baroclinic instabilities in large-scale, low Rossby-number vortices on the f-plane. The study compared four environments: (i) humidity as a passive scalar, (ii) humidity with condensation beyond a saturation threshold, (iii) humidity with condensation and evaporation using three parameterizations. Initial conditions were set using unstable modes from a linear stability analysis of the "dry" model. In the mid-latitude atmospheric vortices configuration, the typical evolution of barotropically unstable vortices—characterized by dipolar breakdown—was significantly altered by condensation and moist convection, particularly with surface evaporation. The simulations revealed cyclone-anticyclone asymmetry in response to moist effects and showed that moist conditions intensified inertia-gravity wave emission during vortex evolution. In a baroclinic configuration reflecting idealized cut-off lows, the azimuthal structure of the leading unstable mode was sensitive to stratification details, leading to different evolution scenarios: one resulting in dipolar breakdown and the other in tripole formation. Moisture effects enhanced perturbations in the lower layer, particularly during tripole formation.
Reference: Rostami, M., & Zeitlin, V. (2017). Influence of condensation and latent heat release upon barotropic and baroclinic instabilities of vortices in a rotating shallow water f-plane model. Geophysical & Astrophysical Fluid Dynamics, 111(1), 1–31. https://doi.org/10.1080/03091929.2016.1269897
2017 (b): Modeling Saturn's Hexagon: Polar Vortex and Jet Instability
Rostami et al. (2017) applied the one-layer moist-convective Rotating Shallow Water (1mcRSW) model to explain Saturn’s long-lived North Polar hexagonal circumpolar jet as an instability of the coupled system involving the polar vortex and circumpolar jet. This model also accounts for the absence of a similar hexagonal structure at Saturn’s South Pole. Using the latest observed winds from Saturn’s polar regions, a detailed linear stability analysis of the circumpolar jet was conducted in two configurations: (i) the “jet-only” configuration (excluding the polar vortex), and (ii) the “jet + vortex” configuration (including the polar vortex). A parameter domain was identified—including the latitude of the circumpolar jet and the curvature of its azimuthal velocity profile—where the system's most unstable mode displays an azimuthal wavenumber of 6. Fully nonlinear simulations were then performed, initialized either with the most unstable small-amplitude mode or with a random combination of unstable modes. Results showed that the development of barotropic instability in the “jet + vortex” configuration produces a long-lived structure resembling the observed hexagon, while the “jet-only” configuration does not, consistent with previous studies. This finding underscores the critical dynamical role of the North Polar vortex. Additionally, the influence of moist convection—recently proposed in the literature as a potential origin of Saturn’s North Polar vortex system—was examined within the framework of the model and found not to affect these conclusions.
Reference: Rostami, M., Zeitlin, V., & Spiga, A. (2017). On the dynamical nature of Saturn’s North Polar hexagon. Icarus, 297, 59–70. https://doi.org/10.1016/j.icarus.2017.06.006
2017 (c): Thermal Instability in RSW with Horizontal Temperature Gradients
This study investigates a thermal instability within the RSW model, highlighting the influence of horizontal density and temperature gradients. By framing the system as a non-isentropic, rotating 2D gas, the authors reveal an instability with convective properties that arises when buoyancy anomalies at the vortex center and ambient vorticity have opposing signs in a f-plane. Distinct from traditional barotropic instability, this thermal instability demonstrates higher growth rates across a range of parameters, enhancing mixing efficiency in the nonlinear phase.
Reference: Gouzien, É., Lahaye, N., Zeitlin, V., & Dubos, T. (2017). Thermal instability in rotating shallow water with horizontal temperature/density gradients. Physics of Fluids, 29(10), 101702. https://doi.org/10.1063/1.4996981
2018 (a): Application of the 1mcRSW Model to Mars' Annular Polar Vortex: Impact of Diabatic Effects
This study investigates the role of spatially inhomogeneous diabatic effects on the evolution of Mars' annular polar vortex, using the 1mcRSW model. The Martian polar vortex is characterized by a potential vorticity (PV) low near the winter pole and asymmetric high-PV patches around this low. A simple parameterization of radiative relaxation and latent heat release from spatially inhomogeneous CO2 deposition is incorporated into the 1mcRSW model, which includes the dependence on the concentration of condensation nuclei. Linear stability analysis of the zonally and time-averaged Martian winter polar vortex identifies unstable modes, which are used to initialize high-resolution numerical simulations of their nonlinear evolution in four configurations: adiabatic, diabatic with only radiative relaxation, only deposition, and both radiative relaxation and deposition. The results show that the combined effects of radiative relaxation and inhomogeneous CO2 deposition can explain the observed unstable structure of the Martian polar vortex, including the high-PV patches. The findings highlight the importance of diabatic effects in shaping the dynamics of Mars' polar vortex.
Reference: Rostami, M., Zeitlin, V., & Montabone, L. (2018). Application of the 1mcRSW model to Mars' annular polar vortex: Impact of diabatic effects. Icarus, 314, 376-388. https://doi.org/10.1016/j.icarus.2018.05.026
2018 (b): Improved 2mcRSW Model and Its Application to Instabilities of Hurricane-like Vortices
This study introduces an improved version of the two-layer mcRSW model. The new improvement incorporates precipitable water, vaporization, entrainment, and precipitation, making the model cloud-resolving. It is applied to investigate the development of instabilities in tropical cyclone-like vortices, demonstrating its ability to capture the dynamics and growth of these atmospheric phenomena. The upgraded mcRSW model offers a more detailed representation of convection and cloud processes, providing a framework for studying tropical storm dynamics and related instabilities.
Reference: Rostami, M., & Zeitlin, V. (2018). An improved moist-convective rotating shallow-water model and its application to instabilities of hurricane-like vortices. Quarterly Journal of the Royal Meteorological Society, 144(712), 1450–1462. https://doi.org/10.1002/qj.3292
2019 (a): Eastward-Moving Convection-Enhanced Modons in Shallow Water on the Equatorial Tangent Plane
This study demonstrates the application of the barotropic mcRSW model. The authors reveal the existence of steady, long-living, slowly eastward-moving, large-scale coherent twin cyclones, known as equatorial modons, within the shallow water model on the equatorial beta-plane. The work begins with the construction of analytical asymptotic modon solutions under the non-divergent velocity approximation. Subsequently, high-resolution simulations show that such configurations evolve into steady dipolar solutions of the full model. In an atmospheric context, these modons persist in the presence of moist convection and are accompanied by distinct patterns of water-vapor condensation, which further enhance their structure.
Reference: Rostami, M., & Zeitlin, V. (2019). Eastward-moving convection-enhanced modons in shallow water in the equatorial tangent plane. Physics of Fluids, 31(2), 021701. https://doi.org/10.1063/1.5080415
2019 (b): Geostrophic Adjustment on the Equatorial Beta-Plane Revisited
Using the 1mcRSW model, the authors demonstrate that the classical Gill theory of tropical circulation induced by localized heating is not universally applicable. It is shown that the standard scenario of generating westward-moving Rossby and eastward-moving Kelvin waves, which forms the basis of the classical Gill theory, is not unique. Depending on the strength and aspect ratio of the initial perturbation, the response in the western sector can be dominated by inertia-gravity waves. The adjustment in the diabatic moist-convective shallow water model can vary significantly and, depending on the parameters, may produce either a Gill-like response or eastward-moving coherent dipolar structures, such as equatorial modons, which do not appear in the "dry" adjustment. Alternatively, vortices may travel northwest in the Northern Hemisphere and southwest in the Southern Hemisphere.
Reference: Rostami, M., & Zeitlin, V. (2019). Geostrophic adjustment on the equatorial beta-plane revisited. Physics of Fluids, 31(8), 081702. https://doi.org/10.1063/1.5110441
2020 (a): One-Layer Moist-Convective Thermal Rotating Shallow Water Model (mcTRSW)
This study shows how the moist-convective rotating shallow water model, in which moist convection and the associated latent heat release are incorporated into the standard rotating shallow water model of the atmosphere, can be improved by introducing, in a self-consistent manner, horizontal gradients of potential temperature and its variations due to condensation heating, radiative cooling, and ocean-atmosphere heat fluxes. The quasi-geostrophic limit of the model in mid-latitudes and its weak-gradient limits in the equatorial region are also demonstrated in this study. The capabilities of the new model are illustrated through examples of convection-coupled gravity waves and equatorial waves generated by the relaxation of localized pressure and potential temperature anomalies in the presence of moist convection.
Reference: KurganovLiu Zeitlin, V. (2020). Moist-convective thermal rotating shallow water model. Physics of Fluids, 32 (6): 066601. https://doi.org/10.1063/5.0007757
2020 (b): A Novel Well-Balanced Central-Upwind Scheme for One-Layer mcTRSW Model
This numerical scheme introduces a new high-resolution, well-balanced central-upwind scheme for the two-dimensional mcTRSW model. The scheme preserves equilibrium states in the presence of topography and temperature/density variations while enabling high-resolution tracking of the active scalar field alongside velocity and pressure fields. The authors employed this new scheme to examine both the similarities and differences in the predictions of the thermal and isothermal shallow water models for fundamental dynamical processes, including the evolution of isolated vortices in the midlatitude β-plane with topography and the relaxation of localized pressure and temperature perturbations in the equatorial β-plane.
Reference: Kurganov, A., Liu, Y., & Zeitlin, V. (2020). Thermal versus isothermal rotating shallow water equations: comparison of dynamical processes by simulations with a novel well-balanced central-upwind scheme. Geophysical & Astrophysical Fluid Dynamics, 115(2), 125–154. https://doi.org/10.1080/03091929.2020.1774876
2020 (c): Eastward-moving Equatorial Modons in mcRSW model
In this study, the authors showed that steady, large-scale, slowly eastward-moving twin-cyclone coherent structures, known as equatorial modons, exist in both one-layer and two-layer versions of the rotating shallow water model on the equatorial beta plane. These structures can emerge through the process of ageostrophic adjustment from the analytic asymptotic modon solutions of the vorticity equation, obtained in the limit of small pressure perturbations. The evolution of these structures in adiabatic and moist-convective environments, as well as in the presence of topography, is analyzed, demonstrating their robustness in the one-layer model. It is shown that moist convection enhances and helps maintain the modons.
In the two-layer model, barotropic and quasi-barotropic modons exhibit features similar to those of the one-layer modon, whereas increasing baroclinicity ultimately leads to a loss of coherence and a halt in eastward propagation. Some characteristics of equatorial modons resemble those observed in Madden-Julian Oscillation (MJO) events in the tropical atmosphere, suggesting their potential relevance to the dynamics of this phenomenon. In future work, the authors further explore this connection using the mcTRSW model.
Reference: Rostami, M., & Zeitlin, V. (2020). Eastward-moving equatorial modons in moist-convective shallow-water models. Geophysical & Astrophysical Fluid Dynamics, 115(3), 345–367. https://doi.org/10.1080/03091929.2020.1805448
2020 (d): Application of the One-Layer mcRSW Model to Understand the Evolution, Propagation, and Interaction with Topography of Hurricane-Like Vortices
The authors used the mcRSW model to analyze how intense localized vortices, with horizontal velocity and relative vorticity distributions similar to those observed in tropical cyclones (TCs), evolve and interact with topography on the β-plane at low latitudes. The instabilities of such TC-like vortices were first examined in the f-plane approximation. Their development, interaction with beta-gyres, and role in vorticity redistribution and intensification were then analyzed along the vortex trajectories on the β-plane, both in dry and moist-convective environments.
The study further investigated the interaction of these vortices with idealized topography, including zonal and meridional ridges and elliptical islands, while assessing the influence of moist convection on these processes. The results reveal complex vortex dynamics and can contribute to better understanding and predicting the evolution of the barotropic component of TCs, their trajectories over the ocean, landfall behavior, and associated condensation and precipitation patterns.
Reference: Rostami, M., & Zeitlin, V. (2020). Evolution, propagation and interactions with topography of hurricane-like vortices in a moist-convective rotating shallow-water model. Journal of Fluid Mechanics. 2020;902:A24. https://doi.org/doi:10.1017/jfm.2020.567
2020 (e): Discovery of Geostrophic Adjustment of Baroclinic Disturbances in the Tropical Atmosphere as a Mechanism to Explain MJO Events
This study is the first in atmospheric science to propose that the geostrophic adjustment of equatorial disturbances in a moist-convective environment serves as a mechanism for the formation of Madden-Julian Oscillation (MJO) events. Using the two-layer moist-convective Rotating Shallow Water (2mcRSW) model, the authors investigated the relaxation (adjustment) of localized large-scale pressure anomalies in the lower equatorial troposphere. Their findings demonstrate that this process generates coherent structures closely resembling MJO events, as observed in vorticity, pressure, and moisture fields.
The study reveals that baroclinicity and moist convection significantly modify the classical quasi-barotropic "dry" adjustment, previously established using the one-layer shallow-water model. Traditionally, this adjustment involves the westward emission of equatorial Rossby waves with dipolar meridional structures and the eastward propagation of equatorial Kelvin waves. However, when moist convection is sufficiently strong, the dipolar cyclonic structure, initially forming as a Rossby-wave response, transforms into a coherent modon-like structure in the lower layer. This structure couples with a baroclinic Kelvin wave through a zone of enhanced convection, leading to the formation of a self-sustained, slowly eastward-propagating, zonally asymmetric quadrupolar vorticity pattern. At the same time, a weaker quadrupolar structure of opposite sign emerges in the upper layer, closely resembling the active phase of MJO events.
As the process continues, the baroclinic Kelvin wave detaches from the dipole, which maintains its slow eastward motion. The detached Kelvin wave then circumnavigates the Equator, later interacting with the dipole, further influencing the evolution of MJO-like structures. These findings suggest that moist-convective geostrophic adjustment may play a fundamental role in the initiation and maintenance of MJO events, providing a novel theoretical framework for understanding intraseasonal tropical variability.
Reference: Rostami, M., & Zeitlin, V. (2020). Can geostrophic adjustment of baroclinic disturbances in the tropical atmosphere explain MJO events? Quarterly Journal of the Royal Meteorological Society, 146(S1), 3998–4013. https://doi.org/10.1002/qj.3884
2021 (a): Application of the mcRSW Model to Low-Latitude Easterly Jets in the Presence of Topography and Simulation of Cyclogenesis
In this study, the authors used the 2mcRSW model to investigate the dynamical processes governing the evolution of easterly waves propagating within a low-latitude easterly jet crossing a land-sea boundary. This setup serves as a simplified representation of the African Easterly Jet (AEJ) over the West African plateau and the Atlantic Ocean.
A thorough linear stability analysis was conducted to identify the unstable modes of the jet, which were then used to initialize fully nonlinear numerical simulations. This approach allowed the authors to determine the nonlinear evolution of unstable perturbations of the jet in both dry and moist-convective environments, revealing critical differences between the two cases.
The study identified a mechanism for the formation of intense lower-layer cyclonic vortices along the northern flank of the jet and assessed the influence of the land-sea contrast on this process. These findings provide valuable insights into the role of moist convection and topography in modulating cyclogenesis in tropical regions.
2021: Application of the One-Layer mcTRSW Model to Understand the Dynamics of Tropical Cyclones
By applying one-layer mcTRSW model, the authors investigated how thermal effects influence the trajectories, intensity, and formation of secondary structures during the passage of strong tropical cyclone-like vortices over oceanic warm and cold pools, as well as over island-type topography.
Reference: Kurganov, A., Liu, Y., & Zeitlin, V. (2021). Interaction of tropical cyclone-like vortices with sea-surface temperature anomalies and topography in a simple shallow-water atmospheric model. Physics of Fluids, 33(10), 106606. https://doi.org/10.1063/5.0064481
2022 (a): Development of a Flux Globalization-Based Well-Balanced Path-Conservative Central-Upwind Scheme for the 1-D Two-Layer TRSW Model
The authors developed a flux globalization-based well-balanced path-conservative central-upwind scheme for the two-layer thermal rotating shallow water (TRSW) equations, which are fundamental in both oceanography and atmospheric sciences. As in all two-layer shallow water models, the studied two-layer TRSW system loses hyperbolicity due to Kelvin-Helmholtz-type instabilities that arise when the vertical velocity shear between the layers becomes sufficiently large. Therefore, before developing the numerical method, the authors examined the hyperbolicity criterion to address this fundamental issue.
Beyond hyperbolicity loss, additional challenges arise in developing numerical methods for this system. These challenges stem from the presence of nonconservative terms modeling layer interaction and the complex structure of steady-state solutions, which an effective well-balanced numerical method must precisely preserve. To handle the nonconservative product terms, the authors employed the path-conservative technique, which was implemented within the flux globalization framework. In this approach, the source and nonconservative terms are incorporated into the fluxes, leading to a quasi-conservative system that is then numerically solved using a Riemann-problem-solver-free central-upwind scheme.
The well-balanced property of the proposed scheme is ensured through several key strategies: performing piecewise linear reconstruction for equilibrium variables instead of conservative variables, developing special quadratures required for the flux globalization procedure, and reducing numerical diffusion when the computed solution is near or at thermo-geostrophic equilibrium. The effectiveness and superior performance of the proposed scheme are demonstrated through multiple numerical experiments, highlighting its advantages in accurately simulating two-layer TRSW dynamics.
2022 (b): Introducing mcTRSW on a Sphere as an Idealized Version of Aeolus 2.0 and a Theory for MJO-Like Structures
Using a new multilayer pseudo-spectral moist-convective thermal rotating shallow-water (mcTRSW) model on a full sphere as an idealized version of Aeolus 2.0, the authors presented a possible equatorial adjustment mechanism beyond Gill’s model for the genesis and dynamics of the Madden–Julian Oscillation (MJO). According to this theory, an eastward-propagating MJO-like structure can emerge in a self-sustained and self-propelled manner due to the nonlinear relaxation (adjustment) of a large-scale positive buoyancy anomaly, a depressed anomaly, or a combination of both, once the anomaly reaches a critical threshold in the presence of moist convection at the Equator.
This MJO-like episode consists of a convectively coupled hybrid structure, which includes a quasi-equatorial modon with an enhanced vortex pair and a convectively coupled baroclinic Kelvin wave (BKW). The BKW exhibits a greater phase speed than the dipolar structure on an intraseasonal time scale. After circumnavigating the entire Equator, the interaction of the BKW with a new large-scale buoyancy anomaly may contribute to the recurrent generation of the next cycle of MJO-like structures.
Overall, the generated hybrid structure captures several fundamental features of the MJO, including its quadrupolar structure, convective activity, condensation patterns, vorticity field, phase speed, and westerly and easterly inflows in the lower and upper troposphere. While moisture-fed convection is a necessary condition for exciting and maintaining the hybrid structure in the proposed theory, it is fundamentally different from moisture-mode theories. Unlike moisture-mode theories, where no equivalent "dry" dynamical structures exist, the barotropic equatorial modon and BKW also exist in dry environments. Thus, the proposed theory provides a possible mechanism to explain the genesis and fundamental structure of the MJO, offering a unifying perspective that bridges previously divergent MJO theories.
Reference: Rostami, M., Zhao, B., & Petri, S. (2022). On the genesis and dynamics of Madden–Julian oscillation-like structure formed by equatorial adjustment of localized heating. Quarterly Journal of the Royal Meteorological Society, 148(749), 3788–3813. https://doi.org/10.1002/qj.4388
2022 (c): Coherent Magnetic Modon Solutions in Quasi-Geostrophic Shallow Water Magnetohydrodynamics
In this article, the authors demonstrate that a class of exact solutions to the magnetohydrodynamic quasi-geostrophic (MQG) equations exists. These solutions arise from rotating shallow water magnetohydrodynamics in the limit of small Rossby and magnetic Rossby numbers. The solutions, known as magnetic modons, are steady-moving dipolar vortices and generalizations of the well-known quasi-geostrophic modons. The study shows that various configurations of magnetic modons are possible, including those with or without an external magnetic field and those with or without an internal magnetic field trapped inside the dipole. Using the modon solutions as initial conditions for direct numerical simulations of the MQG equations, the authors show that the modons remain coherent over long durations—about a hundred deformation radii—without changing form, provided the external and internal magnetic fields are not too strong. This coherence is maintained even when small-amplitude noise is added to the initial conditions.
Reference: Lahaye, N., & Zeitlin, V. (2022). Coherent magnetic modon solutions in quasi-geostrophic shallow water magnetohydrodynamics. Journal of Fluid Mechanics, 941, A15. https://doi.org/10.1017/jfm.2022.289
2023: Application of Aeolus 2.0 to the Dynamics of Localized Extreme Heatwaves in the Mid-Latitude Atmosphere
In this study, the authors investigated the adjustment of large-scale localized buoyancy anomalies in mid-latitude regions and the nonlinear evolution of associated condensation patterns in both adiabatic and moist-convective environments. This analysis was conducted using the two-layer idealized moist-convective thermal rotating shallow water (mcTRSW) model.
The study revealed that the presence of a circular positive potential temperature anomaly in the lower layer initiates an anticyclonic high-pressure rotation, accompanied by a negative buoyancy anomaly in the upper layer. This results in an anisotropic northeast-southwest tilted circulation of heat flux. The evolution of eddy heat fluxes, including poleward heat flux, energy distribution, and meridional elongation of the buoyancy field, strongly depends on the perturbation's strength, size, and vertical structure.
The heatwave induces atmospheric instability, leading to the formation of precipitation systems, such as rain bands and asymmetric latent heat release due to moist convection in a diabatic environment. This process generates a comma cloud pattern in the upper troposphere and a comma-shaped buoyancy anomaly in the lower layer, accompanied by the emission of inertia-gravity waves. The southern and eastern sectors of the buoyancy anomaly exhibit upward flux, leading to the formation of a stronger cross-equatorial flow and inertia-gravity waves propagating southward and eastward.
Furthermore, the simulations reveal a similar asymmetric pattern in the distribution of total condensed liquid water content, accompanied by the intensification of moist convection in the form of rain bands. This intensification is more pronounced in barotropic structures compared to baroclinic configurations with stagnant upper layers.
This study underscores the importance of incorporating moist convection and its interactions with atmospheric and oceanic flows in mid-latitude regions. It also highlights the crucial role of buoyancy anomalies in the development of heatwaves and precipitation patterns, contributing to a better understanding of extreme weather dynamics.
2024 (a): Report on Equatorial Modons in the TRSW Model
In this article, the authors demonstrate the construction of exact, steady, eastward-moving vortex-dipole solutions—known as equatorial modons—within the TRSW model on the equatorial beta-plane. These solutions are derived in the asymptotic limit characterized by low divergence and small temperature variations, a regime that is relevant to the tropical atmosphere. The TRSW model is an extension of the classical rotating shallow water model, which accounts for horizontal temperature gradients.
The asymptotic modons can carry temperature anomalies and exist on an inhomogeneous temperature background. To verify whether such coherent structures can emerge in the full TRSW model, the authors use these modon configurations to initialize numerical simulations. The results confirm that modons can indeed exist in this context.
The study also identifies the parameter regimes and constraints that allow the modons to maintain their structure, particularly with respect to the temperature anomaly inside. Furthermore, it is shown that modons retain their coherence even when evolving on a background with meridionally inhomogeneous temperature fields or interacting with sharp temperature fronts. Finally, the authors present and analyze a general scenario for the disaggregation of the modons when they fall outside the stability domain.
Lahaye, N., Larroque, O., & Zeitlin, V. (2024). Equatorial modons in the thermal rotating shallow water model. Journal of Fluid Mechanics, 984, A58. https://doi.org/10.1017/jfm.2024.253
2024 (b): Flux Globalization-Based Well-Balanced Path-Conservative Central-Upwind Scheme for 2D Two-Layer TRSW Equations
In this work, the authors developed a flux globalization-based, well-balanced, path-conservative central-upwind scheme on Cartesian meshes for the two-dimensional (2-D) two-layer TRSW equations. The scheme is considered well-balanced because it exactly preserves a variety of physically relevant steady states. In the 2-D case, preserving general “moving-water” steady states is challenging, and to the best of the authors' knowledge, no existing schemes can fully achieve this goal. The proposed scheme can precisely preserve both the x- and y-directional jets in the rotational frame, as well as certain genuinely 2-D equilibria. Numerical experiments demonstrate the scheme’s performance in complex scenarios, including the presence of shocks, dry areas, non-trivial topographies (including discontinuous ones), and cases of hyperbolicity loss. The scheme is effective in both the f-plane and beta-plane frameworks.
Cao, Y., Kurganov, A., Liu, Y., & Zeitlin, V. (2024). Flux globalization-based well-balanced path-conservative central-upwind scheme for two-dimensional two-layer thermal rotating shallow water equations. Journal of Computational Physics, 515, 113273. https://doi.org/10.1016/j.jcp.2024.113273
2024 (c): Locally Divergence-Free Well-Balanced Path-Conservative Central-Upwind Schemes for RSW Magnetohydrodynamics (MHD)
In this study, the authors developed a new second-order flux globalization-based path-conservative central-upwind (PCCU) scheme for the rotating shallow water magnetohydrodynamics (RSW-MHD) equations. The scheme is designed to not only maintain the divergence-free constraint of the magnetic field at the discrete level but also to satisfy the well-balanced (WB) property by exactly preserving several physically relevant steady states of the system. The authors considered a Godunov-Powell modified version of the system, introduced additional equations by spatially differentiating the magnetic field equations, and modified the reconstruction procedures for the magnetic field variables. The WB property is achieved through the implementation of a flux globalization approach within the PCCU scheme, resulting in a method capable of preserving both still- and moving-water equilibria exactly. In addition to ensuring both the WB and divergence-free properties, the new method is implemented on an unstaggered grid and does not require any (approximate) Riemann problem solvers. The performance of the proposed method is demonstrated through several numerical experiments, which confirm its robustness, high resolution of results, and absence of spurious oscillations.
Chertock, A., Kurganov, A., Redle, M., & Zeitlin, V. (2024). Locally divergence-free well-balanced path-conservative central-upwind schemes for rotating shallow water MHD. Journal of Computational Physics, 518, 113300. https://doi.org/10.1016/j.jcp.2024.113300
2024 (d): Application of mcRSW in Dynamics of Jupiter’s Equatorial Zone: Instability Analysis and a Mechanism for Y-Shaped Structures
Using the mcRSW model, the authors propose a mechanism for the Y-shaped structure observed on Jupiter. Jupiter’s Equatorial Zone (EZ) is characterized by atmospheric dynamics influenced by strong zonal jets. The study begins with a linear stability analysis of two-layer geostrophic flows to explore the growth and evolution of instabilities associated with equatorial jets. Stability diagrams show that the most unstable baroclinic modes shift to lower wavenumbers as zonal velocities increase, indicating sensitivity to the strength of the zonal wind. Notable differences in phase velocities are found between barotropic and baroclinic jets. The analysis includes phase portraits of various wave types, such as barotropic and baroclinic Kelvin waves, Yanai waves, Rossby waves, and inertia-gravity waves.
Next, the authors employ a two-layer moist convective Rotating Shallow Water (2mcRSW) model to investigate the nonlinear interactions between ammonia-driven convective processes in the shallow upper atmosphere and large-scale atmospheric features in Jupiter’s EZ. The study analyzes the evolution of nonlinear instabilities in moist-convective flows by perturbing a background zonal velocity field with the most unstable mode. The results show that cyclonic and anticyclonic vortices are amplified by moist convection at the boundaries of the zonal jets, while convective vortices in equatorial bright zones are suppressed.
This study highlights the role of moist convection in generating upper-atmosphere cloud clusters and lightning patterns, as well as the chevron-shaped pattern observed on the poleward side of the zonal jets. The authors propose a novel mechanism for the formation of Y-shaped structures on Jupiter, driven by equatorial modons coupled with convectively baroclinic Kelvin waves (CCBCKWs). According to this mechanism, Y-shaped structures result from large-scale localized heating in a diabatic environment. When the heating reaches a critical threshold of negative pressure or positive buoyancy anomaly, it generates a hybrid structure that consists of a quasi-equatorial modon (a coherent dipolar structure) coupled with a CCBCKW, which propagates eastward in a self-sustaining and self-propelled manner. Initially, the hybrid structure moves steadily eastward; however, the larger phase speed of the CCBCKW eventually leads to its detachment from the quasi-equatorial modon. The lifetime of this coupled structure varies from interseasonal to seasonal timescales. Moist convection is identified as a necessary condition for triggering the eastward-propagating structure.
Rostami, M., Fallah, B., & Fazel-Rastgar, F. (2025). Dynamics of Jupiter’s equatorial zone: Instability analysis and a mechanism for Y-shaped structures. Icarus, 429, 116414. https://doi.org/10.1016/j.icarus.2024.116414
2025 (a): A Novel Sea Surface Evaporation Scheme for Aeolus 2.0 and mcTRSW Framework
In this study, the authors propose a novel sea surface evaporation scheme for Aeolus 2.0, which can also be adapted for use with other models after appropriate adjustments. This scheme, along with its corresponding bulk aerodynamic formulation, is designed to estimate sea surface evaporation, columnar humidity, and precipitation distribution within the atmosphere. The approach relies on three distinct functions, each dependent on a single variable: zonal wind velocity, tropospheric (potential) temperature, and free convection.
It is demonstrated that the normalized Clausius–Clapeyron formula requires an adjustable scaling factor for real-world applications, which is calibrated using empirical fitness curves. To validate the proposed approach, the study employs a model based on the pseudo-spectral moist-convective thermal rotating shallow water (mcTRSW) framework, with minimal parameterization over the entire sphere. Model results are compared with observations using ECMWF Reanalysis 5th Generation (ERA5) data.
The scheme is tested across different seasons to evaluate its reliability under various weather conditions. Additionally, the Dedalus algorithm, which utilizes spin-weighted spherical harmonics, is implemented to handle the pseudo-spectral problem-solving tasks within the model.
2025 (b): Aeolus 2.0's TRSW Model Dynamical Core as a New Paradigm for Simulating Extreme Heatwaves, Westerly Jet Intensification, and More
In this study, the authors demonstrate the dynamical core and applicability of Aeolus 2.0, a moist-convective thermal rotating shallow water (mcTRSW) model of intermediate complexity. They incorporate novel bulk aerodynamic and moist-convective schemes to investigate the effects of increased radiative forcing on zonal winds and heatwaves.
Simulations reveal seasonal variations in zonal wind, temperature, and energy anomalies under increased radiative forcing during the summer solstice, winter solstice, and equinoxes. Enhanced radiative forcing increases mid-latitudinal temperatures in the Northern Hemisphere during the summer solstice and in the Southern Hemisphere during the winter solstice. This leads to an intensification of zonal wind velocity in the affected hemisphere, particularly in the subtropics, while causing a reduction in the opposite hemisphere. Additionally, thermal forcing weakens the zonal wind velocity of polar cyclones in the hemisphere experiencing increased radiative forcing.
During the autumn equinox, zonal wind velocity declines in the Southern Hemisphere, while a similar reduction occurs in the Northern Hemisphere during the spring equinox. Strengthened meridional temperature gradients significantly impact the poleward displacement of atmospheric circulation, shifting northward during the summer solstice and southward during the winter solstice. Persistent poleward eddy heat fluxes across hemispheres indicate a consistent atmospheric response to external heating.
Furthermore, increased radiative forcing during solstices amplifies prolonged heatwaves over both land and ocean, with greater impacts compared to the equinoxes. This study underscores Aeolus 2.0’s potential as a powerful framework for simulating extreme climate events under changing radiative conditions.
