Conservation Of Potential Vorticity Research Articles

The Brazil Basin Tracer Release Experiment: Observations

Abstract Lightening of bottom water is required to close the abyssal overturning circulation, believed to play an important role in the climate system. A tracer release experiment and turbulence measurement programs have revealed how bottom water is lightened, and illuminated the associated circulation in the deep Brazil Basin, a representative region of the global ocean. Tracer was released on an isopycnal surface about 4000 m deep, over one of the fracture zones emanating from the Mid-Atlantic Ridge (MAR). Tracer that mixed toward the bottom moved toward the MAR across isopycnal surfaces that bend down to intersect the bottom at a rate implying a near-bottom buoyancy flux of 1.5 × 10−9 m2/s3, somewhat larger than inferred from dissipation measurements. The diffusivity at the level of the tracer release is estimated at 4.4 ± 1 × 10−4 m2/s, again larger than inferred from dissipation rates. The main patch moved southwest at about 2 cm/s while sinking due to the divergence of buoyancy flux above the bottom layer. The isopycnal eddy diffusivity was about 100 m2/s. Westward flow away from the MAR is the return flow balancing the eastward near-bottom upslope flow. The southward component of the flow is roughly consistent with conservation of potential vorticity. The circulation as well as the pattern of diapycnal flux are qualitatively the same as in St. Laurent et al (2001) but are more robust. The results indicate that diapycnal diffusivity is about twice that invoked by Morris et al. (2001) in calculating the basin-wide buoyancy budget.

Potential vorticity conservation for plasma turbulence in an inhomogeneous magnetic field: Theory and implications

The concept and theory of potential vorticity in drift wave turbulence are extended to the case of an inhomogeneous magnetic field. A one-field magnetic potential vorticity conserving equation is derived via the use of conservative gyrokinetics. The similarity between the corresponding systems for drift wave turbulence and shallow water theory is discussed in detail. Zonal flow physics in an inhomogeneous magnetic field is discussed. In particular, a Charney–Drazin type nonacceleration theorem is derived from the novel system, which conserves magnetic potential vorticity. Extensions of the turbulent equipartition theory to the transport of magnetic potential vorticity are proposed.

MQGeometry-1.0: a multi-layer quasi-geostrophic solver on non-rectangular geometries

Abstract. This paper presents MQGeometry, a multi-layer quasi-geostrophic (QG) equation solver for non-rectangular geometries. We advect the potential vorticity (PV) with finite volumes to ensure global PV conservation using a staggered discretization of the PV and stream function (SF). Thanks to this staggering, the PV is defined inside the domain, removing the need to define the PV on the domain boundary. We compute PV fluxes with upwind-biased interpolations whose implicit dissipation replaces the usual explicit (hyper-)viscous dissipation. The discretization presented here does not require tuning of any additional parameter, e.g., additional eddy viscosity. We solve the QG elliptic equation with a fast discrete sine transform spectral solver on rectangular geometry. We extend this fast solver to non-rectangular geometries using the capacitance matrix method. Subsequently, we validate our solver on a vortex-shear instability test case in a circular domain, on a vortex–wall interaction test case, and on an idealized wind-driven double-gyre configuration in an octagonal domain at an eddy-permitting resolution. Finally, we release a concise, efficient, and auto-differentiable PyTorch implementation of our method to facilitate future developments on this new discretization, e.g., machine-learning parameterization or data-assimilation techniques.

Observed 10–20-Day Deep-Current Variability at 5°N, 90.5°E in the Eastern Indian Ocean

Abstract In the eastern off-equatorial Indian Ocean, deep current intraseasonal variability within a typical period of 10–20 days was revealed by a mooring at 5°N, 90.5°E, accounting for over 50% of the total bottom subtidal velocity variability. The 10–20-day oscillations were more energetic in the cross-isobathic direction (STD = 3.02 cm s−1) than those in the along-isobathic direction (STD = 1.50 cm s−1). The oscillations were interpreted as topographic Rossby waves (TRWs) because they satisfied the TRWs dispersion relation that considered the smaller Coriolis parameter and stronger β effect at low latitude. Further analysis indicated significant vertical coupling between the deep cross-slope oscillations and cross-isobathic 10–20-day perturbations at the depth of 300–950 m. The 10–20-day TRWs were generated by cross-isobathic motions under the potential vorticity conservation adjustment. The Mercator Ocean output reproduced the generation of kinetic energy (KE) of deep current variability. The associated diagnostic analysis of multiscale energetics showed that the KE of TRWs was mainly supplied by vertical pressure work. In the seamount region (2°–10°N, 89°–92°E), vertical and horizontal pressure works were identified to be the dominant energy source (contributing to 94% of the total KE source) and sink (contributing to 98% of the total KE sink) of the deep current variability, transporting energy downward and redistributing energy horizontally, respectively.

On the Quartic Korteweg–de Vries hierarchy of nonlinear Rossby waves and its dynamics

A long-standing challenge in exploring the dynamics of large-scale atmospheric or oceanic motions is to find more appropriate theoretical models. This paper aims at the mechanisms of nonlinear Rossby waves by a new obtained nonlinear evolutionary equation hierarchy approach. The multiple scales method and weak nonlinear perturbation method are adopted based on the quasi-geostrophic potential vorticity conservation law for large scale atmospheric or oceanic motions. It is the first time that a Quartic Korteweg–de Vries model equation is derived to describe the propagation of nonlinear Rossby waves amplitude, which provides a new acceptable theoretical model for the study of atmospheric blocking phenomena. Qualitative and quantitative analysis for the new Quartic KdV model are finished to disclose the evolutionary mechanisms of nonlinear Rossby waves. The corresponding results declares that the β effect, topographic features and detuning parameter are all important factors on the nonlinear Rossby waves.

A Perturbative Solution for Nonlinear Stratified Upwelling over a Frictional Slope

Abstract A perturbative solution of simplified primitive equations for nonlinear weakly stratified upwelling over a frictional slope is found that resolves the vertical structure of velocity fields and can satisfy Ertel’s potential vorticity conservation in the stratified inviscid interior. The solution uses assumptions consistent with the model proposed by Lentz and Chapman, including a steady-state, constant cross-shore density gradient, no alongshore gradients, laterally inviscid, and consideration of cross-shore advection of alongshore momentum. The solution resolves the vertical structure of velocity fields (including subsurface maxima of compensational flow, not resolved by Lentz and Chapman) and can satisfy Ertel’s potential vorticity conservation in the stratified inviscid interior. The dynamics are similar to Lentz and Chapman; bottom stress balances alongshore wind stress in a homogeneous density ocean and is replaced by nonlinear cross-shore transport of alongshore momentum as the Burger number (S = αN/f, where α, N, and f are the bottom slope, buoyancy frequency, Coriolis frequency, respectively) increases. When the solution uses the empirical relation between cross-shore and vertical density gradients proposed by Lentz and Chapman, vorticity conservation is not satisfied and the nonlinear momentum transport estimated by the solution linearly increases with S, asymptotically matching Lentz and Chapman for S < 1. When the solution conserves interior potential vorticity, the momentum transport is proportional to S2 for S < 1 and is in better agreement with numerical simulations.

A Mapping Methodology Adapted to all Polar and Subpolar Oceans with a Stretching/Shrinking Constraint

Abstract Polar and subpolar oceans play a particularly important role in the global climate and its temporal changes, yet these regions are less well sampled than the rest of the global ocean. To better understand the physical or biogeochemical properties and their variabilities in these regions, accurate data mapping is crucial. In this paper, we introduce a mapping methodology that includes a water column shrinking and stretching constraint (SSC) based on the principle of conservation of potential vorticity. To demonstrate the mapping scheme efficiency, we map the ocean temperature in the southern Sea of Okhotsk, where the bottom topography comprises a broad and shallow shelf, a sharp continental slope, and a deep oceanic basin. Such topographic features are typical of polar and subpolar marginal seas. Results reveal that the SSC integrated (SSCI) mapping strongly reduces the mapping error in the broad and shallow shelf compared with a recently introduced topographic constraint integrated (TCI) mapping procedure. We also tested our mapping scheme in the Southern Ocean, which has a comparatively slanted shelf, a wider and gentler slope, and a deep and broad oceanic basin. We found that the SSCI and TCI methods are practically equivalent there. The SSCI mapping is thus an effective method to map the ocean’s properties in various topographic environments and should be adequate in all polar and subpolar regions. Importantly, we introduced a standardized procedure for determining the decorrelation length scales—a necessary step prior to implementing any mapping scheme—in any topographic conditions.

Seasonal Variability of the Deep Western Boundary Current in the Philippine Sea

The deep western boundary current (DWBC) in the Philippine Sea has been expected to play a crucial role in transporting lower circumpolar deep water and to contribute to regional and global climate regulation. Two-year-long near-bottom current measurements reveal a southward-flowing DWBC with a mean velocity of 5 cm/s and seasonal variations—weaker in summer and stronger in winter. Seasonal variability in the DWBC is hypothesized to be induced by changes in the North Equatorial Current bifurcation latitude (NECBL) and upper pycnocline depth through potential vorticity conservation. Data-assimilated reanalysis model (GLORYS12V1) outputs, which reproduce the seasonal variability of DWBC similarly to the observation, are used for further analysis. During the seasonal period, the NECBL displays significant coherence (>0.9) with the first-mode empirical orthogonal function principal component of the simulated along-slope DWBC. The upper pycnocline depth, varying seasonally within a range of approximately 27 m, induces seasonal variability in a deep anticyclonic eddy trapped by topography. In summer, the intensified deep anticyclonic eddy obstructs the adjacent southward-flowing DWBC, weakening its strength, whereas in winter, the southward flow of the DWBC is enhanced due to the weakening of the deep anticyclonic eddy.

Hamilton's principle with phase changes and conservation principles for moist potential vorticity

AbstractMany definitions of moist potential vorticity (PV) have been proposed to extend the dry theory of Ertel PV. None of the moist PV definitions seem to have all of the desirable properties of the dry Ertel PV. For instance, dry PV is not only a globally conserved quantity, but also a material invariant that is conserved along fluid parcel trajectories. Therefore, an open question remains: Is there a moist PV that is a material invariant, if clouds and phase changes of water are present? In prior studies, definitions of moist PV have been proposed based on physical and mathematical intuition. Here, a systematic approach is used. In particular, a particle relabeling symmetry is devised for a moist atmosphere and then Noether's theorem is employed to arrive at the associated conservation laws for a moist PV. A priori, it is not clear whether this systematic approach will be viable, since it relies on variational derivatives in Hamilton's principle, and phase changes introduce singularities that could potentially prevent derivatives at the cloud edge. However, it is shown that the energy and the Lagrangian density are sufficiently smooth to allow variational derivatives, in a moist Boussinesq system with reversible phase transitions between water vapor and liquid cloud water. From the particle relabeling symmetry, a moist Kelvin circulation theorem is found, along with a moist PV conservation law that applies not for each individual parcel but for parcel‐integrated PV, integrated over certain local volumes.

Convergence of the Malvinas Current branches near 44°S

Field measurements of the Malvinas Current (MC) velocity distribution were performed at the western slope of the Argentine Basin in the South Atlantic Ocean between 47° and 43°S including several sections across the current. The data were collected in January and March 2020 using a Shipborne Acoustic Current Doppler Profiler (SADCP) and allowed us to study circulation patterns in the upper 700 m of the ocean. The observations reveal substantial differences in the current structures at each location; the SADCP data suggest that two distinct current branches at 46°S converge downstream near 44°S making it difficult to distinguish the high-velocity cores farther north. A detailed comparison between the velocity structures indicates that the branches converge due to the change in the orientation and width of the continental slope, and is consistent with potential vorticity conservation. At the same time, satellite altimetry shows that the branches merge to a single high-velocity jet, suggesting that satellite altimetry does not reproduce all features of the MC internal structure and indicates the importance of further direct velocity observations in this region. Despite the above-mentioned limitations of altimetry, the satellite-derived geostrophic velocities suggest that the pathways of the MC high-velocity jets are quite stable. In addition, both satellite altimetry and direct measurements indicate that the branches tend to converge downstream near 44°S.

Analysis of Stationary Points and Bifurcations of a Dynamically Consistent Model of a Two-Dimensional Meandering Jet

A dynamically consistent model of a meandering jet stream with two Rossby waves obtained using the law of conservation of potential vorticity is investigated. Stationary points are found in the phase space of advection equations and the type of their stability is determined analytically. All topologically different flow regimes and their bifurcations are found for the stationary model (taking into account only the first Rossby wave). The results can be used in the study of Lagrangian transport, mixing, and chaotic advection in problems of cross-frontal transport in geophysical flows with meandering jets.

Observation of Bottom-Trapped Topographic Rossby Waves to the West of the Luzon Strait, South China Sea

Abstract Topographic Rossby waves (TRWs) play an important role in deep-ocean dynamics and abyssal intraseasonal variations. Observational records from 15 current- and pressure-recording inverted echo sounders (CPIESs) and two moorings deployed in the northern Manila Trench (MT), South China Sea (SCS), for over 400 days were utilized to analyze the widely existing near-21-day bottom-trapped TRWs in the trench. The TRWs were generally generated in winter and summer, dominated by perturbations in the upper ocean. Kuroshio intrusion and its related variabilities contributed to the perturbations in winter, whereas the perturbations generated north of Luzon Island dominated in summer. Eddies north of Luzon propagated northwestward in the summer of 2018; however, these eddies caused the Kuroshio meanderings in the Luzon Strait (LS) in the summer of 2019. The variations in the Kuroshio path and the Kuroshio-related eddies induced TRWs in the deep ocean in regions with steep topography. However, the spatiotemporal distributions of TRWs were complex owing to the propagation of the waves. Some cases of TRWs showed no relation to the local upper-layer perturbations but propagated from adjacent regions. Some of these TRWs were induced by perturbations in the upper ocean in adjacent regions, and propagated anticlockwise in the MT with shallow water to their right, while others may be related to the intraseasonal variations in deep-water overflow in the LS and propagated northward. This study suggests that the Kuroshio and Kuroshio-related eddies significantly contribute to the dynamic processes associated with intraseasonal variations in the deep SCS through the generation of TRWs. Significance Statement Topographic Rossby waves (TRWs) are fluctuations generated when water columns travel across sloping topography under potential vorticity conservation. Based on observations of 15 current- and pressure-recording inverted echo sounders (CPIESs) and two moorings in the northern Manila Trench (MT) in the South China Sea (SCS), TRWs with periods of approximately 21 days were observed and analyzed. This study describes the generation, propagation, and spatiotemporal distribution of TRWs west of the LS and confirms that regional Kuroshio meanderings and upper eddies play important roles in the dynamic processes associated with intraseasonal variations in the deep SCS; the study may thus contribute to knowledge on the dynamic response of the abyssal current to mesoscale perturbations in the upper ocean.

Low-Frequency Dynamic Ocean Response to Barometric-Pressure Loading

Abstract Changes in dynamic manometric sea level ζm represent mass-related sea level changes associated with ocean circulation and climate. We use twin model experiments to quantify magnitudes and spatiotemporal scales of ζm variability caused by barometric pressure pa loading at long periods ( month) and large scales () relevant to Gravity Recovery and Climate Experiment (GRACE) ocean data. Loading by pa drives basin-scale monthly ζm variability with magnitudes as large as a few centimeters. Largest ζm signals occur over abyssal plains, on the shelf, and in marginal seas. Correlation patterns of modeled ζm are determined by continental coasts and H/f contours (H is ocean depth and f is Coriolis parameter). On average, ζm signals forced by pa represent departures of and from the inverted-barometer effect ζib on monthly and annual periods, respectively. Basic magnitudes, spatial patterns, and spectral behaviors of ζm from the model are consistent with scaling arguments from barotropic potential vorticity conservation. We also compare ζm from the model driven by pa to ζm from GRACE observations. Modeled and observed ζm are significantly correlated across parts of the tropical and extratropical oceans, on shelf and slope regions, and in marginal seas. Ratios of modeled to observed ζm magnitudes are as large as ∼0.2 (largest in the Arctic Ocean) and qualitatively agree with analytical theory for the gain of the transfer function between ζm forced by pa and wind stress. Results demonstrate that pa loading is a secondary but nevertheless important contributor to monthly mass variability from GRACE over the ocean.

Conservation Laws for Potential Vorticity in a Salty Ocean or Cloudy Atmosphere

AbstractOne of the most important conservation laws in atmospheric and oceanic science is conservation of potential vorticity. The original derivation is approximately a century old, in the work of Rossby and Ertel, and it is related to the celebrated circulation theorems of Kelvin and Bjerknes. However, the laws apply to idealized fluids, and extensions to more realistic scenarios have been problematic. Here, these laws are extended to hold with additional fundamental complexities, including salinity in the ocean, or moisture and clouds in the atmosphere. In the absence of these additional complexities, it is known that potential vorticity is conserved following each fluid parcel; here, for a salty ocean or cloudy atmosphere, the general conserved quantity is potential vorticity integrated over certain pancake‐shaped volumes. Furthermore, the conservation laws are also related to a symmetry in the Lagrangian, which brings a connection to the symmetry‐conservation relationships seen in other areas of physics.

Deep-Current Intraseasonal Variability Interpreted as Topographic Rossby Waves and Deep Eddies in the Xisha Islands of the South China Sea

Abstract Strong subinertial variability near a seamount at the Xisha Islands in the South China Sea was revealed by mooring observations from January 2017 to January 2018. The intraseasonal deep flows presented two significant frequency bands, with periods of 9–20 and 30–120 days, corresponding to topographic Rossby waves (TRWs) and deep eddies, respectively. The TRW and deep eddy signals explained approximately 60% of the kinetic energy of the deep subinertial currents. The TRWs at the Ma, Mb, and Mc moorings had 297, 262, and 274 m vertical trapping lengths, and ∼43, 38, and 55 km wavelengths, respectively. Deep eddies were independent from the upper layer, with the largest temperature anomaly being >0.4°C. The generation of the TRWs was induced by mesoscale perturbations in the upper layer. The interaction between the cyclonic–anticyclonic eddy pair and the seamount topography contributed to the generation of deep eddies. Owing to the potential vorticity conservation, the westward-propagating tilted interface across the eddy pair squeezed the deep-water column, thereby giving rise to negative vorticity west of the seamount. The strong front between the eddy pair induced a northward deep flow, thereby generating a strong horizontal velocity shear because of lateral friction and enhanced negative vorticity. Approximately 4 years of observations further confirmed the high occurrence of TRWs and deep eddies. TRWs and deep eddies might be crucial for deep mixing near rough topographies by transferring mesoscale energy to small scales.

A Large Subsurface Anticyclonic Eddy in the Eastern Equatorial Indian Ocean

AbstractSubsurface eddies are pervasive in the ocean, but those in the eastern equatorial Indian Ocean are not well understood due to the lack of in‐situ observations. Using multiple‐platform observations and reanalysis product, we investigate the characteristics, evolutionary process, origin, and underlying generation mechanism of a subsurface anticyclonic eddy (SAE) in the eastern equatorial Indian Ocean during January‒February 2020. Results show that the horizontal radius of the SAE was slightly greater than 250 km, and the SAE core was located at ∼100‐m depth near the 24.7σ0 isopycnal. This warm, saline and oxygen‐rich SAE was weakly stratified and characterized by tilted lens structures. Further water‐mass tracing analysis indicates that the SAE shifted westward along 4°N with a mean propagation speed of 0.18 m/s from the northwest coast of Sumatra Island. The hydrographic characteristics of the SAE are similar to those of the strong Equatorial Undercurrent, it is speculated that the SAE was probably generated by the north branch flow as the eastward undercurrent reached Sumatra Island. Both lateral shear of undercurrent and conservation of potential vorticity were attributed to the formation of the observed SAE.

Toward Exploring Topographic Effects on Evolution and Propagation of Ocean Mesoscale Eddies Through Life Cycle Across Izu-Ogasawara Ridge in Northwestern Pacific Ocean

Ocean mesoscale eddies contribute significantly to water transport on a global scale, constituting the ubiquitous, irregular, discrete, nonlinear components. In this manuscript, we propose to explore whether and how the topographic effect of one meridional ridge, could exert considerable influences on the evolution and propagation of mesoscale eddies through their life cycle, directly from the perspectives of real observation statistics. We systematically investigate the known variability of mesoscale eddy trajectories, derived by multimission satellite altimetry from 1993 to 2018, of a life cycle more than 6 months, over the Izu-Ogasawara Ridge, and quantitatively examined the eddy-ridge interaction by observation statistics and wavelet coherence map, with respect to the intrinsic attributes, namely, the amplitude, the rotation speed, the radius. Due to the spatial-temporal diversity, a series of correlative steps have been particularly designed along time-frequency domain to trace back mesoscale eddy trajectories in a variety of origins, location, lifespan, polarity, either completely or partially passing over the ridge, and to facilitate the standardization in statistics across three phases of their life cycle, i.e., before, during and after the interaction with the ridge. It has been revealed in our experiment that three intrinsic attributes of mesoscale eddies within 25 years, all demonstrated noticeable correlation with the variation of topographic relief over the ridge. We observed that most of the cyclonic eddies obviously tended to begin to decay or even demise, while on the contrary, some of the anticyclonic eddies preferred to intensify slightly, or making no significant difference when encountering the upslope until climbing across the top, basically consistent with the expectation of potential vorticity (PV) conservation. The drifting velocity agreed with the tendency that the direction would be more probably modified toward equatorward or poleward by forcing to meridional component, with zonal component reduced at the beginning. The mesoscale eddies with the passage over the ridge exhibited the relatively high average horizontal scales, amplitude, rotation speed on the whole, compared to those with only partially passage. The developed scheme could integrate more evidences on how mesoscale eddies response to the topographic effects during their time-varying evolution and propagation process, and help provide opportunities to potentially identify and predict the underlying dynamic patterns and mechanisms that mesoscale eddies engage in ocean dynamics when proceeding toward meridional ridges on a global scale, with the promise of the end-to-end data-driven solution, such as deep learning architecture involved in the future.

A Fast Monotone Discretization of the Rotating Shallow Water Equations

AbstractThis paper presents a new discretization of the rotating shallow water equations and a set of decisions, ranging from a simplification of the continuous equations down to the implementation level, yielding a code that is fast and accurate. Accuracy is reached by using WENO reconstructions on the mass flux and on the nonlinear Coriolis term. The results show that the implicit mixing and dissipation, provided by the discretization, allow a very good material conservation of potential vorticity and a minimal energy dissipation. Numerical experiments are presented to assess the accuracy, which include a resolution convergence, a sensitivity on the free‐slip versus no‐slip boundary conditions, a study on the separation of waves from vortical motions. Speed is achieved by a series of choices rather than a single recipe. The main choice is to discretize the covariant form written in index coordinates. This form, rooted in the discrete differential geometry, removes most of the grid scale terms from the equations, and keeps them only where they should be. The model objects appearing in resulting continuous equations have a natural correspondence with the grid cell features. The other choices are guided by the maximization of the arithmetic intensity. Finally this paper also proves that a pure Python implementation can be very fast, thanks to the possibility of having compiled Python. As a result, the code performs 2 TFlops per second using thousand cores.

Propagation of Topographic Rossby Waves in the Deep Basin of the South China Sea Based on Abyssal Current Observations

AbstractTopographic Rossby waves (TRWs) are oscillations generated on sloping topography when water columns travel across isobaths under potential vorticity conservation. From our large-scale observations from 2016 to 2019, near-65-day TRWs were first observed in the deep basin of the South China Sea (SCS). The TRWs propagated westward with a larger wavelength (235 km) and phase speed (3.6 km day−1) in the north of the array and a smaller wavelength (80 km) and phase speed (1.2 km day−1) toward the southwest of the array. The ray-tracing model was used to identify the energy source and propagation features of the TRWs. The paths of the near-65-day TRWs mainly followed the isobaths with a slightly downslope propagation. The possible energy source of the TRWs was the variance of surface eddies southwest of Taiwan. The near-65-day energy propagated from the southwest of Taiwan to the northeast and southwest of the array over ~100–120 and ~105 days, respectively, corresponding to a group velocity of 4.2–5.0 and 10.5 km day−1, respectively. This suggests that TRWs play an important role in deep-ocean dynamics and deep current variation, and upper-ocean variance may adjust the intraseasonal variability in the deep SCS.

A Validated Study of a Modified Shallow Water Model for Strong Cyclonic Motions and Their Structures in a Rotating Tank

A joint theoretical and numerical study was carried out to investigate the fluid dynamical aspect of the motion of a vortex generated in a rotating tank with a sloping bottom. This study aims at understanding the evolution of strong cyclonic motions on a β-plane in the Northern Hemisphere. The strong cyclonic vortices were characterized by four nondimensional parameters which were derived through a scale analysis of the depth variations of fluid. By simplifying the model flow field and the prototype flow field, respectively, through the conservation of potential vorticity, two sets of dynamic similarity conditions are derived. This study proposed a sophisticated modified shallow water model (MSWM) to investigate the flow features of such strong vortices. A detailed numerical calculation adopted by multidimensional positive definite advection transport algorithm (MPDATA) was carried out to validate those effects considered in the MSWM model, including sloping bottom, parabolic free surface deformation, and viscous dissipation. Close agreements were found between the experimental and numerical results, including the streamlines patterns and the vortex trajectory. Comprehensive simulations for strong cyclonic vortices over different sloping bottoms were investigated to understand the impact of planetary β effect on vortex. The results calculated by MSWM demonstrate a variety of flow features of interactions between the primary vortex and induced secondary Rossby wave wakes that were essential and prominent in environmental geophysical flows.