Barotropic Vorticity Research Articles

Refraction and Straining of Near-Inertial Waves by Barotropic Eddies

AbstractFast-moving synoptic-scale atmospheric disturbances produce large-scale near-inertial waves in the ocean mixed layer. In this paper, we analyze the distortion of such waves by smaller-scale barotropic eddies, with a focus on the evolution of the horizontal wavevector k under the effects of straining and refraction. The model is initialized with a horizontally uniform (k = 0) surface-confined near-inertial wave, which then evolves according to the phase-averaged model of Young and Ben Jelloul. A steady barotropic vortex dipole is first considered. Shear bands appear in the jet region as wave energy propagates downward and toward the anticyclone. When measured at a fixed location, both horizontal and vertical wavenumbers grow linearly with the time t elapsed since generation such that their ratio, the slope of wave bands, is time independent. Analogy with passive scalar dynamics suggests that straining should result in the exponential growth of |k|. Here instead, straining is ineffective, not only at the jet center, but also in its confluent and diffluent regions. Low modes rapidly escape below the anticyclonic core such that weakly dispersive high modes dominate in the surface layer. In the weakly dispersive limit, k = −t∇ζ(x, y, t)/2 provided that (i) the eddy vertical vorticity ζ evolves according to the barotropic quasigeostrophic equation and (ii) k = 0 initially. In steady flows, straining is ineffective because k is always perpendicular to the flow. In unsteady flows, straining modifies the vorticity gradient and hence k, and may account for significant wave–eddy energy transfers.

The barotropic Rossby waves with topography on the earth’sδ-surface

AbstractThe Rossby solitary waves in the barotropic vorticity model which contains the topography on the earth’sδ-surface is investigated. First, applying scale analysis method, obtained the generalized quasi-geostrophic potential vorticity equation (QGPVE). Using The Wentzel–Kramers–Brillouin (WKB) theory, the evolution equation of Rossby waves is the variable-coefficient Korteweg–de Vries (KdV) equation for the barotropic atmospheric model. In order to study the Rossby waves structural change to exist in some basic flow and topography on theδ-surface approximation, the variable coefficient of KdV equation must be explicitly, Chebyshev polynomials is used to solve a Sturm-Liouville-type eigenvalue problem and the eigenvalue Rossby waves, these solutions show that the parameterδusually plays the stable part in Rossby waves and slow down the growing or decaying of Rossby waves with the parameterβ.

Midlatitude unstable air-sea interaction with atmospheric transient eddy dynamical forcing in an analytical coupled model

While recent observational studies have shown the critical role of atmospheric transient eddy (TE) activities in midlatitude unstable air-sea interaction, there is still a lack of a theoretical framework characterizing such an interaction. In this study, an analytical coupled air-sea model with inclusion of the TE dynamical forcing is developed to investigate the role of such a forcing in midlatitude unstable air-sea interaction. In this model, the atmosphere is governed by a barotropic quasi-geostrophic potential vorticity equation forced by surface diabatic heating and TE vorticity forcing. The ocean is governed by a baroclinic Rossby wave equation driven by wind stress. Sea surface temperature (SST) is determined by mixing layer physics. Based on detailed observational analyses, a parameterized linear relationship between TE vorticity forcing and meridional second-order derivative of SST is proposed to close the equations. Analytical solutions of the coupled model show that the midlatitude air-sea interaction with atmospheric TE dynamical forcing can destabilize the oceanic Rossby wave within a wide range of wavelengths. For the most unstable growing mode, characteristic atmospheric streamfunction anomalies are nearly in phase with their oceanic counterparts and both have a northeastward phase shift relative to SST anomalies, as the observed. Although both surface diabatic heating and TE vorticity forcing can lead to unstable air-sea interaction, the latter has a dominant contribution to the unstable growth. Sensitivity analyses further show that the growth rate of the unstable coupled mode is also influenced by the background zonal wind and the air–sea coupling strength. Such an unstable air-sea interaction provides a key positive feedback mechanism for midlatitude coupled climate variabilities.

Four-dimensional structure and sub-seasonal regulation of the Indian summer monsoon multi-decadal mode

A better understanding of the drivers and teleconnection mechanisms responsible for the multi decadal mode (MDM) of variability of the Indian summer monsoon rainfall (ISMR) with major socio-economic impacts in the region through clustering of large-scale floods or droughts is key to improving the poor simulation of ISMR MDM by most climate models. Here, using the longest instrumental record of ISMR available (1813–2006) and longest atmospheric and oceanic re-analyses, the global four dimensional (space–time) structures of atmospheric and oceanic fields of the multi-decadal mode of ISMR and sub-seasonal evolution of the teleconnection mechanism are brought out, essential for understanding underlying drivers but lacking so far. The relationships between the spatial structure of winds, Sea Surface Temperature (SST) and thermocline depth with the ISMR MDM indicate that the tropical ocean over the Indo-Pacific domain is passive responding primarily to the surface winds associated with the mode. A close association between the Atlantic Meridional Overturning Circulation (AMOC), north Atlantic (NA) SST, NA sea surface salinity (SSS) and the ISMR MDM indicate a slow oceanic pathway linking NA SST and the ISMR. In addition to strong correlation (~ 0.9) between global spatial patterns of JJAS SST associated with the MDMs of ISMR, NA SST and AMOC, strong temporal coherence (correlations ~ 0.9) between them is suggestive of regulation of the ISMR MDM (T ~ 65-years) by the NA SST associated with the Atlantic Multidecadal Oscillation (AMO) through a ‘fast’ atmospheric bridge. On a seasonal time scale, the atmospheric bridge manifests in the form of a stationary Rossby wave train generated by an anticyclonic (cyclonic) barotropic vorticity located above positive (negative) SST anomaly over NA in two phases of the AMO. That the AMO SST is the driver of the ISMR MDM is further supported when we unravel the sub-seasonal face of the teleconnection between the two. We show that phase locking of active (break) spells with annual cycle during positive (negative) phases of the ISMR MDM are forced by a similar phase locking of barotropic anticyclonic (cyclonic) vorticity over the NA SST with the annual cycle through the generation of a quasi-stationary Rossby wave train with an anticyclonic (cyclonic) vorticity at upper level over the Indian region with the NA columnar vorticity leading Indian monsoon rainfall by about a week. Our findings provide a basis for enhanced predictability of tropical climate through slow modulation by extra-tropical SST.

Structures and Northward Propagation of the Quasi-Biweekly Oscillation in the Western North Pacific

AbstractThis study investigates the northward-propagating quasi-biweekly oscillation (QBWO) in the western North Pacific by examining the composite meridional structures. Using newly released reanalysis and remote sensing data, the northward propagation is understood in terms of the meridional contrasts in the planetary boundary layer (PBL) moisture and the column-integrated moist static energy (MSE). The meridional contrast in the PBL moisture, with larger values north of the convection center, is predominantly attributed to the moisture convergence associated with barotropic vorticity anomalies. A secondary contribution comes from the meridional moisture advection, for which advections by mean and perturbation winds are almost equally important. The meridional contrast in the MSE tendency, due to the recharge in the front of convection and discharge in the rear of convection, is jointly contributed by the meridional and vertical MSE advections. The meridional MSE advection mainly depends on the moisture processes particularly in the PBL, and the vertical MSE advection largely results from the advection of the mean MSE by vertical velocity anomalies, wherein the upper-troposphere ascending motion related to the stratiform heating in the rear of the convection plays the major role. In addition, partial feedback from sea surface temperature (SST) anomalies is evaluated on the basis of MSE budget analysis. SST anomalies tend to enhance the surface turbulent heat fluxes ahead of the convention center and suppress them behind the convention center, thus positively contributing approximately 20% of the meridional contrast in the MSE tendency.

The Zapiola Anticyclone: A Lagrangian study of its kinematics in an eddy-permitting ocean model

The Zapiola Anticyclone (ZA) is a strong, O(100 Sv), barotropic vortex in the center of the Argentine Basin that is tied to a bathymetric feature called the Zapiola Rise. It is regionally significant for two reasons: first, the strong vortex is a dynamical barrier that inhibits the lateral exchange of water, and hence has the ability to trap water for a long period of time. Second, its dynamics is governed by a balance between eddy-driven mass convergence and divergent Ekman transport, which gives rise to strong downwelling and Ekman pumping into the bottom boundary layer.This study investigates the kinematics of the ZA by studying the fate of the water parcels that are trapped by the ZA. We use output from a five-year simulation with an eddy-permitting ocean model, and we use a Lagrangian approach to track water parcels originating from within the ZA. We determine basic statistics of the parcel trajectories, including retention time, number of revolutions, vertical displacement, and temperature and salinity changes. The picture that emerges is one of water parcels spiraling downward through the water column, undergoing downwelling while they revolve anticyclonically around the center of the ZA. In our experiment, water parcels spend on average 451 days within the ZA, and make 2.6 revolutions around its center, with each revolution taking somewhere between 100 and 200 days. On average, parcels undergo a 94 m descent, 0.03 °C cooling and 0.0042 psu freshening. But individual parcels can undergo more than 800 m of downwelling, 0.2 °C of cooling, and ± 0.02 psu of salinity change. We believe that vertical motions of this order of magnitude, and the associated water mass transformations, are unique in the abyssal mid-latitude oceans.

Asymptotic behavior of solutions to barotropic vorticity equation on a sphere

Abstract The behavior of a viscous incompressible fluid on a rotating sphere is described by the nonlinear barotropic vorticity equation (BVE). Conditions for the existence of a bounded set that attracts all BVE solutions are given. In addition, sufficient conditions are obtained for a BVE solution to be a global attractor. It is shown that, in contrast to the stationary forcing, the dimension of the global BVE attractor under quasiperiodic forcing is not limited from above by the generalized Grashof number.

Explaining the Zonal Asymmetry in the Air‐Sea Net Heat Flux Climatology Over the Antarctic Circumpolar Current

AbstractSurface heating occurs over the streamline of the Antarctic Circumpolar Current (ACC) and balances the heat transport associated with the global meridional overturning circulation. With a combination of ocean assimilation model output, objectively analyzed products, and atmospheric reanalysis, this paper investigates the mechanism of climatological surface cooling in the Pacific sector with zonal asymmetry. The poleward shift of the ACC path in the Pacific with barotropic potential vorticity conservation was found to account for this cooling. The southward transport of warm/wet surface waters encounters relatively cold/dry air at high latitudes, causing strong turbulent heat fluxes. Sensible heat flux related to the sea‐air heat convection plays an equivalent role alongside the sea surface evaporative latent heat flux, both of which dominate the surface cooling in the Pacific sector. Solar radiation decreases with a poleward meandering of the ACC, which aggravates the cooling process. A significant seasonal cycle of the ensemble mean net surface heat flux (Qnet) is demonstrated, that is, approximately half‐year heating (cooling) during austral warm (cool) seasons. The estimated magnitude of Qnet over the ACC is approximately 20 W m−2 by averaging 10 heat flux climatologies and 4 W m−2 in an ocean state estimate model. However, efforts are still needed to reduce the excess heat flux over the sea surface in the Southern Ocean for the heat flux products.

Modelling the marine circulation of the Campania coastal system (Tyrrhenian Sea) for the year 2016: Analysis of the dynamics

Abstract The Campania coastal system (CCS), located in the Tyrrhenian Sea, is characterized by an interesting and complex morphology, being made by a sequence of three gulfs (Gaeta, Naples and Salerno, GG, GN, GS) of different sizes, shapes, and bathymetries. Until now, most of the oceanographic studies in the area have focused on the GN, whereas little is known about the circulation in the GG and GS. Here, for the first time, a high-resolution modelling study of the whole CCS has been carried out, which covers a whole year (2016), allowing for a detailed description of the seasonal variability throughout this year. For each season, the dynamics in the three gulfs have been characterized, assessing the relative roles of the wind forcing, the topographic constraints and the remote large-scale Tyrrhenian Sea circulation. As a first step, the surface circulation patterns in the CCS have been compared with altimeter observations and with the atmospheric forcing. A detailed analysis of the monthly mean surface and intermediate circulation within each gulf has then been performed. Besides, a more quantitative insight into the mechanisms controlling the circulation has been obtained using an integrated vorticity diagnostic, which allows one to separate different contributions to the total barotropic vorticity equation. The results show a strong seasonality of the circulation in the three gulfs, which is mainly controlled by the wind stress input during autumn and winter, whereas in spring and summer the main contribution comes from the combined effect of baroclinicity and topographic gradient (the JBAR term). The exchanges between the gulfs and the Tyrrhenian waters have also been quantified, through the analysis of the transport across specific sections. These transports are found to be highly correlated with the offshore large-scale circulation in the GG, whereas in the GS there is strong correlation with the local wind forcing. Finally, lower correlations are found for the more geometrically complex and semi-enclosed GN.

Preferred equilibrium solutions of the barotropic vorticity equation

The long-term behaviour of the barotropic vorticity equation (BVE), which is beneficial for understanding long-term climate variations, has been investigated by applying an explicit quadratic conserved finite difference integration scheme. The results suggest that an initial pattern predominated at the beginning of time evolves to an equilibrium state after a long transition period in which the conserved prerequisites, such as the integral kinetic energy, square vorticity, and vorticity, are broken by accumulated errors. This could cause the BVE to be indeterministic. Similar phenomena could reappear in integration cases starting at the same initial pattern with different small perturbations, initial patterns, time and grid intervals, and difference schemes. The eventual equilibrium states for the above cases are different from each other but spatially similar. They all possess a single-wave structure in the horizontal plane but with random phases. The results further imply that despite the indeterministic characteristics due to the nonlinearity, the long-term behaviour of the BVE is deterministic in a spatial structure, shedding light on long-term climate change studies.

Barotropic vorticity balance of the North Atlantic subpolar gyre in an eddy-resolving model

Abstract. The circulation in the North Atlantic subpolar gyre is complex and strongly influenced by the topography. The gyre dynamics are traditionally understood as the result of a topographic Sverdrup balance, which corresponds to a first-order balance between the planetary vorticity advection, the bottom pressure torque, and the wind stress curl. However, these dynamics have been studied mostly with non-eddy-resolving models and a crude representation of the bottom topography. Here we revisit the barotropic vorticity balance of the North Atlantic subpolar gyre using a new eddy-resolving simulation (with a grid space of ≈2 km) with topography-following vertical coordinates to better represent the mesoscale turbulence and flow–topography interactions. Our findings highlight that, locally, there is a first-order balance between the bottom pressure torque and the nonlinear terms, albeit with a high degree of cancellation between them. However, balances integrated over different regions of the gyre – shelf, slope, and interior – still highlight the important role played by nonlinearities and bottom drag curls. In particular, the Sverdrup balance cannot describe the dynamics in the interior of the gyre. The main sources of cyclonic vorticity are nonlinear terms due to eddies generated along eastern boundary currents and time-mean nonlinear terms in the northwest corner. Our results suggest that a good representation of the mesoscale activity and a good positioning of mean currents are two important conditions for a better representation of the circulation in the North Atlantic subpolar gyre.

New multipliers of the barotropic vorticity equations

The barotropic vorticity equation is a classical model in atmospheric sciences. In this paper, we study the symmetry invariance properties of multipliers (integrating factors) admitted by this equation. The results are classified according to the ratio of the characteristic length scale to the Rossby radius of deformation and the variation of earth’s angular rotation. A plethora of conservation laws can be obtained by studying the interaction between Lie point symmetry generators and multipliers.

Multidecadal variations in ENSO-Indian summer monsoon relationship at sub-seasonal timescales

Customarily, the strength of the impact of El Nino-Southern Oscillation (ENSO) on Indian summer monsoon is evaluated with respect to the seasonal mean rainfall. As the rainfall occurring over the Indian subcontinent experiences strong variations intraseasonally, the impact of ENSO on these intraseasonal fluctuations is often more important for the agribusiness and economy when contrasted with the seasonal mean. The annual cycle of ISM rainfall peaks during July and August months. In this study, we investigate the impact of ENSO on ISM precipitation during July and August. We show that the relationship between ENSO and ISM rainfall during July and August has experienced significant changes at multidecadal timescales. While the impact of ENSO was significantly strong in August and significantly weak in July during 1948–1980, post-1980s August shows a weak ENSO-Monsoon relationship than that in July. We investigate these multidecadal changes in the ENSO-monsoon relationship using 68 years of observational records. ENSO produces strong (weak) upper tropospheric divergence over equatorial eastern Pacific Ocean in August (July) before 1980. A stronger divergence helps Rossby wave within the Pacific-Asian jet cools the upper tropospheric mid-latitude region by modulating the vorticity there. A colder mid-latitude temperature weakens the Indian summer monsoon. Thus, the impact of ENSO on the Indian summer monsoon was weaker (stronger) in July (August) before 1980 and vice versa after the 1980s. Further, we deploy a linear barotropic vorticity model to assess the association between upper tropospheric divergence over the Pacific Ocean region and vorticity (temperature) over the mid-latitude Asian region. A stronger forcing of divergence in the upper tropospheric Pacific region reinforces stronger positive vorticity in mid-latitude Asia resembling the findings above. Our study suggests that these multidecadal fluctuations in the sub-seasonal ENSO-monsoon relationship is linked to the physical changes in the state of the climate and could not be attributed to the stochastic processes. Such insight into the variability in ENSO-monsoon relationship at sub-seasonal timescales would help predictability and decision-making.

Barotropic instability of a zonal jet on the sphere: from non-divergence through quasi-geostrophy to shallow water

Two common approximations to the full Shallow Water Equations (SWEs) are non-divergence and quasi-geostrophy, and the degree to which these approximations lead to biases in numerical solutions are explored using the test bed of barotropic instability. Specifically, we examine the linear stability of strong polar and equatorial jets and compare the growth rates obtained from the SWEs along with those obtained from the Non-Divergent barotropic vorticity (ND) equation and the Quasi-Geostrophic (QG) equation. The main result of this paper is that the depth over which a layer is barotropically unstable is a crucial parameter in controlling the growth rate of small amplitude perturbations and this dependence is completely lost in the ND equation and is overly weak in the QG system. Only for depths of 30 km or more are the growth rates predicted by the ND and QG systems a good approximation to those of the SWEs, and such a convergence for deep layers can be explained using theoretical considerations. However, for smaller depths, the growth rates predicted by the SWEs become smaller than those of the ND and QG systems and for depths of between 5 and 10 km they can be smaller by more than . For polar jets, and for depths below 2 km the mean height in geostrophic balance with the strong zonal jet becomes negative and hence the barotropic instability problem is ill-defined. While in the SWEs an equatorial jet becomes stable for layer depths smaller than 3–4 km, in the QG and ND approximations it is unstable for layer depths down to 1 km. These result may have implications for the importance of barotropic instability in Earth's upper stratosphere and perhaps also other planets such as Venus.

Stability of Rossby–Haurwitz waves

AbstractExploiting a factorized form of the linear perturbation equation valid around Rossby–Haurwitz waves in the nonlinear barotropic vorticity equation system on the sphere, an elementary discrete numerical method for analysing the stability of these waves is proposed. In contrast with former approaches based on wave‐interaction theory and its cumbersome triad‐interaction coefficients, the discrete analysis proposed here is inspired by the spectral‐transform technique, where nonlinearities are treated in physical space. This approach, based only on standard linear algebra techniques, is simpler than former ones and allows a large number of degrees of freedom to be retained in perturbation space. The merits and possible limitations of the method are discussed; some validations and results are presented.

Influence of Bottom Topography on Vortex Stability

AbstractThe effects of topography on the linear stability of both barotropic vortices and two-layer, baroclinic vortices are examined by considering cylindrical topography and vortices with stepwise relative vorticity profiles in the quasigeostrophic approximation. Four vortex configurations are considered, classified by the number of relative vorticity steps in the horizontal and the number of layers in the vertical: barotropic one-step vortex (Rankine vortex), barotropic two-step vortex, and their two-layer, baroclinic counterparts with the vorticity steps in the upper layer. In the barotropic calculation, the vortex is destabilized by topography having an oppositely signed potential vorticity jump while stabilized by topography of same-signed jump, that is, anticyclones are destabilized by seamounts while stabilized by depressions. Further, topography of appropriate sign and magnitude can excite a mode-1 instability for a two-step vortex, especially relevant for topographic encounters of an otherwise stable vortex. The baroclinic calculation is in general consistent with the barotropic calculation except that the growth rate weakens and, for a two-step vortex, becomes less sensitive to topography (sign and magnitude) as baroclinicity increases. The smaller growth rate for a baroclinic vortex is consistent with previous findings that vortices with sufficient baroclinic structure could cross the topography relatively easily. Nonlinear contour dynamics simulations are conducted to confirm the linear stability analysis and to describe the subsequent evolution.

A Barotropic Vorticity Budget for the Subtropical North Atlantic Based on Observations

AbstractTo ground truth the large-scale dynamical balance of the North Atlantic subtropical gyre with observations, a barotropic vorticity budget is constructed in the ECCO state estimate and compared with hydrographic observations and wind stress data products. The hydrographic dataset at the center of this work is the A22 WOCE section, which lies along 66°W and creates a closed volume with the North and South American coasts to its west. The planetary vorticity flux across A22 is quantified, providing a metric for the net meridional flow in the western subtropical gyre. The wind stress forcing over the subtropical gyre to the west and east of the A22 section is calculated from several wind stress data products. These observational budget terms are found to be consistent with an approximate barotropic Sverdrup balance in the eastern subtropical gyre and are on the same order as budget terms in the ECCO state estimate. The ECCO vorticity budget is closed by bottom pressure torques in the western subtropical gyre, which is consistent with previous studies. In sum, the analysis provides observational ground truth for the North Atlantic subtropical vorticity balance and explores the seasonal variability of this balance for the first time using the ECCO state estimate. This balance is found to hold on monthly time scales in ECCO, suggesting that the integrated subtropical gyre responds to forcing through fast barotropic adjustment.

Barotropic Instability of a Cyclone Core at Kilometer‐Scale Resolution

AbstractSecondary disturbances spawning frontal waves along the fronts of mature midlatitude low‐pressure systems were identified decades ago from satellite images and during field campaigns. Today's flagship supercomputers allow performing simulations at kilometer‐scale resolution on computational domains covering the entire lifecycle of synoptic‐scale systems and thus enable explicit representation of small‐scale disturbances embedded in large‐scale circulations. Here we demonstrate these capabilities in two different types of kilometer‐scale simulations. The first is a 10‐day‐long near‐global simulation of an idealized moist baroclinic wave, performed at 1 km grid spacing and employing 16,001 × 36,006 × 60 grid points. The second is a real‐case simulation of an extratropical low‐pressure system, driven by the European Centre for Medium‐Range Weather Forecasts's operational analysis. At kilometer‐scale resolution, both simulations display clear evidence of embedded mesoscale vortices spawning along frontal systems of mature extratropical cyclones. The vortices appearing in the real‐case simulation can also be identified in satellite imagery of the system. The simulated developments are due to a barotropic instability mechanism and driven by strong low‐level horizontal wind shear. While the simulation of the frontal systems is amenable at model resolutions around 10–50 km, the instability mechanism itself relies on the representation of a narrow shear zone, requiring about 5 times finer resolution. Results suggest that the flow regimes suppressing or fostering barotropic vortices can coexist in the same synoptic system. Far away from the cyclone core, the instability is suppressed by deformation associated with the large‐scale flow, while close to the mature cyclone core, the narrow frontal structure becomes unstable.

New model and dynamics of higher-dimensional nonlinear Rossby waves

In this work, the propagation of higher-dimensional nonlinear Rossby waves under the generalized beta effect is considered. Using the methods of weak nonlinear perturbation expansions and the multiple scales, we obtain a new (2 + 1)-dimensional generalized Boussinesq equation from the barotropic potential vorticity equation for the first time. Furthermore, a new dispersion relation for the linear Rossby waves is given corresponding to the linearized Boussinesq equation. More importantly, based on the methods of the traveling wave setting and the Jacobi elliptic function expansions, several kinds of exact traveling wave solutions for the higher-dimensional nonlinear Rossby waves, including the periodic solutions, solitary solutions and others are obtained. Finally, we simulate the solitary solutions obtained by using the method of the Jacobi elliptic function. The numerical results show that the amplitude of the Rossby solitary waves is decreasing with the increase of generalized beta effect.

Dynamical Analysis and Exact Solutions of a New (2+1)-Dimensional Generalized Boussinesq Model Equation for Nonlinear Rossby Waves**Supported by the National Natural Science Foundation of China under Grant Nos. 11562014, 11762011, 11671101, 71471020, 51839002; the Natural Science Foundation of Inner Mongolia under Grant No. 2017MS0108; Hunan Provincial Natural Science Foundation of China under Grant No. 2016JJ2061; the Scientific Research Fund of

In this paper, we study the higher dimensional nonlinear Rossby waves under the generalized beta effect. Using methods of the multiple scales and weak nonlinear perturbation expansions [Q. S. Liu, et al., Phys. Lett. A 383 (2019) 514], we derive a new (2+1)-dimensional generalized Boussinesq equation from the barotropic potential vorticity equation. Based on bifurcation theory of planar dynamical systems and the qualitative theory of ordinary differential equations, the dynamical analysis and exact traveling wave solutions of the new generalized Boussinesq equation are obtained. Moreover, we provide the numerical simulations of these exact solutions under some conditions of all parameters. The numerical results show that these traveling wave solutions are all the Rossby solitary waves.