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

The Rossby solitary waves in the barotropic vorticity model which contains the topography on the earth’s δ-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 the δ-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 parameter δ usually plays the stable part in Rossby waves and slow down the growing or decaying of Rossby waves with the parameter β.

Asymptotic behavior of solutions to barotropic vorticity equation on a sphere

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.

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

This 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.

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

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.

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

<p>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 testbed 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 50%. 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 approximation it is unstable for layer depths down to 1 km. These results may have implications for the importance of barotropic instability in Earth's upper stratosphere and perhaps also other planets such as Venus.</p>

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

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

The circulation in the North Atlantic Subpolar gyre is complex and strongly influenced by the topography. The gyre dynamics is 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, this dynamics has 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 high resolution simulation (≈ 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 each other. However, balances integrated over different regions of the gyre – shelf, slope and interior – still highlight the important role played by nonlinearities and the bottom drag curls. In particular the topographic Sverdrup balance cannot describe the dynamics in the interior of the gyre. The main sources of cyclonic vorticity are the nonlinear terms due to eddies generated along eastern boundary currents and the time-mean nonlinear terms from the Northwest Corner. Our results suggest that a good representation of the mesoscale activity along with a good positioning of the Northwest corner are two important conditions for a better representation of the circulation in the North Atlantic Subpolar Gyre.