Abstract
Oceanic mesoscale eddies are common, especially in areas where zonal currents with meridional shear exists. The nonlinear effects complicate the analysis of mesoscale eddy dynamics. This study proposes a solitary (eddy) solution based on an asymptotic expansion of the nonlinear potential vorticity equation with a constant meridional shear of zonal current. This solution reveals several important consequences. For example, cyclonic (anticyclonic) eddies can be generated by the negative (positive) shear of the zonal current. Furthermore, the meridional structure of an eddy is asymmetrical, and the center of a cyclonic (anticyclonic) eddy tilts poleward (equatorward). Eddy width is inversely proportional to shear intensity. Eddy phase speed is proportional to shear intensity and the wave amplitude, and their spatial distribution show band-like pattern as they propagate westward. This nonlinear solitary solution is an extension of classical linear Rossby theory. Moreover, these findings could be applied to other areas with similar zonal current shear.
Highlights
Flow EffectsIf there is no shear in the background flow, the solution of the eigenvalue equations (8) can be obtained analytically: ψ1 = sinnπy, n = 1, 2, ..., c0 = u β+[2 ] Fu +F, where c0 is the phase speed of the linear long mode n Rossby wave (k→0, where k represents the wavenumber in the horizontal direction)
This study proposes a solitary solution based on an asymptotic expansion of the nonlinear potential vorticity equation with a constant meridional shear of zonal current
If there is shear in the background flow, uy ≠ 0, and as u is function of variable y, it is difficult to obtain the analytic solution of eigenvalue equations (8); but it can be solved using numerical methods or asymptotic analytical method
Summary
This study proposes a solitary (eddy) solution based on an asymptotic expansion of the nonlinear potential vorticity equation with a constant meridional shear of zonal current. The influences of background flow shear on the spatial structure, propagation velocity and wave width of solitary Rossby waves remain absent.
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