Southward Translation of Strongly Nonlinear Warm Eddies in a 2½-Layer β-Plane Model

Abstract

The relation between lens translation speed and potential thickness anomaly in the second layer is investigated in a 2½-layer ?-plane primitive model in the case of southward movement of lens-shaped eddies. The trapped dipole in the second layer under the lens generated by the initial westward movement of the lens drives the first-layer lens southward. The subsequent southward translation has an almost steady stage before the lens succumbs to baroclinic instability, and the lens in the first layer and a negative potential thickness anomaly in the second layer remain coupled. It is shown that the translation speed is related to the potential thickness anomaly and that the ? effect in the first and second layers plays an important role in sustaining the steady translation. To examine this relation and discuss the dynamic balance of the steadily translating eddy, an analytic solution in a 2½-layer f-plane model is derived, assuming that the relative vorticity in the second layer is negligible. The solution shows the following: 1) If the translation speed is not zero, the area integral of the potential thickness anomaly in the second layer is constant irrespective of the translation speed. 2) The lens speed is related to the area average of the potential thickness anomaly in the second layer. 3) For steady translation, the area average of the potential thickness anomaly must be larger than a certain value. On the ? plane, Rossby wave radiation, leakage of the potential thickness anomaly, and meridional displacement of the vortex structure lead to a transformation of the potential vorticity anomaly, and the constraints of the f plane are thus difficult to hold. From the comparison between the f-plane theory and the numerical experiments, however, these constraints are found to be almost satisfied on the ? plane if the effect of the relative vorticity is included in the f-plane theory. This suggests that the increasing of the potential thickness anomaly due to the second-layer ? during the southward translation balances the leakage of the potential thickness anomaly from the lens region, with the result that the constraints obtained by the f-plane theory hold.