Eddy memory in weakly nonlinear two-layer quasi-geostrophic ocean flows

Abstract

In this paper, we study the origin of eddy-memory effects in a weakly nonlinear regime of a baroclinically unstable zonal ocean flow in a zonal channel. In this weakly nonlinear regime, the memory kernel can be analytically derived in case of an externally imposed time-dependent wind-stress forcing. Here, the memory arises because it takes a finite time for the nonlinear flow to equilibrate and the memory kernel is a decaying (in time) exponential function. When there is no external forcing, eddy-memory effects arise due to successive rectification of the background flow which is due to the self-interaction of the unstable modes. While the memory kernel cannot explicitly be calculated in this case, it is also argued to be a decaying exponential function. In both cases, the memory strength is inversely proportional to the growth rate of the instabilities at criticality.