Stationary Rossby waves and shocks on the Sverdrup coordinate

Abstract

Gyre-scale frontal structures, e.g., the Subtropical Front, have been well documented in the oceans. Although the generation mechanism of such a front remains unclear, it may be ascribed to the steepening of nonlinear planetary waves as discussed by Dewar (1992). To discuss the stationary wave characteristics and their shock formation in a two-layer wind-driven gyre, the present paper introduces a new coordinate, referred to as theSverdrup coordinate here, in which the Sverdrup function is used instead of the longitudinal coordinate, and especially, investigates the possibility of the frontgenesis caused by the Rossby waves emanating from the western boundary region. On theSverdrup coordinate, since the advection by the Sverdrup flow is in the direction normal to that of the Rossby wave propagation, the system becomes much simpler than that on the (x,y)-coordinate, and the solution to this coordinate does not explicitly depend on the distribution of the Ekman pumping, i.e., we can treat cases, in which the Ekman pumping is a function of bothx andy, in a similar way to the case with zonally uniform Ekman pumping.