Long planetery waves in a three layer ocean with a wind-driven steady circulation

Planetary waves play an important role in the adjustment of ocean circulation to long-period forcing. To better understand this role, we considered small-amplitude long planetary waves propagating through a simple three-layer model of a steady wind-driven anticyclonic gyre. The steady gyre consists of an eastern zone (EZ) where only the surface layer is in motion and a western zone (WZ) where the top two layers are moving and the lower layer is homogenized in potential vorticity. The fluctuations are forced at annual period.

The long-wave equations in both EZ and WZ are of hyperbolic type and can be solved numerically by the method of characteristics using the Runge-Kutta technique. For a choice of parameters typical of the north Pacific subtropical gyre, the waves are baroclinically unstable in the southwest part of the gyre, growing exponentially towards the west.

The effects of bottom slope and of non zonality and magnitude of the background flow on the instability can be studied by means of a local WKB analysis.

The discrete numerical scheme for solving across coupled characteristics was examined by using a method analogous to the classical von Neuman analysis. An important result is that naive refinement of resolution does not necessarily yield more accurate or more stable solutions. We show examples of this.