On the theory of thin rotating jets: A quasi‐geostrophic time dependent model

Abstract

The time‐dependent meandering in a thin baroclinic jet over bottom topography is discussed in the quasi‐geostrophic approximation. The motion of the axis of the jet is taken to be vertically coherent and the axis itself is defined as inextensible. The motion is examined from a frame of reference moving with the axis but fixed at an arbitrary longitude in terms of an open ocean spatial initial value problem. The velocities of the axis and of the jet are quasi‐geostrophic, and vorticity conservation for the first non‐geostrophic components constrains the evolution of the axis and gives a path equation. The spatial linearized stability problem is studied and the jet is found to be baroclinically unstable to path disturbances of sufficiently high frequency which amplify downstream. An exact solution is obtained to the nonlinear path equation over a flat bottom with no s‐effect. The evolution of the path of these unstable meanders is such that the path closes itself and forms rings (at which point the analysis...