Multiple states for quasi-geostrophic channel flows

Abstract

We consider nonlinear baroclinic instabilities of two-layer quasi-geostrophic flow in a rectilinear channel. The full potential vorticity equations are shown to possess a countable infinity of invariant wavenumber sets. Each set is composed of a particular pattern in wavenumber space in which many Fourier modes have zero energy. Solutions with initial conditions confined to a particular wavenumber pattern will remain forever in that pattern. There is also a general asymmetric state with non-zero energy in all wavenumbers. The final state of a long-time evolution calculation depends on initial conditions and internal stability.

Key Words:

• Baroclinic instability
• nonlinear instability
• channel flow