MULTIPLE STATES FOR QUASI-GEOSTROPHIC CHANNEL FLOWS

We consider nonlinear baroclinic instabilities of two-layer quasigeostrophic 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 nonzero energy in all wavenumbers. The final state of a long-time evolution calculation depends on initial conditions and internal stability. These fundamental ideas are illustrated with high resolution numerical calculations of finite-amplitude baroclinic instability for meridionally constant basic currents, and for a horizontally sheared zonal flow. Multiple states appear in both situations. The motion for a particular invariant wavenumber set can be steady, periodic, or chaotic. © 1990, Taylor & Francis Group. All rights reserved.