Inertial Instability of Nonparallel Flow on an Equatorial β Plane

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  • 1 Northwest Research Associates, Bellevue, Washington
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Abstract

A simple theoretical model was developed to investigate the inertial instability of zonally nonuniform, non-parallel flow near the equator. The basic state was independent of height and time but included cross-equatorial shear with longitudinal variation, as observed in the tropical mesosphere and elsewhere. Numerical solutions were obtained for the most unstable modes.

It is shown that, in addition to previously known “global” (symmetric and nonsymmetric) modes of inertial instability, there exist “local” modes within regions of anomalous potential vorticity. Local modes may be exactly stationary or display zonal phase propagation, but are distinguished from global modes by their zero group velocity and concentration of amplitude within, or downstream from, the region of most unstable flow. Local stationary instability has the largest growth rate and occurs in strong inhomogeneous shear when the in situ mean flow is near zero, that is, quasi-stationary with respect to the (stationary) basic-state pattern. This situation is expected in an equatorial Rossby wave critical layer.

The local mode has properties similar to those of “absolute” instability of nonparallel flow as discussed elsewhere in fluid dynamics.

Abstract

A simple theoretical model was developed to investigate the inertial instability of zonally nonuniform, non-parallel flow near the equator. The basic state was independent of height and time but included cross-equatorial shear with longitudinal variation, as observed in the tropical mesosphere and elsewhere. Numerical solutions were obtained for the most unstable modes.

It is shown that, in addition to previously known “global” (symmetric and nonsymmetric) modes of inertial instability, there exist “local” modes within regions of anomalous potential vorticity. Local modes may be exactly stationary or display zonal phase propagation, but are distinguished from global modes by their zero group velocity and concentration of amplitude within, or downstream from, the region of most unstable flow. Local stationary instability has the largest growth rate and occurs in strong inhomogeneous shear when the in situ mean flow is near zero, that is, quasi-stationary with respect to the (stationary) basic-state pattern. This situation is expected in an equatorial Rossby wave critical layer.

The local mode has properties similar to those of “absolute” instability of nonparallel flow as discussed elsewhere in fluid dynamics.

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