The quasi-three-dimensional instability of an elliptical vortex subject to a strain field in a rotating stratified fluid

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摘要：

The linear instability of a steady elliptical vortex in a stably stratified rotating fluid is investigated, using the quasi-geostrophic, f -plane approximation. The vortex is embedded in a uniform background straining field e with uniform vorticity 2γ (the Moore-Saffman vortices). An elliptical vortex in an irrotational strain field (γ = 0) is shown to be unstable to long wave quasi-three-dimensional disturbances of azimuthal wavenumber m = 1 (bending wave). The long wave instability has a two-dimensional origin. An elliptical vortex in a simple shear, whose major axis is parallel to the shear streamlines ( e = γ ), is stable against any disturbance. In contrast, an ellipse in a simple shear, whose major axis is perpendicular to the shear streamlines ( e = γ ), is unstable to quasi-three-dimensional bending modes irrespective of ja:math . Short wave quasi-three-dimensional disturbances grow faster than two-dimensional instability modes in the parameter range 0.5 < γ < 0. The origin of short wave instability is attributed to resonance between inertial waves and the imposed strain field e .

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Theoretical or Mathematical/ flow instability rotational flow stratified flow vortices/ quasi-three-dimensional instability steady elliptical vortex imposed strain field rotating stratified fluid linear instability bending wave stably stratified rotating fluid quasi-geostrophic f-plane approximation embedded vortex uniform background straining field uniform vorticity Moore-Saffman vortices irrotational strain field long wave quasi-three-dimensional disturbances azimuthal wavenumber long wave instability elliptical vortex shear streamlines quasi-three-dimensional bending modes Short wave quasi-three-dimensional disturbances inertial waves resonance/ A4730 Rotational flow, vortices, buoyancy and other flows involving body forces A4720 Hydrodynamic stability and instability A4755H Stratified flows