Experimental evidence for a new instability of a vertical columnar vortex pair in a strongly stratified fluid

Abstract

This paper shows that a long vertical columnar vortex pair created by a double flap apparatus in a strongly stratified fluid is subjected to an instability distinct from the Crow and short-wavelength instabilities known to occur in homogeneous fluid. This new instability, which we name zigzag instability, is antisymmetric with respect to the plane separating the vortices. It is characterized by a vertically modulated twisting and bending of the whole vortex pair with almost no change of the dipole's cross- sectional structure. No saturation is observed and, ultimately, the vortex pair is sliced into thin horizontal layers of independent pancake dipoles. For the largest Brunt–Väisälä frequency N = 1.75 rad s⁻¹ that may be achieved in the experiments, the zigzag instability is observed only in the range of Froude numbers: 0.13 < F_h0 < 0.21 (F_h0 = U₀/NR, where U₀ and R are the initial dipole travelling velocity and radius). When F_h0 > 0.21, the elliptic instability develops resulting in three-dimensional motions which eventually collapse into a relaminarized vortex pair. Irregular zigzags are then also observed to grow. The threshold for the inhibition of the elliptic instability F_h0 = 0.2±0.01 is independent of N and in good agreement with the theoretical study of Miyazaki & Fukumoto (1992). Complete stabilization for F_h0 < 0.13 is probably due to viscous effects since the associated Reynolds number is low, Re₀ < 260. In geophysical flows characterized by low Froude numbers and large Reynolds numbers, we conjecture that this viscous stabilization will occur at much lower Froude number.

It is tentatively argued that this new type of instability may explain the layering widely observed in stratified turbulent flows.