Small-scale instabilities of an island wake flow in a rotating shallow-water layer

Abstract

Unlike the standard two-dimensional Kármán street, the oceanic vortex streets which may occur behind isolated islands are affected by the earth’s rotation and the vertical stratification of the thermocline. These effects induce a selective destabilisation of anticyclonic vorticity regions. Several experimental studies were devoted to the inertial instability, which induces transient and three-dimensional perturbations in a rotating fluid layer. However, these previous experiments correspond to a large or finite vertical h to horizontal L aspect ratio ( α = h / L ) while in an oceanic context this ratio is much smaller than unity ( α ≃ 0.01 ) . This vertical confinement induces a cutoff vertical scale for unstable perturbations. But, since dissipation preferentially damps smaller scales, the shallow-water aspect ratio α may become so small that no growth will occur. We present here the first experimental investigation of three-dimensional destabilizations of an island wake flow in a shallow-water configuration. These laboratory experiments where performed on the LEGI Coriolis Platform, with small aspect ratio ( α = 0.1 ) and large Reynolds numbers ( R e = 5000 – 35 , 000 ) . We have shown that unstable three-dimensional perturbations occur when the island Rossby number R o = V / ( Ω 0 D ) is large enough ( R o > 0.8 ) while the Reynolds number seems to control the duration of this transient instability. Qualitative dye visualisation reveals various types of passive tracer dispersion in the wake. Moreover, according to PIV measurements we have shown that, unlike experiments having large or finite aspect ratio ( α ≥ 1 ) , the small-scale perturbations do not significantly reduce the local vorticity inside the unstable anticyclone. Hence, the shallow-water configuration ( α ≪ 1 ) seems to reduce the intensity and the impact of three-dimensional instabilities in the vortex street. Finally, for high Froude numbers, when the flow becomes supercritical and owing to the generation of large amplitude waves in the wake, the vortex street intensity is strongly reduced.