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Secondary instability and three-dimensionalization in a laboratory accelerating shear layer with varying density differences
Authors:C. P. Caulfield   S. Yoshida  W. R. Peltier
Abstract:We investigate the processes by which an accelerating stratified shear flow undergoes the transition to turbulence in a sequence of experiments in a tilted tank. We observe that the processes by which the flow undergoes breakdown are both complex and diverse, and suggest that the ratio, D, of the depth of the shear layer to the total tank depth and/or the (nondimensional) total density difference are important parameters in the determination of the dominant structures. In general, inherently three-dimensional, and relatively large-scale, flow structures strongly suppress simple subharmonic vortex pairing, and appear to dominate totally the transition to turbulence. In certain circumstances, the primary instabilities of the flow, namely Kelvin-Helmholtz billows, are able to develop in a quasi-two-dimensional manner before interaction between neighbouring billows becomes significant. In these circumstances, narrow secondary streamwise ‘tubes’ of vorticity are observed between neighbouring billows. Alternatively subharmonic, quasi-two-dimensional vortex mergings may be observed; these are not just simple pairings, but also three vortices are observed to merge into a single secondary billow, or two merge and the other persists, as predicted theoretically by Klaassen and Peltier (J. Fluid Mech., 202: 367–402, 1989). Three-dimensional vortex merging (knotting) of initially quasi-two-dimensional billows is also observed. Such knots are observed not only as pairwise transitions, as discussed by Thorpe (Geophys. Astrophys. Fluid Dyn., 34: 175–199, 1985), but also single billows are observed to knot with both adjacent neighbours simultaneously. Also, billows are observed to bow during merging events. However, particularly at larger density differences, higher Reynolds number and when the depth ratio, D, is sufficiently small, billow-billow interactions are apparent essentially immediately upon instability onset. Although the structures which develop resemble secondary tubes, these structures appear to be a primary instability of the flow, analogous to an instability observed by other researchers in both forced and unforced homogeneous shear layers.
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