An experimental investigation of spin-up from rest of a stratified fluid

摘要

We examine the spin-up from rest of a stratified fluid with initial Brunt-Vaisala frequency N bound within a cylindrical container of height 2H and radius R which is set to rotate impulsively with angular speed f/2. Particular attention is given to characterizing the dependence of the form of the resulting flow on the governing parameters. Our experimental study reveals a wealth of flow behaviours and instabilities. In all experiments, the initial phase of motion is marked by the establishment of mixed axisymmetric corner regions fed by radial Ekman transport, a process detailed in Flor et al. (Flor, J.B., Ungarish, M. and Bush, J.W.M., "Spin-up from rest of a stratified fluid: boundary flows'', J. Fluid Mech., 472, 51-82 (2002).).The subsequent evolution of the central vortex depends critically on the Burger number B-core=NcH/(fR), where N-c=N(1-0.2B(-1))(1/2) is the buoyancy frequency of the central core following the establishment of the corner regions. For B>1.0, the axisymmetry of the system is retained throughout the spin-up process: the central vortex attains a state of near solid body rotation by the diffusion of vorticity from the sidewalls. For B<1.0, the central core becomes baroclinically unstable, and its streamlines strained from circles into ellipses. Subsequently, for N-c/f<1 (and B<1.0), the symmetry of the central core is broken in a manner reminiscent of the elliptical instability. For short tanks (2H/R<1), the instability is marked by a simple tip-over of the central core in the laboratory frame that is resisted by the core stratification. For 2H/R>1, the centreline of the stratified core is deflected into a helical form before the core breaks into a series of stacked vortices. A Burger number criterion, B=NH/(fR)<1.0, for the baroclinic instability of the central core is derived and found to be consistent with the experimental observations.