We consider the nonlinear spin-up of a rotating stratified fluid in a conical container. An analysis of similarity-type solutions to the relevant boundary-layer problem (Duck et al, 1997) has revealed three types of behavior for this geometry. In general, the boundary-layer evolves to either a steady state, a growing boundary-layer, or a finite-time singularity depending on the initial to final rotation rate ratio, and a “modified Burger number.” We emphasize the experimental aspects of our continuing spin-up investigations and make some preliminary comparisons with the boundary-layer theory, showing good agreement. The experimental data presented is obtained through particle tracking velocimetry. We briefly discuss the qualitative features of the spin-down experiments which, in general, are dominated by nonaxisymmetric effects. The experiments are performed using a conical container filled with a linearly stratified fluid, the generation of which is nontrivial. We present a general method for creating a linear density profile in containers with sloping boundaries.
Nonlinear Spin-Up of a Rotating Stratified Fluid: Experimental Method and Preliminary Results
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Hewitt, R. E., Davies, P. A., Duck, P. W., Foster, M. R., and Smith, F. W. (December 1, 1998). "Nonlinear Spin-Up of a Rotating Stratified Fluid: Experimental Method and Preliminary Results." ASME. J. Fluids Eng. December 1998; 120(4): 667–671. https://doi.org/10.1115/1.2820720
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