We consider the boundary layer that forms on the wall of a rotating container of stratified fluid when altered from an initial state of rigid body rotation. The container is taken to have a simple axisymmetric form with sloping walls. The introduction of a non-normal component of buoyancy into the velocity boundary-layer is shown to have a considerable effect for certain geometries. We introduce a similarity-type solution and solve the resulting unsteady boundary-layer equations numerically for three distinct classes of container geometry. Computational and asymptotic results are presented for a number of parameter values. By mapping the parameter space we show that the system may evolve to either a steady state, a double-structured growing boundary-layer, or a finite-time breakdown depending on the container type, rotation change and stratification. In addition to extending the results of Duck et al. (1997) to a more general container shape, we present evidence of a new finite-time breakdown associated with higher Schmidt numbers.
Nonlinear Spin-Up of a Rotating Stratified Fluid: Theory
- Views Icon Views
- Share Icon Share
- Search Site
Hewitt, R. E., Duck, P. W., Foster, M. R., and Davies, P. A. (December 1, 1998). "Nonlinear Spin-Up of a Rotating Stratified Fluid: Theory." ASME. J. Fluids Eng. December 1998; 120(4): 662–666. https://doi.org/10.1115/1.2820719
Download citation file: