Nonlinear spin-up of a rotating stratified fluid: Theory

TY - JOUR

T1 - Nonlinear spin-up of a rotating stratified fluid

T2 - Theory

AU - Hewitt, Richard E.

AU - Duck, Peter W.

AU - Foster, Michael R.

AU - Davies, Peter A.

PY - 1998/12

Y1 - 1998/12

N2 - We consider the boundary layer that forms on the wall of a relating 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.

AB - We consider the boundary layer that forms on the wall of a relating 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.

U2 - 10.1115/1.2820719

DO - 10.1115/1.2820719

M3 - Article

SN - 0098-2202

VL - 120

SP - 662

EP - 666

JO - Journal of Fluids Engineering

JF - Journal of Fluids Engineering

IS - 4

ER -