Nonlinear Spin-Up of a Rotating Stratified Fluid: Theory

Richard E. Hewitt, Peter W. Duck, Michael R. Foster, Peter A. Davies

    Research output: Contribution to journalArticlepeer-review

    Abstract

    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.
    Original languageEnglish
    Pages (from-to)662-666
    Number of pages4
    JournalJournal of Fluids Engineering, Transactions of the ASME
    Volume120
    Issue number4
    DOIs
    Publication statusPublished - Dec 1998

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