Shear flow instabilities in a rotating system
Abstract
Instabilities of viscous shear flows in a fluid layer rotating about a vertical axis were investigated. Two basic states were considered: (1) a baroclinic linear shear flow, which is associated with an imposed horizontal temperature gradient, and (2) double Ekman layers, which are produced by the relative motion of the two horizontal boundaries. Two instability mechanisms are present in this system, the inflection point mode and the symmetric mode. The linear theory of these instabilities is considered in the case baroclinic flow and Ekman layer flow. A RungeKutta shooting method was used in the numerical analysis. In special cases the nonlinear properties of the instabilites were studied. Finite amplitude disturbances in the form of rolls were investigated using the Galerkin technique. It was found that the existence of multiple solutions is a common feature. Moreover, finite amplitude disturbances can exist at Reynolds numbers lower than that predicted by the linear analysis. To test whether the finite amplitude rolls are realized, a stability analysis of the combined circulation was also performed.
 Publication:

Ph.D. Thesis
 Pub Date:
 1981
 Bibcode:
 1981PhDT........76C
 Keywords:

 Flow Stability;
 Rotating Bodies;
 Rotating Fluids;
 Shear Flow;
 Baroclinic Instability;
 Baroclinity;
 Boundary Layer Transition;
 Galerkin Method;
 Nonlinear Systems;
 RungeKutta Method;
 Temperature Gradients;
 Fluid Mechanics and Heat Transfer