The interaction of time-dependent rotating and stratified flow with isolated topography

Abstract

Laboratory experiments concerned with a time-varying, spatially homogeneous, free stream current past truncated right circular cylinders in the presence of a linear stratification and uniform background rotation are discussed. The current is composed of a sinusoidal component superimposed on a uniform flow. It is shown that such a flow can be investigated by the suitable translation of an obstacle through a fluid otherwise at rest with respect to a rotating observer. The principal dynamical parameters of the system are the Burger, Ekman, Rossby and temporal Rossby numbers and the velocity ratio u1u0 where u1 is the amplitude of the oscillating component and u0 is the magnitude of the uniform flow. The ranges of dynamical parameters considered are of relevance to certain oceanographic current systems. A series of characteristic flow regimes are described for u1u0 = 1.0 and fixed Burger and Ekman numbers; these characteristic flows are depicted on a Rossby against temporal Rossby number flow regime diagram. Emphasis is given to those flow features that are dependent on the time-varying nature of the free stream. For example, for the velocity ratio u1u0 = 1.0, the free stream comes to rest at a given time in each flow cycle. At this instant, for sufficiently small Rossby and temporal Rossby numbers, a residual anticyclonic motion around the obstacle is present. In another region of the flow regime diagram, the wake flow at this phase consists of a jet-like motion toward the topography. Quantitative measures are made of such observable features as the maximum bubble extent for non eddy-shedding flow regimes and eddy speeds for cases of vortex shedding. Some qualitative observations are also made for cases in which there is no background rotation.