Ordered and chaotic states following boundary layer separation in a rotating fluid

Abstract

Abstract Laboratory measurements of the transition to chaos in separated boundary layer flow in a rotating annulus of homogeneous fluid are presented. The boundary layers are formed along the sidewalls of the annulus, which has a slightly sloped bottom topography and a differentially rotating lid. When the bottom friction is large the flow is fully attached. As the friction is decreased the boundary layer at the inner wall separates, and a steady separation bubble forms. Further decreases in the friction lead to a singly-periodic formation of cyclonic eddies at the leading edge of the bubble. The eddies propagate to the trailing edge where they are reabsorbed. This sinusoidal flow bifurcates to one of two quasi-periodic states with a modulation of the eddy generation process. These two multiple states are characterized by different eddy generation frequencies and different modulation patterns. The vacillations ultimately becomes chaotic when the advection time is typically about one tenth the spin down time.