An experiment on two aspects of the interaction between strain and vorticity

Abstract

Presented here are two results concerning the interaction between vorticity and strain. Both are obtained experimentally by investigating the hyperbolic flow created in Taylor's four-roll mill. It is first shown that this pure straining flow becomes intrinsically unstable through a supercritical bifurcation to form an array of counter-rotating vortices aligned in the stretching direction. The dimensionless parameter characterizing the flow is the internal Reynolds number Re = γΔ2/v based on the velocity gradient γ and on the gap between the rollers Δ, and the threshold value is Rec = 17. Near the threshold, the transverse velocity profiles of these vortices are in excellent agreement with those predicted by the theory of Kerr & Dold (1994) in the case of an infinite hyperbolic flow. A second result is obtained at high Reynolds number. Measurements of the velocity profile in the direction parallel to the vortices show that the velocity gradient (the stretching) is systematically weaker inside the vortices than elsewhere. This demonstrates experimentally the existence of a negative feedback of rotation on stretching. This effect is ascribed to the two-dimensionalization due to the vortex fast rotation. An implication of these results for turbulent flows is a nonlinear limitation of the vorticity stretching, an effect characterized recently by Ohkitani 1998.