Centrifugal instability of Stokes layers in crossflow: the case of a forced cylinder wake

TL;DR

This paper reveals a new three-dimensional instability mechanism in cylinder wake flows at moderate Reynolds numbers, caused by a centrifugal instability of the oscillating Stokes layer, explaining turbulence-like features observed experimentally.

Contribution

It introduces a previously unreported centrifugal instability mechanism in oscillating Stokes layers that occurs below the typical three-dimensionalization threshold in cylinder wakes.

Findings

Identification of a centrifugal instability in the Stokes layer at low forcing frequencies.

Explanation of turbulence-like features in cylinder wakes at moderate Reynolds numbers.

Proposal of a physical mechanism for observed three-dimensional structures.

Abstract

The wake flow around a circular cylinder at $Re\approx100$ performing rotatory oscillations has been thoroughly discussed in the literature, mostly focusing on the modifications to the natural B\'enard-von K\'arm\'an vortex street that result from the forced shedding modes locked to the rotatory oscillation frequency. The usual experimental and theoretical frameworks at these Reynolds numbers are quasi-two-dimensional, since the secondary instabilities bringing a three-dimensional structure to the cylinder wake flow occur only at higher Reynolds numbers. In the present paper we show that a three-dimensional structure can appear below the usual three-dimensionalization threshold, when forcing with frequencies lower than the natural vortex shedding frequency, at high amplitudes, as a result of a previously unreported mechanism: a pulsed centrifugal instability of the oscillating Stokes layer at the wall of the cylinder. The present numerical investigation lets us in this way propose a physical explanation for the turbulence-like features reported in the recent experimental study of D'Adamo et al. (2011).