Convective instability in inhomogeneous media: impulse response in the subcritical cylinder wake

TL;DR

This study investigates how localized convective instabilities in a subcritical cylinder wake amplify initial perturbations transiently, using experimental velocity measurements to analyze wave packet evolution.

Contribution

It provides experimental quantification of convective instability effects in a subcritical cylinder wake, focusing on transient amplification and decay of perturbations.

Findings

Transient algebraic growth of energy at short times

Exponential decay of perturbations after initial amplification

Dependence of wave evolution on Reynolds number and perturbation magnitude

Abstract

We study experimentally the impulse response of a cylinder wake below the critical Reynolds number of the B\'enard-von K\'arm\'an instability. In this subcritical regime, a localized inhomogeneous region of convective instability exists which causes initial perturbations to be transiently amplified. The aim of this work is to quantify the evolution resulting from this convective instability using two-dimensional particle image velocimetry in a hydrodynamic tunnel experiment. The velocity fields allow us to describe the evolution of wave packets in terms of two control parameters: the Reynolds number and the magnitude of the imposed perturbation. The temporal evolution of energy exhibits a transient algebraic growth at short times followed by an exponential decay.