Effect of compliance on the stability of jets and wakes

Abstract

Starting from the system of PDEs which govern the motion of a fluid, known as the Navier-Stokes equations, we use a piece-wise linear base flow approximation to model a jet/wake flow, assuming zero surface tension between fluid layers, to obtain the Rayleigh equation, which describes the instabilities of the flow. We then bound this flow by compliant walls, modelled by a spring backed elastic plate.

Upon making a point like disturbance in this flow, we use the Rayleigh equation to obtain a relationship between the spatial wave number α and temporal frequency ω, from which we can infer the behaviours of the various instabilities found in the flow, and how they vary as we vary wall and flow parameters.

Fluid instabilities have a range of real-world applications, such as the breaking up of jets of fuel in engines to make for an efficient burn, various cloud formation and drag reduction to name a few.