Stability of oscillatory flows past compliant surfaces

Abstract

The stability of oscillatory flows over compliant surfaces is studied analytically and numerically. The types of compliant surfaces studied are the spring backed wall model, which permits tangential motion of the surface, and the incompressible viscoelastic gel model. The stability is determined using the Floquet analysis, where amplitude of perturbations at time intervals separated by one time period is examined to determine whether perturbations grow or decay. The oscillatory flows past both the spring backed wall model and the viscoelastic gel model exhibit an instability in the limit of zero Reynolds number, and the transition amplitude of the oscillatory velocity increases with the frequency of oscillations. The transition amplitude has a minimum at zero wave number for the spring backed plate model, whereas the minimum occurs at finite wavenumber for the viscoelastic gel model. For the spring backed plate model, it is shown that the instability due to steady mean flow and the purely oscillatory instability reinforce each other, and the regions of instability are mapped in the ( Λ-A) plane, where Λ is the steady strain rate and A is the oscillatory strain rate. For the viscoelastic gel model, the instability is found to depend strongly on the gel viscosity η_g, and the effect of oscillations on the continuation of viscous modes at intermediate Reynolds number shows a complicated dependence on the oscillation frequency.