Streak evolution in viscoelastic Couette flow

The combined effect of inertia and elasticity on streak amplification in planar Couette flow of an Oldroyd-B fluid is examined. The linear perturbation equations are solvedin the form of a forced-response problem to obtain the wall-normal vorticity responseto a decaying streamwise vortex. With significant disparity between the solvent diffusion and polymer relaxation time scales, two distinct responses are possible. The first is termed ‘quasi-Newtonian’ because the streak evolution collapses ontothe Newtonian behaviour at the same total and solvent Reynolds numbers when relaxation is very fast or slow, respectively. The second response is labelled ‘elastic’: with a long relaxation time, the streaks can reach significant amplitudes even withvery weak inertia. If the diffusion and relaxation time scales are commensurate, thestreaks are able to re-energize in a periodic cycle within an envelope of overall decay. This behaviour is enhanced in the instantaneously elastic limit, where the governing equation reduces to a forced wave equation. The streak re-energization is demonstrated to be a superposition of trapped vorticity waves.