The effect of base-flow changes in Kelvin-Helmholtz instability

Resumo

Using linear stability analysis, we determine base-flow modifications to a mixing layer velocity profile that maximise changes in the eigenvalues of Kelvin-Helmholtz instability. This is done by studying both the temporal and spatial stability problems given by the Orr-Sommerfeld equation and its adjoint, leading to an expression for the sensitivity of the eigenvalue to base-flow changes. Two objectives are pursued separately. First, we determine base-flow changes for reduction of growth rates; then, the same procedure is applied so as to obtain lower phase speeds. Both modifications would potentially reduce acoustic radiation by wavepackets. We see that changes in eigenvalues result from appropriate manipulation of the velocity profile near its inflection point. Reductions of growth rate are obtained for velocity profiles with lower shear around the inflection point, and reductions of phase speed result from a shift of the inflection point towards the slower stream. Reductions in the growth rate are obtained in a similar manner for both temporal and spatial instability of a mixing layer; however, although significant reductions of phase speed are obtained for temporal instability, modifying the base flow with this objective is less effective in the spatial problem. A feature observed in all cases is that the modifications of the base flow aimed at changing the Kelvin-Helmholtz mode lead to the appearance of new discrete modes in the eigenspectrum. These modes are stable for small perturbations of the base flow, but can become unstable if the base flow is significantly modified. © 2013 by A. V. G. Cavalieri.