Optimal two-dimensional perturbations in a stretched shear layer
The evolution of 2D linear perturbations in a uniform shear layer stretched along the streamwise direction is considered in this work. The shear layer is assumed to have an error function profile. The width and strength of the shear layer evolve in time due to the combined effect of viscous diffusion and stretching. The time-dependent basic flow is therefore characterised by two parameters: the stretching rate γ and the Reynolds number Re. Using a direct-adjoint technique, perturbations which maximise the energy gain during a time interval (0, t f ) are computed for various t f , γ and Re. The results are compared with those obtained using a normal mode decomposition of the perturbations (WKBJ approach). Transient growths are shown to be weak in a stretched shear layer by opposition to what is observed in boundary layer flows.
KeywordsShear Layer Energy Gain Streamwise Direction Transient Growth Optimal Perturbation
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