Non-modal disturbances growth in a viscous mixing layer flow

The non-modal transient growth of disturbances in an isothermal viscous mixing layer flow is studied for Reynolds numbers varying from 100 up to 5000 at different streamwise and spanwise wavenumbers. It is found that the largest non-modal growth takes place at the wavenumbers for which the mixing layer flow is stable. In linearly unstable configurations, the non-modal growth can only slightly exceed the exponential growth at short times. Contrarily to the fastest exponential growth, which is two-dimensional, the most profound non-modal growth is attained by oblique three-dimensional waves propagating at an angle with respect to the base flow. By comparing the results of several mathematical approaches, it is concluded that within the considered mixing layer model with a tanh base velocity profile, the non-modal optimal disturbances growth is governed only by eigenvectors that are decaying far from the mixing zone. Finally, a full three-dimensional DNS with optimally perturbed base flow confirms the presence of the structures determined by the transient growth analysis. The time evolution of optimal perturbations is presented. It exhibits a growth and a decay of flow structures that sometimes become similar to those observed at the late stages of the time evolution of the Kelvin-Helmholtz billows. It is shown that non-modal optimal disturbances yield a strong mixing without a transition to turbulence.