  Non-modal transient growth of disturbances in a viscous mixing layer flow is
studied for the Reynolds numbers varying from 100 up to 5000 at different
streamwise and spanwise wavenumbers. By comparing results of several
mathematical approaches, it is concluded that the non-modal optimal
disturbances growth results from the discrete part of the spectrum only. It is
found that in the linearly unstable configurations the non-modal growth cannot
be larger than the exponential one. At the same time, the largest non-modal
growth takes place at the wavenumbers for which the mixing layer flow is
stable. The most profound growth is attained by oblique three-dimensional waves
that propagate at the angle close to 45o with respect to the base flow. Results
of the non-modal analysis are followed by the fully non-linear
three-dimensional time-dependent solutions, initial conditions for which are
taken as the calculated optimal vectors. The fully 3D non-linear calculations
exhibit growth and decay of flow structures that sometimes become similar to
those observed at late stages of time evolution of the Kelvin-Helmholtz
billows. It is shown that non-modal optimal disturbances yield a strong mixing
without a transition to turbulence.
