Spectral analysis of optimal disturbances of stratified turbulent Couette flow

For a stratified turbulent Couette flow, the eigenmodes and optimal disturbances of corresponding simplified equations linearized around a steady state are considered. It is shown that the spectrum of these equations is symmetric with respect to the real axis and lies strictly in the left half-plane, i.e., all eigenmodes are stable, and the main part of an optimal disturbance is a linear combination of a large number of modes corresponding to eigenvalues with largest real parts. The number of the most significant modes in this linear combination grows with increasing Reynolds number.