Some asymptotic solutions of linearized Navier–Stokes equations

We consider examples that illustrate in various situations the time evolution of asymptotic solutions of linearized Navier–Stokes equations. We give formulas that describe short-wave perturbations of plane-parallel flows. These perturbations grow linearly over time. For a wide class of two-dimensional flows with closed flow lines we prove the exponential growth of three-dimensional short-wave asymptotic solutions.