Rapid Approach to Resolving the Adequacy Problem of Mathematical Modeling of Physical Phenomena by the Example of Solving One Problem of Hydrodynamic Instability

摘要

The linear stability problem of steady-state plane-parallel shear flows of a continuously stratified in density inviscid incompressible fluid in the gravity field between two immovable impermeable solid parallel planes in the Boussinesq approximation is studied. With the use of the direct Lyapunov method, it is proved that from the theoretical consideration (on semi-infinite temporal intervals) these flows are absolutely unstable with respect to small plane perturbations. Namely, a priory lower estimate is constructed; the estimate displays exponential in time growth of the considered perturbations. At that increment of containing in this estimate exponent is any positive constant. Using the direct Lyapunov method, constructive sufficient conditions of practical instability (on finite temporal intervals) are also found for these flows with respect to small plane perturbations.