Abstract
This paper is devoted to a theoretical analysis of nonlinear two-dimensional waves using the Navier-Stokes equations in their full statement. Steady-state travelling wave regimes have been found and an analysis of their linear stability has been carried out. It is shown that the flow regimes obtained using the Navier-Stokes equations are qualitatively different from the solutions of Shkadov’s integral approach starting from some values of the Kapitza number. It is also found that the wave regimes of the Navier-Stokes equations have an internal vortex at moderate Reynolds numbers. The results obtained using “the regularized integral model” are in excellent agreement with the Navier-Stokes calculations for Re/Ka ≤2. Unlike the solutions found using an integral approach, it is shown that only a few types of nonlinear waves exist when the full Navier-Stokes equations are considered.
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