Numerical solutions of the three-dimensional Navier-Stokes equations for the stability problem of the plate boundary-layer flow

The present study is concerned with the transition from laminar to turbulent flow in the case of the plate boundary-layer flow, taking into account the development of a mixed spectral and difference procedure for a numerical simulation of the transition process. The Navier-Stokes equations are used as a basis for the derivation of a number of dimensionless quantities. A system of equations is obtained, and its solution is discussed. The results of test calculations are also considered, giving attention to a specific test case. It is found that the described procedure makes it possible to simulate spatially incited, three-dimensional interference waves. It is expected that certain improvements will make it feasible to determine computationally the developments which occur until a time shortly before the laminar-turbulent flow transition.