Book Description

The problem of nonlinear development of Goertler vortices on a curved wall is studied within the framework of incompressible Navier-Stokes equations which are solved by a Fourier-Chebyshev spectral method. The results show that higher harmonics grow due to nonlinear effects; however, most of the energy remains in the fundamental mode. The computed flow field in the presence of a Goertler vortex is in qualitative agreement with the experimental data. The interaction of the Goertler vortex with a two-dimensional Tollmien-Schlichting wave is also studied and it is shown that the Tollmien-Schlichting wave grows faster than its linear theory growth rate when the amplitude of the Goertler vortex is sufficiently large. Due to nonlinear effects this interaction further leads to the development of oblique waves with spanwise wavelength equal to the Goertler vortex wavelength. The numerical method is also applied to study the nonlinear development of a stationary crossflow vortex in a Falkner-Skan-Cooke boundary layer. The crossflow vortex develops in a manner similar to that found earlier for rotating disk flow. The fundamental and the higher harmonics all tend to saturate when the integration is carried to large amplitudes. The computed velocity distribution clearly shows the emergence of the superharmonic which, however, does not dominate the fundamental mode. The Falkner-Skan-Cooke flow, modulated by the presence of the crossflow vortex, is found to be subject to a new secondary instability with large growth rates. (JHD).