Fully Nonlinear Development of the Most Unstable Gortler Vortex in a Three Dimensional Boundary Layer
INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA
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In this paper we investigate the nonlinear development of the most unstable Gortler mode within a general three-dimensional boundary layer upon a suitably concave surface. The structure of this mode was first identified by Denier, Hall and Seddougui 1991 who demonstrated that the growth rate of this instability is 0G35 where G is the Gortler number taken to be large here, which is effectively a measure of the curvature of the surface. Previous researches have described the fate of the most unstable mode within a two- dimensional boundary layer. Denier and Hall 1992 discussed the fully nonlinear development of the vortex in this case and showed that the nonlinearity causes a breakdown of the flow structure. The effect of crossflow and unsteadiness upon an infinitesimal unstable mode was elucidated by Bassom and Hall 1991. They demonstrated that crossflow tends to stabilise the most unstable Gortler mode, and for certain crossflowfrequency combinations the Gortler mode may be made neutrally stable. These vortex configurations naturally lend themselves to a weakly nonlinear stability analysis work which is described in a previous article by the present authors. Here we extend the ideas of Denier and Hall 1992 to the three-dimensional boundary layer problem. It is found that the numerical solution of the fully nonlinear equations is best conducted using a method which is essentially an adaption of that utilised by Denier and Hall 1992. The influence of crossflow and unsteadiness upon the breakdown of the flow is described.
- Fluid Mechanics