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The Effect of Crossflow on Gortler Vortices
INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA
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It is well known that the boundary layer flow over a surface with a region of concave curvature is susceptible to centrifugal instabilities in the form of Gortler vortices. In the limit of large Gortler number a parameter which is a measure of the curvature of the surface the effect of a crossflow component in the underlying basic flow has been shown to stabilises these modes and thus render the Gortler vortex mechanism inoperable in these situations. Here we consider the effect of crossflow when the Gortler number and the scaled spanwise wavenumber of the vortex are both order one quantities. The parabolic partial differential equations governing the linear evolution of a Gortler vortex in a three-dimensional boundary layer are solved numerically. Our results suggest that, at least for small magnitude crossflows, the Gortler vortex instability mechanism is still operable. In addition we consider the effect of an applied pressure gradient within the boundary layer on the instability mechanism and demonstrate that a favourable pressure gradient renders the boundary layer more susceptible to the Gortler vortex instability this is in stark contrast to the case of Tollmien-Schlichting waves where a favourable pressure gradient stabilises the flow.
APPROVED FOR PUBLIC RELEASE