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Spatial evolution of supersonic streamwise vortices
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In this paper, the spatial developments of high Mach number streamwise vortices have been investigated using direct numerical simulations for Mach numbers from 2.5 to 9.0. The particular streamwise vortices studied here are those with uniform stagnation temperatures and those with constant entropy. For vortices with uniform stagnation temperatures, the calculated spatial evolutions show that for small swirl parameters, a bending wave mode is excited and spiral structures of low-wavenumber modes only develop downstream. In contrast, for swirl parameters larger than a moderate amount (approximately 0.5), relaminarization occurs downstream. This study also found that the relation between the circulation and the freestream Mach number contributes to a necessary condition as to whether perturbations can grow in supersonic flows. For isentropic streamwise vortices, instability properties at high Mach numbers parallel those in low-speed flows because the evolution can give rise to high-wavenumbers within the core. The resulting entropy instability is analogous to the Rayleigh-Taylor instability and has the advantage of being insensitive to compressibility effects in supersonic flows.
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