Summary
The two-dimensional nonlinear evolution of a second-mode instability wave in a flat plate boundary layer at a free-stream Mach number of M ∞ = 5 is investigated by direct numerical simulation. An explicit spectral/finite-difference scheme employing the temporal model is used. A nonlinear saturation process is found, during which initially a weak viscous shock develops near the wall. A comparison of the numerical result obtained in the shock region with a one-dimensional analytic weak-shock solution is made and a good agreement of the shock-normal velocity distribution and shock thickness is found. The nonlinear saturation is characterized by a cascade of states with alternating high and low energy levels of the higher Fourier-modes. The system evolves on a slow time scale towards a steady state which appears to be different from the undisturbed laminar state.
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Adams, N.A., Kleiser, L. (1995). Two-Dimensional Nonlinear Saturation Behaviour of Instability Waves in a Boundary Layer at Mach 5. In: Leutloff, D., Srivastava, R.C. (eds) Computational Fluid Dynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79440-7_14
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DOI: https://doi.org/10.1007/978-3-642-79440-7_14
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