Stability of compressible three-dimensional boundary layers on a swept wing model is studied within the framework of the linear theory. The analysis based on the approximation of local self-similarity of the mean flow was performed within the Falkner-Skan-Cooke solution extended to compressible flows. The calculated characteristics of stability for a subsonic boundary layer are found to agree well with the measured results. In the case of a supersonic boundary layer, the results calculated for a Mach number M = 2 are also in good agreement with the measured spanwise scales of nonstationary vortices of the secondary flow. The calculated growth rates of disturbances, however, are substantially different from the measured values. This difference can be attributed to a high initial amplitude of disturbances generated in the experiment, which does not allow the linear stability theory to be applied. The evolution of natural disturbances with moderate amplitudes is fairly well predicted by the theory. The effect of compressibility on crossflow instability modes is demonstrated to be insignificant.
Stability of a hypersonic shock layer on a flat plate is examined with allowance for disturbances conditions on the shock wave within the framework of the linear stability theory. The characteristics of the main flow are calculated on the basis of the Full Viscous Shock Layer model. Conditions for velocity, pressure, and temperature perturbations are derived from steady Rankine-Hugoniot relation on the shock wave. These conditions are used as boundary conditions on the shock wave for linear stability equations. The growth rates of disturbances and density fluctuations are compared with experimental data obtained at ITAM
Introduction. The nonlinear evolution of disturbances in boundary-layer flows is a determining factor of the laminar-turbulent transition (LTT). Weakly nonlinear theory has been developed [1, 2] to study the evolution of weak pulsations. This theory is based on the assumption of local proximity of the hydrodynamic field to the distribution formed by linear disturbances. Viscous effects dominate in this process. Nonlinearity introduces corrections of higher order (with respect to fluctuation amplitude), which can, nevertheless, change considerably the spectrum and amplification rates of these fluctuations. Weakly nonlinear theory ensures a successful interpretation of subharmonic S-transition phenomena. The latter occurs at low initial disturbance amplitudes. It is characterized by an outstripping growth of low-frequency, three-dimensional, TollmienSchlichting waves, in particular, subharmonic waves with respect to the wave revealed in the initial stage. The main mechanism involves nonlinear resonance interactions in wave triads [2][3][4][5].The region of applicability of weakly nonlinear theory is rather limited. As the disturbance intensity increases, nonlinearity can play a dominant role in flow-field structuring. This occurs primarily in the critical layer (CL) of the wave, in which the phase velocity of the wave coincides with the local flow velocity. Along with the wall layer (WL), the CL region is of significance for the mechanism of energy exchange between the disturbances and the mean flow [6][7][8][9][10].Three CL types are identified in accord with which effect is most pronounced: unsteadiness, viscosity, or nonlinearity. Their thicknesses are [10]
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