On the formation of the disturbance-field structure in a transitional boundary layer

Abstract

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]

The Nonlinear Critical‐Wall Layer in a Parallel Shear Flow

“…We know of no other published paper where this phenomenon has been reported to occur in the absence of external forcing. However, in an as yet uncompleted investigation of long waves in a supersonic mixing layer, Balsa [20] finds this to be the case and in the averaging approach used by Zelman and Smorodsky [21] to investigate the Blasius boundary layer all harmonics are included. We expect that for smaller values of A the higher harmonics will be more prominent because at fixed R a smaller A implies a larger value of E, the perturbation amplitude.…”