Resonant growth of three-dimensional modes in trnsitioning Blasius boundary layers

Abstract

By carefully controlled phase-coupled input of simultaneous two- and three-dimensional disturbances, the nonlinear evolution and breakdown of the laminar flow in a boundary layer was examined. This involved the generation of plane Tollmien–Schlichting waves and pairs of oblique waves so as to promote nearresonance conditions which have been theoretically shown to lead to the rapid development of three-dimensionality in unstble boundary layers. Special emphasis is placed on the two prominent mechanisms, namely resonant-triads of Orr–Sommerfeld modes and the secondary instability of the streamwise periodic flow to spanwise periodic three-dimensional disturbances. The sensitivity of these mechanisms on the amplitudes and wavenumbers of the input disturbances was of special focus.The simultaneous two- and three-dimensional wave generation was accomplished using a spanwise array of line heaters suspended just above the wall at the approximate height of the critical layer in the laminar boundary layer. These were operated to produce, through local heating, time-periodic spanwise-phase-varying velocity perturbations. Of primary emphasis in this paper are conditions obtained by the combined forcing of fundamental plane waves with wavenumbers (α, 0) and pairs of subharmonic oblique waves (½α, ± β). The reslults document resonant growth of energy in the subharmonic modes, the formation of staggered lambda vortex patterns with a cross-stream scale commensurate with the seeded ± β condition, and their subsequet transition to turbulence. Complete documentation of the flow field at these various stages is presented using smoke-wire flow visualization and through phase-conditioned hot-wire surveys measuring all three velocity components in three space dimensions.