THE INITIAL EVOLUTION OF A WAVE-PACKET IN A LAMINAR BOUNDARY-LAYER

The initial evolution of a wave packet in a laminar boundary layer is examined. By comparing the experimental streamwise growth of individual modes with the prediction of a linear model, two kinds of nonlinearities are explored. The first of which is associated with oblique waves with a frequency range centered around half the frequency of the most amplified linear mode. This type of nonlinear growth of subharmonic waves has been observed in the past in cases in which artificial excitations of a single two-dimensional (2-D) fundamental wave, with or without simultaneous excitations of three-dimensional (3-D) subharmonic waves were used, and in the case in which the disturbance was generated by a continuous harmonic point source disturbance. However, unlike all the cases mentioned above, the nonlinear growth of subharmonic waves in the present case begins well upstream of the neutral point of the fundamental wave at branch II, long before the streamwise position, where the amplitudes of the fundamental Tollmien-Schlichting (TS) waves (in the previous cases), attained a saturation level. The second type of nonlinear growth is associated with waves having shorter wavelengths than the wavelengths of the most amplified waves. In this case the nonlinear growth of the waves is first observed at their neutral points (at branch II), characterized by an enhanced streamwise growth rate of their amplitudes. The linear model, which includes the solution of the vertical vorticity equation in addition to the Orr-Sommerfeld equation and accounts for the effect of the mean flow divergence, is found to be very successful in predicting the downstream growth of the most amplified modes and the normalized cross-stream distributions of the various modes of all three velocity components.