LINEAR AND NONLINEAR DEVELOPMENT OF LOCALIZED DISTURBANCES IN ZERO AND ADVERSE PRESSURE-GRADIENT BOUNDARY-LAYERS

Localized disturbances in laminar boundary-layers at Reynolds number R e delta 950' were studied using direct numerical simulation. Instabil ity mechanisms in both an adverse and zero pressure gradient were inve stigated by introducing three different three-dimensional disturbances . The first disturbance was centered around a pair of oblique waves in Fourier space, the second around a plane wave, while the third was ax isymmetric. For small amplitudes, the first disturbance developed into a wave-packet of oblique waves in adverse pressure gradient and into a streaky structure with a trailing wave-packet in a zero pressure gra dient. The second disturbance developed into a wave-packet centered ar ound plane waves in both pressure gradients. The third disturbance dev eloped into a wave-packet of plane waves in adverse pressure gradient and, due to the transient growth mechanism, into a streaky structure i n a zero pressure gradient. For finite-amplitude plane wave-packets in a zero pressure gradient, a subharmonic secondary instability was obs erved which subsequently developed into an elongated Lambda structure. The secondary instability was less significant in adverse pressure gr adient due to the large growth rate of the primary instability. Breakd own was observed as high-frequency oscillations an the spike over the head of the Lambda vortices. Providing the initial amplitude was suffi ciently large, the vortex pair yielded the fastest route to turbulence . The main growth mechanism in this scenario, in addition to the expon ential growth in the adverse pressure gradient case, was the nonlinear excitation of transient growth of streaks by interacting oblique mode s. Disturbances dominated by streaks needed substantially larger ampli tudes before secondary instability or breakdown occurred. In that case , breakdown was shifted from the spike to an instability of the rear p art of the streaks. (C) 1998 American Institute of Physics.