TRANSIENT GROWTH IN 2-DIMENSIONAL AND 3-DIMENSIONAL BOUNDARY-LAYERS

The evolution of localized three-dimensional disturbance in two- and t hree-dimensional laminar boundary layers is examined. The linearized N avier-Stokes equations for three-dimensional disturbances in a three-d imensional parallel shear flow are solved numerically using Fourier tr ansform Chebyshev collocation techniques. Modal analysis shows that su bstantial short-term energy growth can be obtained even when all insta bility waves are damped. This transient growth can increase the initia l disturbance energy by two or three orders of magnitude, at which sta ge nonlinear interactions might lead to a breakdown to turbulent flow, bypassing the traditional Tollmien-Schlichting instability mechanism. The dependence of the transient growth on wave number, Reynolds numbe r, sweep angle and Hartree parameter is determined and a method for pr edicting the maximum transient growth is proposed and found to be reas onably accurate over a wide parameter range. Localized disturbances ar e also examined and it is found that the bypass growth mechanism can e nhance the formation of cross-flow vortices in a three-dimensional flo w. Some implications are discussed, particularly with respect to the o bserved effects of roughness on transition location.