Wave interaction and stability problems
Abstract
Two classes of stability problems are discussed. The first pertains to the possibility of linear resonance between the vertical velocity and vertical vorticity modes in parallel flows. Resonances of laminar flows are associated with threedimensional disturbances and correspond to slightly damped modes. As the Reynolds number of each resonance increases these waves become longitudinal streaks with a welldefined wavelength. Nonlinear consequences of such disturbances are described. The second class of problems pertains to a theoretical approach to the threedimensional instability of parallel flows that involves interactions between first harmonics and the mean flow. Since they are nonlinear at high Reynolds numbers such interactions occur on a relatively fast time scale. Different waves interact with each other through the mean flow which is modified to zeroth order. A comparison between the stability characteristics of a given flow with those of the same flow together with a small amplitude wave is presented. Possible extensions of these ideas are considered.
 Publication:

NearWall Turbulence
 Pub Date:
 1990
 Bibcode:
 1990nrw..book..692B
 Keywords:

 Flow Stability;
 Flow Velocity;
 Parallel Flow;
 Turbulent Boundary Layer;
 Velocity Distribution;
 Vorticity;
 High Reynolds Number;
 Laminar Flow;
 Vertical Distribution;
 Wave Interaction;
 Fluid Mechanics and Heat Transfer