Secondary instability of wall-bounded shear flows

摘要: An analysis is given of a secondary instability that obtains in wide class wall-bounded parallel shear flows, including plane Poiseuille flow, Couette flat-plate boundary layers, and pipe flow. In these flows it shown two-dimensional finite-amplitude waves are (exponentially) unstable to infinitesimal three-dimensional disturbances. This seems be the prototype transitional has characteristic (convective) timescales observed typical transitions. case nonlinear equilibria quasi-equilibria exist, stability flow determined by linear eigenvalue calculation. without (e.g. flow), time-dependent performed direct spectral numerical calculation incompressible Navier–Stokes equations.The energetics vorticity dynamics discussed. It wave mediates transfer energy from mean perturbation but does not directly provide disturbance. The an inviscid character as persists high Reynolds numbers grows on convective timescales. Maximum (inflexion-point) arguments predict some features like phase-locking waves, they do explain its essential three-dimensionality. shows vortext-stretching tilting effects both required persistent exponential growth. centrifugal nature.The requires threshold amplitude achieved (about 1% centreline velocity flow): growth rates relatively insensitive for moderate amplitudes. With amplitudes, critical substantial about 1000 several thousand asymptotic (as R approaches infinity) rate approximately 0·15h/U0, where h half-channel width U0 velocity.It possible make progress identifying experimental spot structure with aspects two-dimensional/linear instability. principal excitation eigenfunction (growing) disturbance localized within periodicity length (in stream cross-stream directions) near maxima flow; planwise corresponds streaks early spots; vortical resembles streamwise vortex lifting off wall. As finite amplitude, become chaotic statistical similar experimentally moderate-Reynolds-number turbulent flows.