Nonlinear effects in absolute and convective instabilities of a near-wake

Linear and nonlinear initial-value problems are discussed for planar invisc id disturbances in streamlined near-wakes. This is mostly for those areas o f near-wake Row where the basic motion comprises nearly uniform shear with or without normal influx into the accompanying viscous interfacial layer, a lthough agreement is found with linear properties for full velocity profile s of double-Blasius, double-Jobe-Burggraf, Hakkinen-Rott and Goldstein form . With nonlinear disturbances, wavelike initial conditions yield a known cr itical-layer development, whereas more general, non-wave, initial condition s lead to a new integro-partial-differential amplitude equation which is st udied analytically and numerically. The solutions show decay, finite-time b lowup or nonlinear upstream-travelling disturbances. The normal influx prov es crucial. Absolute and upstream- or downstream-convective instability is encountered (depending on the profiles, and Row reversal, for example); and in generic cases (for any thin airfoil) nonlinearity is shown analytically to provoke upstream convection. Increased nonlinearity drives the typical transition point extremely close to the trailing edge. Comparisons are made with three-dimensional behaviour in the linear case and with a direct simu lation in the nonlinear regime. (C) 2000 Editions scientifiques et medicale s Elsevier SAS.