The IUTAM Symposium on Nonlinear Instability of Nonparallel Flows was held at Clarkson University, Potsdam, NY 13699-5725, USA from 26 to 31 July 1993. It consisted of 9 general speeches, 35 lectures and 15 poster-seminar presentations. The papers were grouped in fairly focused sessions on boundary layers, shear flows, vortices, wakes, nonlinear waves and jets. The symposium was fol lowed by a workshop in which the subject matter discussed was sum marized and some further work for future investigation was recom mended. The highlights of the workshop will be reported elsewhere. In this book many of the papers that describe the ideas presented at the symposium are collected to provide a reference for researchers in charting the future course of their studies in the area of nonlinear instability of nonparallel flows. The papers in this book are grouped under the following headings: • Boundary layers and shear flows • Compressibility and thermal effects • Vortices and wakes • Nonlinear waves and jets In the lead paper ofthis book M. E. Goldstein describes an asymp totic theory of nonlinear interaction between two spatially growing oblique waves on nonparallel boundary and free-shear layers. The wave interaction originates from the nonlinear critical layer and is responsive to weakly nonparallel effects. The theory results in a sys tem of integral differential equations which appear to be relevant near the upper branch of the neutral curve.

Inhalt

1. Boundary layers and shear flows.- Nonlinear interactions between oblique instability waves on nearly parallel shear flows.- Nonlinear breakdown of laminar boundary layer.- The development of nonlinear oscillations in a boundary layer and the onset of random disturbances.- Experimental study of nonlinear stages of a boundary layer breakdown.- Asymptotic analysis of resonant interactions in a boundary layer.- Stability and transition to turbulence in 2-D boundary layer under the influence of adverse pressure gradients.- Computational aspects of nonparallel effects in boundary-layer receptivity.- Influence of Pressure Gradient on the Nonlocalized receptivity of boundary layers.- Strongly nonlinear oblique-wave solutions in wall-bounded shear flows.- Nonlinear spatial dynamics in a growing boundary layer.- Weakly-nonlinear evolution of a nearly-plane wave in the boundary layer of a flat plate.- The nonlinear evolution of modulated waves in a boundary layer.- A new technique of Tollmien-Schlichting wave cancellation in a sound-exposed boundary layer.- Numerical simulation of the high Reynolds number flow in the non-uniform duct.- The convergence for nonlinear Galerkin method in fluid dynamics system.- 2. Compressibility and thermal effects.- Thermal convection in fluid layers with nonuniform thickness or surface temperature.- Experiments on the nonlinear instability of supersonic boundary layers.- Excitation of instability waves in the supersonic boundary layer by sound.- Some problems in the shock wave turbulent boundary layer interactions.- Nonlinear stability of a Mach 1.6 flat plate boundary layer.- Numerical simulation of thermal boundary layer instabilities in porous media.- 3. Vortices and wakes.- Nonlinear instability of free shear layers: subharmonic resonance and three dimensional vortex dynamics.- The instability of Long's vortex.- On the secondary instability of the most dangerous Görtler vortex.- The nonlinear stability of vortex flows and vortex breakdown.- On the onset of nonsteadiness in the flows with vortex breakdown in a cylindrical container.- Stability of nonparallel periodic flow with bottom friction.- Nonlinear effects of 2-D and 3-D disturbances on laminar separation bubbles.- Coherent vortical structures in plane far wakes at moderate Reynolds numbers.- A mechanism for oblique wave resonance in the far wake.- 4. Nonlinear waves and jets.- Stability of nonlinear waves resonantly sustained.- The stability of some three-dimensional and time-dependent flows.- On the stability of standing solitons in Faraday resonance.- Quasi-stationary wave evolution on a falling film.- Instabilities in a three-dimensional heated draining film.- Long-disturbance stability of nonlinear wave regimes in a falling liquid film.- Bifurcation cascade in a diverging flow.- Nonlinear dynamics of forced transitional jets: Temporal attractors and transitions to chaos.