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.

Most fluid flows of practical importance are fully three-dimensional, so the non-linear instability properties of three-dimensional flows are of particular interest. In some cases the three-dimensionality may have been caused by a finite amplitude disturbance whilst, more usually, the unperturbed state is three-dimensional. Practical applications where transition is thought to be associated with non-linearity in a three- dimensional flow arise, for example, in aerodynamics (swept wings, engine nacelles, etc.), turbines and aortic blood flow. Here inviscid `cross-flow' disturbances as well as Tollmien-Schlichting and Görtler vortices can all occur simultaneously and their mutual non-linear behaviour must be understood if transition is to be predicted. The non-linear interactions are so complex that usually fully numerical or combined asymptotic/numerical methods must be used. Moreover, in view of the complexity of the instability processes, there is also a growing need for detailed and accurate experimental information. Carefully conducted tests allow us to identify those elements of a particular problem which are dominant. This assists in both the formulation of a relevant theoretical problem and the subsequent physical validation of predictions. It should be noted that the demands made upon the skills of the experimentalist are high and that the tests can be extremely sophisticated - often making use of the latest developments in flow diagnostic techniques, automated high speed data gathering, data analysis, fast processing and presentation.

Instabilities are present in all natural fluids from rivers to atmospheres. This book considers the physical processes that generate instability. Part I describes the normal mode instabilities most important in geophysical applications, including convection, shear instability and baroclinic instability. Classical analytical approaches are covered, while also emphasising numerical methods, mechanisms such as internal wave resonance, and simple `rules of thumb' that permit assessment of instability quickly and intuitively. Part II introduces the cutting edge: nonmodal instabilities, the relationship between instability and turbulence, self-organised criticality, and advanced numerical techniques. Featuring numerous exercises and projects, the book is ideal for advanced students and researchers wishing to understand flow instability and apply it to their own research. It can be used to teach courses in oceanography, atmospheric science, coastal engineering, applied mathematics and environmental science. Exercise solutions and MATLAB® examples are provided online. Also available as Open Access on Cambridge Core.

The Origin of Species Charles Darwin The origin of turbulence in fluids is a long-standing problem and has been the focus of research for decades due to its great importance in a variety of engineering applications. Furthermore, the study of the origin of turbulence is part of the fundamental physical problem of turbulence description and the philosophical problem of determinism and chaos. At the end of the nineteenth century, Reynolds and Rayleigh conjectured that the reason of the transition of laminar flow to the 'sinuous' state is in stability which results in amplification of wavy disturbances and breakdown of the laminar regime. Heisenberg (1924) was the founder of linear hydrody namic stability theory. The first calculations of boundary layer stability were fulfilled in pioneer works of Tollmien (1929) and Schlichting (1932, 1933). Later Taylor (1936) hypothesized that the transition to turbulence is initi ated by free-stream oscillations inducing local separations near wall. Up to the 1940s, skepticism of the stability theory predominated, in particular due to the experimental results of Dryden (1934, 1936). Only the experiments of Schubauer and Skramstad (1948) revealed the determining role of insta bility waves in the transition. Now it is well established that the transition to turbulence in shear flows at small and moderate levels of environmental disturbances occurs through development of instability waves in the initial laminar flow. In Chapter 1 we start with the fundamentals of stability theory, employing results of the early studies and recent advances.