Hydrodynamic Instabilities and the Transition to Turbulence - Hardcover

Inhaltsangabe

Although much of the universe is filled with fluids in turbulent motion, the processes by which turbulence develops are poorly understood. When a fluid is driven away from thermal and mechanical equilibrium, it will often undergo a sequence of instabilities, each of which leads to a change in the spatial or temporal structure ofthe flow. The nature oftheseinstabilities, which sometimes lead to turbulence, is the subject of this volume. Hydrodynamicinstabilities and turbulence have been extensivelystudied for more than a century, but the research has been primarily concerned with either the first instability that occurs with increasing Reynolds number or with turbulence at very large Reynolds number. The transition from laminar to turbulent flow has until recently been largely beyond the reach of both theory and experiment. This situation has been changed dramatically by the use of computers in laboratory experiments and in numerical analyses of nonlinear systems. While past experiments were primarily photographic or measured time-averaged quantities, recent experiments using computers and modern optical and cryogenic techniques have distinguished between many different dynamical regimes of flows undergoing transition. Numerical studies of nonlinear models have also revealed entirely unexpected results, such aschaotic behavior in a system with only three variables. Another development of great potential importance is the application of new mathematical concepts from the qualitative theory of differential equations, sometimes known as dynamical systems theory, to the transition to turbulence problem. More traditional methods such as bifurcation theory and stability analysis also continue to contribute major new insights.

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