Nonlinear Dynamics Temporal and Spatial Structures in Fluid Mechanics

  • H. OertelJr.
Part of the Lecture Notes in Engineering book series (LNENG, volume 13)


Fluid mechanical instabilities are the primary cause of well-organized structures of different characteristic wavelengths in a flow field. The key to a physical understanding of the laminar-turbulent transition process lies in understanding the temporal and spatial development and decay of these flow structures. In this volume, we will be concerned with selected examples of the formation of structures. In the fluid mechanical part, we will deal only with transcritical flows, i.e., flows across and beyond a critical state and therefore beyond one or more fluid mechanical instabilities. Figs. 1 and 2 portray transcritical flows. The first photograph of Fig. 2 shows a carbon dioxide jet in air, which is coming out of a round nozzle. The jet flow is laminar at first; however, after a characteristic length, it becomes unstable, forming vortex rings, and the transition to turbulence occurs, at which point a characteristic microscale structure becomes visible. A mixing layer allows us to observe a plane transcritical flow. Again it starts with a laminar shear flow, which becomes unstable and causes vortices with a spatially increasing flow amplitude. With increasing relative velocity of the upper and lower portions of the flow forming the shear layer, the transition to a turbulent flow takes place.


Lyapunov Exponent Rayleigh Number Chaotic Attractor Critical Reynolds Number Wake Flow 
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© Springer-Verlag Berlin, Heidelberg 1985

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