By H. L. Swinney, J. P. Gollub (auth.), Professor Harry L. Swinney PhD, Professor Jerry P. Gollub PhD (eds.)

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Math. Surv. 32, No. Katok: The estimation from above for the topological entropy of a diffeomorphism; in Global Theory of Dynamical Systems, ed. by Z. Netecki, C. Robinson, Lecture Notes in Mathematics, Vol. 819 (Springer, Berlin, Heidelberg, New York 1980) pp. Ruelle: Ergodic theory of differentiable dynamical systems. Publ. Math. IHES 50, 27-58 (1979) 3. Hydrodynamic Stability and Bifurcation D. D. Joseph With 14 Figures The goal of hydrodynamics is to describe and predict the motions of fluids under applied forces.

The dimensionless and dimensional equations are identical except that the kinematic viscosity v is replaced with the reciprocal of the Reynolds number R = Ul/v. Then all conclusions about the Navier-Stokes equations hold for all flows with different velocities U, in different domains ~e" (proportional to/a) and for fluids with different v provided only that they share a common R. 1) as the Reynolds number. I call the boundary velocities U = U s and the body forces G which drive the motion, the data.

2). The second example is Couette flow between rotating cylinders when the inner cylinder is at rest and the outer one rotates with a steady angular velocity 132 F. H. 7 Concluding Remarks There are two major aspects of thermal convection that are of importance for the understanding of the general phenomenon of fluid turbulence. One of these aspects is the existence of discrete structure in turbulent convection as indicated by the kinks in the heat transport dependence and by the evidence for discrete wave numbers in the horizontal spectrum of convection.