Transition and Turbulence in Fluid Flows and Low-Dimensional Chaos

Recent studies of the dynamics of low-dimensional nonlinear systems with chaotic solutions have produced very interesting and profound results with several implications in many disciplines dealing with nonlinear equations. However, the interest of fluid dynamicists in these studies stems primarily from the expectation that they will help us understand better the onset as well as dynamics of turbulence in fluid flows. At this time, much of this expectation remains untested, especially in ‘open’ or unconfined fluid flows. This work is aimed at filling some of this gap.

[1]  James P. Crutchfield,et al.  Low-dimensional chaos in a hydrodynamic system , 1983 .

[2]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[3]  H. Swinney,et al.  Dynamical instabilities and the transition to chaotic Taylor vortex flow , 1979, Journal of Fluid Mechanics.

[4]  R. M. Thomas Conditional sampling and other measurements in a plane turbulent wake , 1973, Journal of Fluid Mechanics.

[5]  H. Swinney,et al.  Experimental observations of complex dynamics in a chemical reaction , 1982 .

[6]  Carl A. Friehe,et al.  Vortex shedding from cylinders at low Reynolds numbers , 1980, Journal of Fluid Mechanics.

[7]  A. Roshko Experiments on the flow past a circular cylinder at very high Reynolds number , 1961, Journal of Fluid Mechanics.

[8]  H. Swinney,et al.  Onset of Turbulence in a Rotating Fluid , 1975 .

[9]  D. J. Tritton,et al.  A note on vortex streets behind circular cylinders at low Reynolds numbers , 1971, Journal of Fluid Mechanics.

[10]  F. Takens,et al.  On the nature of turbulence , 1971 .

[11]  M. Dubois,et al.  Dimension of strange attractors : an experimental determination for the chaotic regime of two convective systems , 1983 .

[12]  P. Grassberger,et al.  Characterization of Strange Attractors , 1983 .

[13]  D. Coles Transition in circular Couette flow , 1965, Journal of Fluid Mechanics.

[14]  G. Schewe On the force fluctuations acting on a circular cylinder in crossflow from subcritical up to transcritical Reynolds numbers , 1983, Journal of Fluid Mechanics.

[15]  D. Tritton Experiments on the flow past a circular cylinder at low Reynolds numbers , 1959, Journal of Fluid Mechanics.

[16]  F. Takens,et al.  Occurrence of strange AxiomA attractors near quasi periodic flows onTm,m≧3 , 1978 .

[17]  J. Barrow Chaotic behaviour in general relativity , 1982 .

[18]  P. Holmes,et al.  Nonlinear Problems: Present and Future , 1983 .

[19]  Celso Grebogi,et al.  Are three-frequency quasiperiodic orbits to be expected in typical nonlinear dynamical systems , 1983 .

[20]  J. Gollub,et al.  Many routes to turbulent convection , 1980, Journal of Fluid Mechanics.

[21]  J. W. Schaefer,et al.  An analysis of the vortex street generated in a viscous fluid , 1959, Journal of Fluid Mechanics.

[22]  Colin Sparrow,et al.  The Lorenz equations , 1982 .

[23]  Michael Gaster,et al.  Vortex shedding from slender cones at low Reynolds numbers , 1969, Journal of Fluid Mechanics.