Recent insights into instability and transition to turbulence in open-flow systems

Roads to turbulence in open-flow shear layers are interpreted as sequences of often competing instabilities. These correspond to primary and higher order restructurings of vorticity distributions which culminate in convected spatial disorder (with some spatial coherence on the scale of the shear layer) traditionally called turbulence. Attempts are made to interpret these phenomena in terms of concepts of convective and global instabilities on one hand, and of chaos and strange attractors on the other. The first is fruitful, and together with a review of mechanisms of receptivity provides a unifying approach to understanding and estimating transition to turbulence. In contrast, current evidence indicates that concepts of chaos are unlikely to help in predicting transition in open-flow systems. Furthermore, a distinction should apparently be made between temporal chaos and the convected spatial disorder of turbulence past Reynolds numbers where boundary layers and separated shear layers are formed.

[1]  Chester E. Grosch,et al.  The continuous spectrum of the Orr-Sommerfeld equation. Part 2. Eigenfunction expansions , 1981, Journal of Fluid Mechanics.

[2]  K. Sreenivasan,et al.  HOPF BIFURCATION, LANDAU EQUATION, AND VORTEX SHEDDING BEHIND CIRCULAR CYLINDERS. , 1987 .

[3]  Kunihiko Kaneko,et al.  Velocity-dependent Lyapunov exponents as a measure of chaos for open-flow systems , 1987 .

[4]  Harry L. Swinney,et al.  Characterization of hydrodynamic strange attractors , 1986 .

[5]  S. A. Thorpe,et al.  Experiments on the instability of stratified shear flows: immiscible fluids , 1969, Journal of Fluid Mechanics.

[6]  E. Naudascher,et al.  Self-Sustained Oscillations of Impinging Free Shear Layers , 1979 .

[7]  P. Monkewitz,et al.  Absolute instability in hot jets and their control , 1986 .

[8]  Gerald C. Lauchle,et al.  Laminar boundary-layer transition on a heated underwater body , 1984, Journal of Fluid Mechanics.

[9]  Eli Reshotko,et al.  BOUNDARY LAYER STABILITY AND TRANSITION , 1976 .

[10]  Michio Nishioka,et al.  Measurements of velocity distributions in the wake of a circular cylinder at low Reynolds numbers , 1974, Journal of Fluid Mechanics.

[11]  Stephen P. Wilkinson,et al.  Stability experiments in the flow over a rotating disk , 1985 .

[12]  M. V. Morkovin,et al.  Experiments on transition enhancement by distributed roughness , 1986 .

[13]  L. Kovasznay.  Turbulence in Supersonic Flow , 1953 .

[14]  Ron F. Blackwelder,et al.  The growth and breakdown of streamwise vortices in the presence of a wall , 1987, Journal of Fluid Mechanics.

[15]  Noise-sustained structure, intermittency, and the Ginzburg-Landau equation , 1985 .

[16]  Katepalli R. Sreenivasan,et al.  Transition and Turbulence in Fluid Flows and Low-Dimensional Chaos , 1985 .

[17]  Libchaber,et al.  Transitions to turbulence in helium gas. , 1987, Physical review. A, General physics.

[18]  P. Monkewitz,et al.  On turbulent jet flows - A new perspective , 1980 .

[19]  E. Reshotko,et al.  Environment and Receptivity , 1984 .

[20]  D. M. Bushnell,et al.  Transition prediction in external flows via linear stability theory , 1989 .

[21]  D. Arnal,et al.  Description and prediction of transition in two-dimensional, incompressible flow , 1984 .

[22]  Sheila E. Widnall,et al.  The two- and three-dimensional instabilities of a spatially periodic shear layer , 1982, Journal of Fluid Mechanics.

[23]  J. Lumley,et al.  A First Course in Turbulence , 1972 .

[24]  L. Mack.  The wave pattern produced by a point source on a rotating disk , 1985 .

[25]  Michio Nishioka,et al.  Mechanism of determination of the shedding frequency of vortices behind a cylinder at low Reynolds numbers , 1978, Journal of Fluid Mechanics.

[26]  P. S. Klebanoff,et al.  The three-dimensional nature of boundary-layer instability , 1962, Journal of Fluid Mechanics.

[27]  Peter A. Monkewitz,et al.  The absolute and convective nature of instability in two-dimensional wakes at low Reynolds numbers , 1988 .

[28]  Y. Pomeau,et al.  Order within chaos , 1986 .

[29]  J. Sternberg.  THE TRANSITION FROM A TURBULENT TO A LAMINAR BOUNDARY LAYER , 1954 .

[30]  M V Morkovin,et al.  Instability, Transition to Turbulence and Predictability, , 1978 .

[31]  W. Koch,et al.  Local instability characteristics and frequency determination of self-excited wake flows , 1985 .

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

[33]  J. V. Ingen.  A suggested semi-empirical method for the calculation of the boundary layer transition region , 1956 .

[34]  Peter A. Monkewitz,et al.  Influence of the velocity ratio on the spatial instability of mixing layers , 1982 .

[35]  K. Hannemann,et al.  Numerical simulation of the absolutely and convectively unstable wake , 1989 .

[36]  M. Morkovin.  Understanding Transition to Turbulence in Shear Layers. , 1983 .

[37]  L. Mack.  Boundary-Layer Linear Stability Theory , 1984 .

[38]  P. Huerre.  Spatio-Temporal Instabilities in Closed and Open Flows , 1987 .

[39]  Experiments on the forced wake of an airfoil , 1988 .

[40]  Hassan M. Nagib,et al.  Control of Free-Stream Turbulence by Means of Honeycombs: A Balance Between Suppression and Generation , 1976 .

[41]  P. Monkewitz,et al.  Absolute and convective instabilities in free shear layers , 1985, Journal of Fluid Mechanics.

[42]  B. Stahl,et al.  Excitation of instability waves in free shear layers Part 2. Experiments , 1988, Journal of Fluid Mechanics.

[43]  Harry L. Swinney,et al.  Flow regimes in a circular Couette system with independently rotating cylinders , 1986, Journal of Fluid Mechanics.