What is the status of developed turbulence?
Abstract
Developed turbulence which is concerned with the behavior of turbulent flows at high Reynolds numbers for which there is evidence of scaling, is discussed. The 1941 Kolmogorov theory and the invariance properties of the NavierStokes equation are considered. The role of real and complex singularities of solutions of the NavierStokes equation is examined in connection with smallscale intermittency. Computer simulations provide strong evidence for the existence of singularities in the complex spacetime domain. It is shown that the complex space singularities within less than one meanfreepath of the real domain could invalidate the hydrodynamical approximation. Three explanations for the unpredictable character of the turbulence include: (1) loss of uniqueness through singularities, (2) intrinsic stochasticity, and (3) extrinsic stochasticity. The problem of the minimum number of degrees of freedom needed for high Reynolds number flow is considered. The impact on turbulence of attempts to introduce methods based on the phase transition and quantum field theories is assessed.
 Publication:

Physica Scripta
 Pub Date:
 1985
 Bibcode:
 1985PhyS....9..137F
 Keywords:

 Flow Theory;
 Turbulent Flow;
 Chaos;
 Computational Fluid Dynamics;
 Hydrodynamics;
 Kolmogoroff Theory;
 Singularity (Mathematics);
 Stochastic Processes;
 Strange Attractors;
 Vortices;
 Fluid Mechanics and Heat Transfer