Finite dimensional aspects of turbulent flows
Abstract
The timeasymptotic behavior of the solutions of the threedimensional NavierStokes equations of turbulent flow is investigated analytically, summarizing the results obtained by Constantin et al. (1984). The intrinsically finite number of degrees of freedom (DOFs) is studied both in terms of determining modes and in terms of the fractal dimension of the attractors, and the relationship between the number of DOFs and the Reynolds number (R) of the flow is explored. It is found that the conventional estimate (varying as R to the 9/4ths) requires a priori knowledge of the spectrum of homogeneous isotropic turbulence and is applicable only at high R, and a more conservative estimate which varies as R cubed and is independent of spectrum knowledge is proposed.
 Publication:

Chaos in Nonlinear Dynamical Systems
 Pub Date:
 1984
 Bibcode:
 1984cnds.proc..165M
 Keywords:

 Asymptotic Properties;
 Computational Fluid Dynamics;
 Degrees Of Freedom;
 Fractals;
 NavierStokes Equation;
 Reynolds Number;
 Turbulent Flow;
 Dimensional Analysis;
 Estimates;
 Incompressible Flow;
 Strange Attractors;
 Three Dimensional Flow;
 Viscous Flow;
 Fluid Mechanics and Heat Transfer