Estimates of intermittency, spectra, and blowup in developed turbulence
Abstract
It is pointed out that no analysis of the properties of the inertial range based on the equations of fluid flow has been successfully performed to date. The considered investigation has the objective to fill this gap at least in part by computing properties of the inertial range numerically with a vortex method. A value of 0.84 with a standard deviation of 0.03 is obtained for the inertial range exponent. It is found that the vorticity stretches unevenly, and that the highly stretched vorticity collects itself into a body with a shrinking volume. The numerical results are compatible with the conjecture of Mandelbrot (1976, 1977) that this body approximates a set with Hausdorff dimension approximately 2.5. The conducted calculations also suggest that if the flow can be described by Euler's equations, the vorticity becomes infinite in a finite time for all but special initial data
 Publication:

Communications in Pure Applied Mathematics
 Pub Date:
 November 1981
 Bibcode:
 1981CPAM...34..853C
 Keywords:

 Computational Fluid Dynamics;
 Flow Equations;
 Intermittency;
 Turbulent Flow;
 Vorticity;
 Energy Spectra;
 Euler Equations Of Motion;
 Inertia;
 Fluid Mechanics and Heat Transfer