Statistics of incompressible hydrodynamic turbulence: An alternative approach
Résumé
Using a recent alternative form of the Kolmogorov-Monin exact relationfor fully developed hydrodynamics (HD) turbulence, the incompressibleenergy cascade rate ? is computed. Under this current theoreticalframework, for three-dimensional (3D) freely decaying homogeneousturbulence, the statistical properties of the fluid velocity (u ),vorticity (? =? ×u ), and Lamb vector (L =? ×u ) are numericallystudied. For different spatial resolutions, the numerical results showthat ? can be obtained directly as the simple products of two-pointincrements of u and L , without the assumption of isotropy. Finally, theresults for the largest spatial resolutions show a clear agreement withthe cascade rates computed from the classical four-thirds law forisotropic homogeneous HD turbulence.