Statistics of incompressible hydrodynamic turbulence: An alternative approach

Abstract

Using a recent alternative form of the Kolmogorov-Monin exact relation for fully developed hydrodynamics (HD) turbulence, the incompressible energy cascade rate is computed. Under this current theoretical framework, for three-dimensional (3D) freely decaying homogeneous turbulence, the statistical properties of the fluid velocity (u), vorticity (ω= ×u), and Lamb vector (L=ω×u) are numerically studied. For different spatial resolutions, the numerical results show that can be obtained directly as the simple products of two-point increments of u and L, without the assumption of isotropy. Finally, the results for the largest spatial resolutions show a clear agreement with the cascade rates computed from the classical four-thirds law for isotropic homogeneous HD turbulence.