Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2002-07-10
Physica D; 1 Feb. 2003; vol.175, no.3-4, p.167-76
Nonlinear Sciences
Chaotic Dynamics
24 pages, 1 figure. Version 2 (Final). To be published in Physica D
Scientific paper
10.1016/S0167-2789(02)00695-4
We study the isotropic, helical component in homogeneous turbulence using statistical objects which have the correct symmetry and parity properties. Using these objects we derive an analogue of the K\'arm\'an-Howarth equation, that arises due to parity violation in isotropic flows. The main equation we obtain is consistent with the results of O. Chkhetiani [JETP, 63, 768, (1996)] and V.S. L'vov et al. [chao-dyn/9705016, (1997)] but is derived using only velocity correlations, with no direct consideration of the vorticity or helicity. This alternative formulation offers an advantage to both experimental and numerical measurements. We also postulate, under the assumption of self-similarity, the existence of a hierarchy of scaling exponents for helical velocity correlation functions of arbitrary order, analogous to the Kolmogorov 1941 prediction for the scaling exponents of velocity structure function.
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