Isotropic thirdorder statistics in turbulence with helicity: the 2/15law
Abstract
The socalled 2/15law for twopoint thirdorder velocity statistics in isotropic turbulence with helicity is computed for the first time from a direct numerical simulation of the Navier Stokes equations in a 512(3) periodic domain. This law is a statement of helicity conservation in the inertial range, analogous to the benchmark Kolmogorov 4/5law for energy conservation in highReynoldsnumber turbulence. The appropriately normalized paritybreaking statistics, when measured in an arbitrary direction in the flow, disagree with the theoretical value of 2/15 predicted for isotropic turbulence. They are highly anisotropic and variable and remain so over long times. We employ a recently developed technique to average over many directions and so recover the statistically isotropic component of the flow. The angleaveraged statistics achieve the 2/15 factor to within about 7% instantaneously and about 5% on average over time. The inertial and viscousrange behaviour of the helicitydependent statistics and consequently the helicity flux, which appear in the 2/15law, are shown to be more anisotropic and intermittent than the corresponding energydependent reflectionsymmetric structure functions, and the energy flux, which appear in the 4/5law. This suggests that the Kolmogorov assumption of local isotropy at high Reynolds numbers needs to be modified for the helicitydependent statistics investigated here.
 Publication:

Journal of Fluid Mechanics
 Pub Date:
 September 2004
 DOI:
 10.1017/S0022112004000424
 arXiv:
 arXiv:nlin/0409030
 Bibcode:
 2004JFM...515...87K
 Keywords:

 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 11 pages, 9 figures, appeared in J. Fluid Mech. vol 515, pp 8797 (2004)