Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2004-09-15
J. Fluid Mech. vol 515, pp 87-97 (2004)
Nonlinear Sciences
Chaotic Dynamics
11 pages, 9 figures, appeared in J. Fluid Mech. vol 515, pp 87-97 (2004)
Scientific paper
10.1017/S0022112004000424
The so-called 2/15-law for two-point, third-order 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 4/5-law for energy conservation in high-Reynolds number turbulence. The appropriately normalized parity-breaking 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 a long times. We employ a recently developed technique to average over many directions and so recover the statistically isotropic component of the flow. The angle-averaged statistics achieve the 2/15 factor to within about 7% instantaneously and about 5% on average over time. The inertial- and viscous-range behavior of the helicity-dependent statistics and consequently the helicity flux, which appear in the 2/15-law, are shown to be more anisotropic and intermittent than the cor- responding energy-dependent reflection-symmetric structure functions, and the energy flux, which appear in the 4/5-law. This suggests that the Kolmogorov assumption of local isotropy at high Reynolds numbers needs to be modified for the helicity-dependent statistics investigated here.
Kurien Susan
Matsumoto Takeshi
Taylor Mark A.
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