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Susan Kurien, Mark A. Taylor and Takeshi Matsumoto, "Cascade time-scales of energy and helicity in homogeneous, isotropic turbulence", Phys. Rev. E, vol. 69, pp. 066313, 2004


We extend the Kolmogorov phenomenology for the scaling of energy spectra in high-Reynolds-number turbulence, to explicitly include the effect of helicity. There exists a time scale tH for helicity transfer in homogeneous, isotropic turbulence with helicity. We arrive at this time scale using the phenomenological arguments used by Kraichnan to derive the time scale tE for energy transfer [R. H. Kraichnan, J. Fluid Mech. 47, 525 (1971)]. We show that in general tH may not be neglected compared to tE, even for rather low relative helicity. We then deduce an inertial range joint cascade of energy and helicity in which the dynamics are dominated by tE in the low wave numbers with both energy and helicity spectra scaling as k5/3; and by tH at larger wave numbers with spectra scaling as k4/3. We demonstrate how, within this phenomenology, the commonly observed bottleneck in the energy spectrum might be explained. We derive a wave number kh which is less than the Kolmogorov dissipation wave number, at which both energy and helicity cascades terminate due to dissipation effects. Data from direct numerical simulations are used to check our predictions.

BibTeX Entry

author = {Susan Kurien and Mark A. Taylor and Takeshi Matsumoto},
title = {Cascade time-scales of energy and helicity in homogeneous, isotropic turbulence},
year = {2004},
urlpdf = {http://math.lanl.gov/~skurien/papers/KurTayMat_pre04.pdf},
journal = {Phys. Rev. E},
volume = {69},
pages = {066313}