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Author(s):
S. Kida and S. Goto
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Title:
Lagrangian Direct-interaction Approximation for Homogeneous Isotropic Turbulence
Date of publication:
July 1996
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Key words:
Lagrangian direct-interaction approximation, Isotropic turbulence, Kolmogorov spectrum
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Abstract:
A perturbation method developed by Kraichnan [ J. Fluid Mech. 5 (1959) 497 ], which is based upon an extraction of direct interactions among Fourier modes of a velocity field, is applied to the Lagrangian velocity correlation and response functions. The resultant set of integro-differential equations for these functions obtained for homogeneous isotropic turbulence, which has no adjustable free parameters, happens to be identical to the one derived before by using a different perturbation method [ Kaneda, J. Fluid Mech. 107 (1981) 131]. The shape of the energy spectrum function is determined numerically in the universal range for stationary turbulence, and in the whole wavenumber range in a similarly evolving form for freely decaying case. The energy spectrum in the universal range takes same shape in the both cases, which also agrees excellently with many measurements of various kinds of real turbulence as well as numerical results obtained by Gotoh et al. [ J. Phys. Soc. Japan, 57 (1988) 866] as an initial value problem. Skewness factor of the longitudinal velocity derivative is calculated to be -0.66 for stationary turbulence. Wavenumber dependence of the eddy-viscosity is also determined.
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