Numerical solutions of the direct interaction approximation equations for anisotropic turbulence

1987 ◽  
Vol 2 (3) ◽  
pp. 227-248 ◽  
Author(s):  
J. Andrzej Domaradzki ◽  
Steven A. Orszag
Keyword(s):  
Numerical Solutions ◽  
Direct Interaction ◽  
Anisotropic Turbulence ◽  
Direct Interaction Approximation ◽  
Interaction Approximation

Self-consistent effective-medium parameters for oceanic internal waves

1984 ◽  
Vol 146 ◽  
pp. 253-270 ◽  
Author(s):  
R. J. Dewitt ◽  
Jon Wright
Keyword(s):  
Internal Waves ◽  
Direct Interaction ◽  
Decay Rates ◽  
The Self ◽  
Time Behaviour ◽  
Equilibrium Time ◽  
Self Consistent ◽  
Direct Interaction Approximation ◽  
Interaction Approximation ◽  
Extra Parameter

In this paper we apply a formalism introduced in a previous paper to write down a self-consistent set of equations for the functions that describe the near-equilibrium time behaviour of random oceanic internal waves. These equations are based on the direct-interaction approximation. The self-consistent equations are solved numerically (using the Garrett-Munk spectrum as input) and the results are compared to parameters obtained in the weak-interaction approximation (WIA). The formalism points out that an extra parameter that is implicitly vanishingly small in the WIA has a significant effect on decay rates when computed self-consistently. We end by mentioning possible future self-consistent calculations that would improve upon our own.

KOLMOGOROV CONSTANT IN LARGE SPACE DIMENSIONS

2002 ◽  
Vol 16 (32) ◽  
pp. 4839-4845 ◽  
Author(s):  
MALAY K. NANDY
Keyword(s):  
Eddy Viscosity ◽  
Energy Equation ◽  
Space Dimension ◽  
Direct Interaction ◽  
Large Space ◽  
Distant Interaction ◽  
Direct Interaction Approximation ◽  
Dimension Expansion ◽  
Kolmogorov Constant ◽  
Interaction Approximation

A large d (space dimension) expansion together with the ∊-expansion is implemented to calculate the Kolmogorov constant from the energy equation of Kraichnan's direct-interaction approximation using the Heisenberg's eddy-viscosity approximation and Kraichnan's distant-interaction algorithm. The Kolmogorov constant C is found to be C = C0 d1/3 in the leading order of a 1/d expansion. This is consistent with Fournier, Frisch, and Rose. The constant C0 evaluated in the above scheme, is found to be C0 = (16/27)1/3.

Lagrangian velocity covariance in helical turbulence

1977 ◽  
Vol 81 (2) ◽  
pp. 385-398 ◽  
Author(s):  
Robert H. Kraichnan
Keyword(s):  
Correlation Time ◽  
Perturbation Expansion ◽  
Direct Interaction ◽  
Helical Turbulence ◽  
Quantitative Accuracy ◽  
Lagrangian Velocity ◽  
Thin Spherical Shell ◽  
Direct Interaction Approximation ◽  
Interaction Approximation ◽  
Substantial Factor

The effect of helicity on the Lagrangian velocity covarianceUL(t) in isotropic, normally distributed turbulence is examined by computer simulation and by a renormalized perturbation expansion forUL(t). The first term of the latter represents Corrsin's (1959) conjecture (extrapolated to allt), which relatesUL(t) to the Eulerian covariance and the distributionG(x, t) of fluid-element displacement. Truncation of the expansion at the first term yields the direct-interaction approximation forG(x, t). The expansion suggests that with or without helicity Corrsin's conjecture is valid ast→ ∞ and that in either caseUL(t) behaves asymptotically like$t^{-(r+\frac{3}{2})}$if the spectrum of the Eulerian field varies likekr+2at small wavenumbers. Corrsin's conjecture breaks down at small and moderatetif there is strong helicity while remaining accurate at alltin the mirror-symmetric case. Computer simulations for a frozen Eulerian field with spectrum confined to a thin spherical shell inkspace indicate that strong helicity induces an increase in the Lagrangian correlation time by a factor of approximately three. Direct-interaction equations are constructed for the Lagrangian space-time covariance and the resulting prediction forUL(t) is compared with the simulations. The effect of helicity is well represented quantitatively by the direct-interaction equations for small and moderatetbut not for larget. These frozen-field results imply good quantitative accuracy at alltin time-varying turbulence whose Eulerian correlation time is of the order of the eddy-circulation time. In turbulence with weak helicity, the directinteraction equations imply that the Lagrangian correlation of vorticity with initial velocity is more persistent thanUL(t), by a substantial factor.

scholarly journals An Approach to Glassy Systems with Direct-Interaction Approximation

2012 ◽  
Vol 195 ◽  
pp. 157-166 ◽  
Author(s):  
Takeshi Ooshida ◽  
Susumu Goto ◽  
Takeshi Matsumoto ◽  
Akio Nakahara ◽  
Michio Otsuki
Keyword(s):  
Direct Interaction ◽  
Glassy Systems ◽  
Direct Interaction Approximation ◽  
Interaction Approximation
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