Direct interaction approximation and plasma turbulence theory

1978 ◽  
Vol 20 (12) ◽  
pp. 1209-1239 ◽  
Author(s):  
D F DuBois ◽  
M Espedal
Keyword(s):  
Direct Interaction ◽  
Plasma Turbulence ◽  
Turbulence Theory ◽  
Direct Interaction Approximation ◽  
Interaction Approximation

scholarly journals Theory of Strongly Turbulent Two-Dimensional Cross Field Convection of Current Carrying Space Plasmas

1985 ◽  
Vol 107 ◽  
pp. 475-475
Author(s):  
M. J. Keskinen
Keyword(s):  
Numerical Simulations ◽  
Power Law ◽  
Direct Interaction ◽  
Turbulence Theory ◽  
Space Plasmas ◽  
Nonlinear Frequency ◽  
Two Dimensional ◽  
Strong Turbulence ◽  
Direct Interaction Approximation ◽  
Interaction Approximation

The “direct interaction approximation” of Kraichnan as modified by Kadomtsev is employed to develop a two-dimensional strong turbulence theory which predicts both nonlinear frequency broadening and a power law for the spectrum of a convecting plasma containing a gravitationally induced cross field current. These results are favorably compared with experimental observations, numerical simulations, and previous studies1 of turbulent cross field convection of current-carrying plasma.

Eulerian and Lagrangian renormalization in turbulence theory

1977 ◽  
Vol 83 (2) ◽  
pp. 349-374 ◽  
Author(s):  
Robert H. Kraichnan
Keyword(s):  
Direct Interaction ◽  
Exact Result ◽  
Passive Scalar ◽  
Turbulence Theory ◽  
Perturbation Expansions ◽  
Gaussian Form ◽  
Lagrangian Velocity ◽  
Direct Interaction Approximation ◽  
Gaussian Statistics ◽  
Interaction Approximation

Systematic renormalized perturbation expansions for turbulence and turbulent convection are constructed which are invariant at each order under random Galilean transformations. Two types of expansion are developed whose lowest truncations give, respectively, the Lagrangian-history direct-interaction approximation and the abridged Lagrangian-history direct-interaction approximation. These approximations previously were derived as heuristic modifications of the Eulerian direct-interaction approximation (Kraichnan 1965). The techniques used involve reversion of primitive perturbation expansions for the generalized velocity field u(x, t/s), defined as the velocity measured at time s in the fluid element which passes through x at time t. The new expansions are illustrated by application to a random linear oscillator, to passive-scalar convection by a random velocity and to the Lagrangian velocity covariance. The lowest term of the expansion for the passive scalar gives Taylor's (1921) exact result for dispersion of fluid elements, and higher terms describe the deviations of the particle-displacement distribution from Gaussian form. In all the applications the assumed underlying statistics are more general than Gaussian statistics, which appear as a special case.

A strain-based Lagrangian-history turbulence theory

1978 ◽  
Vol 88 (2) ◽  
pp. 355-367 ◽  
Author(s):  
Robert H. Kraichnan ◽  
Jackson R. Herring
Keyword(s):  
Energy Transfer ◽  
Velocity Field ◽  
Direct Interaction ◽  
Initial Position ◽  
Turbulence Theory ◽  
Navier Stokes ◽  
Lagrangian Velocity ◽  
Direct Interaction Approximation ◽  
Derivatives Of ◽  
Interaction Approximation

The Lagrangian-history method in turbulence theory (Kraichnan 1977) is modified such that triple moments are expanded in functional powers of the Lagrangian covariance of the symmetric rate-of-strain field instead of the Lagrangian covariance of the velocity field. The simplest approximation which results corresponds to the abridged Lagrangian-history direct-interaction approximation. It is illustrated by application to the Lagrangian properties of a random velocity field whose Eulerian values are frozen in time. Then it is formulated for isotropic Navier-Stokes turbulence. The new approximation is expected to give reduced energy transfer in the dissipation range because the rate of strain along a fluid-element trajectory is statistically stationary in stationary homogeneous turbulence while the derivatives of the Lagrangian velocity with respect to initial position tend to grow and thereby have a longer correlation time. The correlation times of these two entities play corresponding roles in the new and old approximations for energy transfer, respectively.

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.

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