Book ChapterDOI
Comparison of some approximations for isotropic turbulence
Jackson R. Herring,Robert H. Kraichnan +1 more
- Vol. 12, pp 148-194
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In this article, a study of several related turbulence approximations with regard to dynamical properties and agreement of numerical predictions with laboratory and computer experiments is presented. But the authors do not discuss the physical and mathematical differences between the model dynamics and actual Navier-Stokes dynamics.Abstract:
Study of several related turbulence approximations with regard to dynamical properties and agreement of numerical predictions with laboratory and computer experiments. The approximations considered include the direct-interaction equations (Kraichnan, 1964), Herring's (1966) self-consistent-field theory, a generalization of Edwards' (1964) theory, the abridged Lagrangian-history, direct-interaction approximation (Kraichnan, 1966), the test-field model (Kraichnan, 1971), and an approximation, not previously described, in which one velocity field passively suffers convection by another. Most of the cited approximations are representable by stochastic model equations for the velocity amplitude. Explicit constructions are given for the stochastic models, in a form that can be approximated on a digital computer. These constructions are used to discuss the physical and mathematical differences between the model dynamics and actual Navier-Stokes dynamics.-read more
Citations
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Book ChapterDOI
Theory of Homogeneous Turbulence
TL;DR: An overview of the theory of homogeneous turbulence is given in this paper, where concepts of quasi-normality of large-scale motions are explained and modified zero cumulant approximation is presented.
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TL;DR: In this paper, the authors provide the user with tools for the solution of linear differential equations with random coefficients, where the true coefficients of the stochastic equation are replaced by random step functions with the same first and second order moments and probability distributions, chosen in such a way that the equation can be solved analytically.
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Decay of two-dimensional homogeneous turbulence
TL;DR: In this paper, the decay of two-dimensional, homogeneous, isotropic, incompressible turbulence is investigated both by means of numerical simulation (in spectral as well as in grid-point form), and theoretically by use of the direct-interaction approximation and the test-field model.
References
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Inertial-range transfer in two- and three-dimensional turbulence
TL;DR: In this paper, an almost-Markovian Galilean-in variant turbulence model was proposed for the k−3 enstrophy-transfer range in two-dimensional turbulence.
Journal ArticleDOI
Turbulence spectra from a tidal channel
TL;DR: In this article, the authors used a hot film flowmeter in the sea and presented experimental measurements of the downstream component of turbulent velocity in a tidal channel, where the Reynolds number of the flow is about 108 and the scale of the turbulence is so large that a ship is carried about to a considerable extent by the energy-containing eddies.
Journal ArticleDOI
Lagrangian‐History Closure Approximation for Turbulence
TL;DR: In this paper, the direct interaction approximation for turbulence is extended to predict the covariance and average Green's function of a generalized velocity u(x, t|r), defined as the velocity measured at time r in the fluid element which passes through the point x at time t.
Journal ArticleDOI
Atmospheric Predictability and Two-Dimensional Turbulence
TL;DR: In this article, the eddy-damped Markovian approximation to two-dimensional turbulence is applied to these motions to predict for an observed energy spectrum the nonlinear transfer rates, characteristic error spectra, and the rate of error growth.
Journal ArticleDOI
Kolmogorov's Hypotheses and Eulerian Turbulence Theory
TL;DR: In this article, it was argued that low-order Eulerian moments do not express sufficiently well a statistical dependence of nonsimultaneous amplitudes that accompanies the convection of small spatial scales by large spatial scales.