Effect of spatial dimension on a model of fluid turbulence

  title={Effect of spatial dimension on a model of fluid turbulence},
  author={Daniel Clark and Richard D.J.G. Ho and Arjun Berera},
  journal={Journal of Fluid Mechanics},
Abstract A numerical study of the $d$-dimensional eddy damped quasi-normal Markovian equations is performed to investigate the dependence on spatial dimension of homogeneous isotropic fluid turbulence. Relationships between structure functions and energy and transfer spectra are derived for the $d$-dimensional case. Additionally, an equation for the $d$-dimensional enstrophy analogue is derived and related to the velocity derivative skewness. Comparisons are made to recent four-dimensional… 
Critical transition to a non-chaotic regime in isotropic turbulence
We study the properties of homogeneous and isotropic turbulence in higher spatial dimensions through the lens of chaos and predictability using numerical simulations. We employ both direct numerical


Mean-field approximation and a small parameter in turbulence theory.
  • V. Yakhot
  • Mathematics, Medicine
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2001
It is shown that in the vicinity of d=d(c) the ratio of the relaxation and translation characteristic times decreases to zero, thus giving rise to a small parameter of the theory, and predicted that the single-point probability density function of transverse velocity components in developing as well as in the large-scale stabilized two-dimensional turbulence is a Gaussian.
Homogeneous isotropic turbulence in four spatial dimensions
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Influence of helicity on the evolution of isotropic turbulence at high Reynolds number
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Local flow structure of turbulence in three, four, and five dimensions.
It is suggested that a driving motor of most intermittent turbulent structure is the compression along a single direction, which is consistent with the dynamics of the Burgers turbulence in d dimensions.
A simple dynamical model of intermittent fully developed turbulence
We present a phenomenological model of intermittency called the P-model and related to the Novikov-Stewart (1964) model. The key assumption is that in scales N &2-” only a fraction /3n of the total
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A recapitulation is first given of a recent theory of homogeneous turbulence based on the condition that the Fourier amplitudes of the velocity field be as randomly distributed as the dynamical
Reynolds number effect on the velocity increment skewness in isotropic turbulence
Second and third order longitudinal structure functions and wavenumber spectra of isotropic turbulence are computed using the eddy-damped quasi-normal Markovian model (EDQNM) and compared to results
Statistical properties of four-dimensional turbulence.
The energy transfer and small-scale intermittency in decaying turbulence in four dimensions (4D) are studied by direct numerical simulation and by spectral theory in comparison with three dimensions (3D), and the importance of the longitudinal component of turbulent velocity field in the energy transfer toward small scales are discussed.
Finite Reynolds number effect on the scaling range behaviour of turbulent longitudinal velocity structure functions
The effect of large-scale forcing on the second- and third-order longitudinal velocity structure functions, evaluated at the Taylor microscale $r=\unicode[STIX]{x1D706}$ , is assessed in various
Non‐Gaussian statistics in isotropic turbulence
Several measures of non‐Gaussian behavior in simulations of decaying isotropic turbulence are compared with predictions of the direct‐interaction approximation (DIA) at an initial Rλ≈35. The