Spectral modelling of homogeneous non-isotropic turbulence

Cambon, Claude; Jeandel, D.; Mathieu, J.

doi:10.1017/s0022112081002905

Cited by 103 publications

(69 citation statements)

References 12 publications

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“…In a second step, a tractable model is obtained in terms of spherically-averaged descriptors, so that the state vector depends only on the wavenumber modulus k: the integration on spherical shells is performed analytically. This procedure in two steps generalizes the pioneering work of Cambon et al (1981) for the velocity field, and consistently extends the recent model by Mons et al (2016) to the scalar and velocity-scalar correlations modelling.…”

Section: Introductionmentioning

confidence: 60%

Spectral modelling for passive scalar dynamics in homogeneous anisotropic turbulence

2016

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The present work aims at developing a spectral model for a passive scalar field and its associated scalar flux in homogeneous anisotropic turbulence. This is achieved using the paradigm of eddy-damped quasi-normal markovian (EDQNM) closure extended to anisotropic flows. In order to assess the validity of this approach, the model is compared to several detailed DNS and experiments of shear-driven flows and isotropic turbulence with a mean scalar gradient at moderate Reynolds numbers. This anisotropic modelling is then used to investigate the passive scalar dynamics at very high Reynolds numbers. In the framework of homogeneous isotropic turbulence submitted to a mean scalar gradient, decay and growth exponents for the cospectrum and scalar energies are obtained analytically and assessed numerically thanks to EDQNM closure. With the additional presence of a mean shear, the scaling of the scalar flux and passive scalar spectra in the inertial range are investigated and confirm recent theoretical predictions. Finally, it is found that in shear-driven flows, the small scales of the scalar second-order moments progressively return to isotropy when the Reynolds number increases.

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Section: Introductionmentioning

confidence: 60%

Spectral modelling for passive scalar dynamics in homogeneous anisotropic turbulence

2016

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“…Even in the isotropic case, the eddy damping allows a posteriori Markovianization to be justified, arguing that the time variation is much more rapid in the exponential eddy-damping term than in the second-order moments present in the quasinormal term. Further details can be found in Cambon et al (1981) and Sagaut & Cambon (2008). In the end, this anisotropic EDQNM closure for the tensor τ ij (k, t) defined by (2.6) amounts to…”

Section: (Iv)mentioning

confidence: 99%

“…This is done following the procedure described in Cambon et al (1981). Performing the spherical integration of the linear terms in (2.3) or that of the linear terms in (2.12), (2.13) with the representation (3.1) or (3.2) leads to…”

Section: Dynamics Final Closurementioning

confidence: 99%

“…However, discussions in Choi & Lumley (2001), Kassinos et al (2001) and Zusi & Perot (2013 about possible nonlinear return to isotropy can eventually motivate the use of anisotropic EDQMN closure and the distinction between directional anisotropy and polarization anisotropy. One can also mention the model of Cambon, Jeandel & Mathieu (1981), where a closure for nonlinear terms using anisotropic EDQNM was proposed, but without a separation of directional anisotropy and polarization anisotropy. Spherical integration requires a parametrization of the second-order spectral tensor to restore at least a part of its angular dependence, leading to a mathematically consistent model reduced to spherically averaged descriptors.…”

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confidence: 99%

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A spectral model for homogeneous shear-driven anisotropic turbulence in terms of spherically averaged descriptors

2015

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International audienceA nonlinear spectral model in terms of spherically averaged descriptors is derived for the prediction of homogeneous turbulence dynamics in the presence of arbitrary mean-velocity gradients. The governing equations for the tensor $\hat{R}_{ij}(\mathbf k,t)$, the Fourier transform of the two-point second-order correlation tensor, are first closed by an anisotropic eddy-damped quasinormal Markovian procedure. This closure is restricted to turbulent flows where linear effects induced by mean-flow gradients have no essential qualitative effects on the dynamics of triple correlations compared with the induced production effects in the equations for second-order correlations. Truncation at the first relevant order of spectral angular dependence allows us to derive from these equations in vector $\mathbf k$ our final model equations in terms of the wavenumber modulus $k$ only. Analytical spherical integration results in a significant decrease in computational cost. Besides, the model remains consistent with the decomposition in terms of directional anisotropy and polarization anisotropy, with a spherically averaged anisotropic spectral tensor for each contribution. Restriction of anisotropy to spherically averaged descriptors, however, entails a loss of information, and realizability conditions are considered to quantify the upper boundary of anisotropy that can be investigated with the proposed model. Several flow configurations are considered to assess the validity of the present model. Satisfactory agreement with experiments on grid-generated turbulence subjected to successive plane strains is observed, which confirms the capability of the model to account for production of anisotropy by mean-flow gradients. The nonlinear transfer terms of the model are further tested by considering the return to isotropy (RTI) of different turbulent flows. Different RTI rates for directional anisotropy and polarization anisotropy allow us to correctly predict the apparent delayed RTI shown after axisymmetric expansion. The last test case deals with homogeneous turbulence subjected to a constant pure plane shear. The interplay between linear and nonlinear effects is reproduced, yielding the eventual exponential growth of the turbulent kinetic energy

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“…The evolution equation of this quantity for the case of homogeneous shear flow can be found for example in Cambon et al [22]:…”

Section: Governing Equationsmentioning

confidence: 99%

Influence of initial mean helicity on homogeneous turbulent shear flow

et al. 2011

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Helicity statistics are studied in homogeneous turbulent shear flow. Initial mean helicity is imposed on an isotropic turbulence field using a decomposition of the flow into complex-valued helical waves. The initial decay of the turbulent kinetic energy is weakened in the presence of strong mean helicity, consistent with an analytic analysis of the spectral tensor of velocity correlations. While exponential growth of the mean turbulent kinetic energy is obtained, the mean helicity decays. Probability distribution functions (PDFs) of helicity are skewed and show that the imposed mean helicity prevails throughout the simulations. A waveletbased scale-dependent analysis shows a trend to two dimensionalization for large scales of motion and a preference for helical motion at small scales. The magnitude of the skewness of the PDFs decreases for smaller scales. Joint PDFs indicate a strong correlation of the signs of both, helicity and superhelicity, for all cases. This correlation supports the conjecture that superhelicity dissipates helicity. Helicity statistics are studied in homogeneous turbulent shear flow. Initial mean helicity is imposed on an isotropic turbulence field using a decomposition of the flow into complex-valued helical waves. The initial decay of the turbulent kinetic energy is weakened in the presence of strong mean helicity, consistent with an analytic analysis of the spectral tensor of velocity correlations. While exponential growth of the mean turbulent kinetic energy is obtained, the mean helicity decays. Probability distribution functions (PDFs) of helicity are skewed and show that the imposed mean helicity prevails throughout the simulations. A wavelet-based scale-dependent analysis shows a trend to two dimensionalization for large scales of motion and a preference for helical motion at small scales. The magnitude of the skewness of the PDFs decreases for smaller scales. Joint PDFs indicate a strong correlation of the signs of both, helicity and superhelicity, for all cases. This correlation supports the conjecture that superhelicity dissipates helicity.

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Spectral modelling of homogeneous non-isotropic turbulence

Cited by 103 publications

References 12 publications

Spectral modelling for passive scalar dynamics in homogeneous anisotropic turbulence

Spectral modelling for passive scalar dynamics in homogeneous anisotropic turbulence

A spectral model for homogeneous shear-driven anisotropic turbulence in terms of spherically averaged descriptors

Influence of initial mean helicity on homogeneous turbulent shear flow

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