Perturbative evaluation of universal numbers in homogeneous shear turbulence

Dutta, Kishore; Nandy, Malay K.

doi:10.1103/physreve.87.053007

Cited by 4 publications

(4 citation statements)

References 36 publications

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“…They are simply discarded to avoid mathematical diculties. This assumption, although crude, makes the anisotropic problems analytically tractable and provides results that are consistent with the experimental and numerical simulations, as shown in [45,67]. Thus the appearance of infinitesimal…”

Section: Analytical Resultssupporting

confidence: 64%

Anisotropic distribution of scalar in stably stratified turbulence

Dutta¹,

Nandy²

2018

J. Stat. Mech.

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We derive the anisotropic mean-square scalar (or temperature variance) spectrum and the buoyancy (or heat) flux for a stably stratified turbulent fluid by assuming the buoyancy terms in the governing dynamical equations as perturbations of the otherwise isotropic dynamics. This allows us to investigate their anisotropic distribution across scales larger and smaller than the Ozmidov scale. The ensuing 1D vertical wavenumber temperature spectrum at large scales is found to be in good agreement with stratospheric observations. The polar plot of the angle-dependent expression for temperature variance signifies the enhanced anisotropy with decreasing Froude number. It also indicates that with increasing stratification, the anisotropy persists down to smaller and smaller scales. In addition, we also display various polar plots for the components of buoyancy current, showing their anisotropic distribution.

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Section: Analytical Resultssupporting

confidence: 64%

Anisotropic distribution of scalar in stably stratified turbulence

Dutta¹,

Nandy²

2018

J. Stat. Mech.

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“…Despite the abovementioned constraints, it may be noted that our derived results are direct analytical consequences of the underlying equation of the homogeneous shear turbulence. Owing to its relative simplicity, although the capability of Leslie's perturbation scheme in capturing the experimental results for pressure related spectra is not satisfactory, it has correctly captured the eect of anisotropy in the inertial range of homogeneous shear [39] and stably stratified turbulence [40]. For the case of homogeneous shear turbulence [39], it yields encouraging results for the universal numbers associated with the anisotropic part of the velocity correlation tensor.…”

Section: J Stat Mech (2018) 023204mentioning

confidence: 99%

“…Owing to its relative simplicity, although the capability of Leslie's perturbation scheme in capturing the experimental results for pressure related spectra is not satisfactory, it has correctly captured the eect of anisotropy in the inertial range of homogeneous shear [39] and stably stratified turbulence [40]. For the case of homogeneous shear turbulence [39], it yields encouraging results for the universal numbers associated with the anisotropic part of the velocity correlation tensor. For the case of stably stratified turbulence [40], it has not only allowed us to calculate the prefactors associated with the velocity-velocity, temperature-temperature, and velocity-temperature correlations, but also correctly captured the trend of observed layered structure.…”

Section: J Stat Mech (2018) 023204mentioning

confidence: 99%

Spectral calculations for pressure–velocity and pressure–strain correlations in homogeneous shear turbulence

Dutta¹

2018

J. Stat. Mech.

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Theoretical analyses of pressure related turbulent statistics are vital for a reliable and accurate modeling of turbulence. In the inertial subrange of turbulent shear flow, pressure–velocity and pressure–strain correlations are affected by anisotropy imposed at large scales. Recently, Tsuji and Kaneda (2012 J. Fluid Mech. 694 50) performed a set of experiments on homogeneous shear flow, and estimated various one-dimensional pressure related spectra and the associated non-dimensional universal numbers. Here, starting from the governing Navier–Stokes dynamics for the fluctuating velocity field and assuming the anisotropy at inertial scales as a weak perturbation of an otherwise isotropic dynamics, we analytically derive the form of the pressure–velocity and pressure–strain correlations. The associated universal numbers are calculated using the well-known renormalization-group results, and are compared with the experimental estimates of Tsuji and Kaneda. Approximations involved in the perturbative calculations are discussed.

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“…An improved version of Leslie's perturbative procedure was formulated in Refs. [42,43], where it was found that such treatment could reproduce the experimental results of homogeneous shear turbulence satisfactorily.…”

Section: B Present Motivationmentioning

confidence: 93%

Spectral calculations in stably stratified turbulence

Dutta

Nandy

2014

Phys. Rev. E

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We perform a Leslie-type perturbative treatment on stably stratified turbulence with Boussinesq approximation, where the buoyancy terms in the corresponding dynamical equations are treated as perturbations against the isotropic background fields. Thus we calculate the anisotropic corrections to various correlation functions, namely, velocity-velocity, temperature-temperature, and velocity-temperature correlations, up to second order in this scheme. We find that the prefactors associated with the anisotropic corrections depend on the energy flux, scalar flux, Kolmogorov constant, Batchelor constant, and the eddy-damping amplitudes. The correlation functions further yield the anisotropic parts of the energy and mean-square temperature spectra as k(-3) and the anisotropic buoyancy spectrum as k(-7/3). The resulting angle-dependent energy density is found to be concentrated predominantly around the vertical wave vector signifying layered structures in the physical space.

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Perturbative evaluation of universal numbers in homogeneous shear turbulence

Cited by 4 publications

References 36 publications

Anisotropic distribution of scalar in stably stratified turbulence

Anisotropic distribution of scalar in stably stratified turbulence

Spectral calculations for pressure–velocity and pressure–strain correlations in homogeneous shear turbulence

Spectral calculations in stably stratified turbulence

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