Probability distribution and spectra of potential hydrodynamic turbulence

Гурбатов, С. Н.; Саичев, А. И.

doi:10.1007/bf01036611

Cited by 43 publications

(63 citation statements)

References 8 publications

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“…Here ∆ψ 0 is the characteristic change in amplitude of ψ 0 , and Re 0 is the initial Reynolds number. From (16) it is easy to get the well known result, that for Re 0 ≫ 1 the initial harmonic waves asymptotically has also harmonics form, but with the amplitude not depending on the initial amplitude [1,2]. At large initial Reynolds number the homogeneous Gaussian field v 0 (x) at the nonlinear stage transforms into series of sawtooth waves with strong non-Gaussian statistical properties [3,35].…”

Section: Multi-dimensional Burgers Equation the Limit Of Vanishimentioning

confidence: 99%

“…For the multi-dimensional Burgers turbulence the twodimensional probability distribution, correlation function and energy spectrum where found in [3,16] using so called "cellular" model. In this model is assumed that in different elementary volumes the initial potential are independent and that the potential has a Gaussian distribution.…”

Section: B Isotropisation Of the Multidimensional Burgers Turbulencementioning

confidence: 99%

“…The three-dimensional form of equation has been used to model the formation of the large scale structure of the Universe when pressure is negligible. Known as "adhesion" approximation this equation describes the nonlinear stage of gravitational instability arising from random initial perturbation [16,17,18,19,20]. Other problems leading to the multi-dimensional Burgers equation, or variants of it, include surface growth under sputter deposition and flame front motion [21,22].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Evolution of anisotropic structures and turbulence in the multidimensional Burgers equation

Гурбатов¹,

Moshkov²,

Noullez

2010

Phys. Rev. E

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The goal of the present paper is the investigation of the evolution of anisotropic regular structures and turbulence at large Reynolds number in the multi-dimensional Burgers equation. We show that we have local isotropization of the velocity and potential fields at small scale inside cellular zones. For periodic waves, we have simple decay inside of a frozen structure. The global structure at large times is determined by the initial correlations, and for short range correlated field, we have isotropization of turbulence. The other limit we consider is the final behavior of the field, when the processes of nonlinear and harmonic interactions are frozen, and the evolution of the field is determined only by the linear dissipation.

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Section: Multi-dimensional Burgers Equation the Limit Of Vanishimentioning

confidence: 99%

Section: B Isotropisation Of the Multidimensional Burgers Turbulencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Evolution of anisotropic structures and turbulence in the multidimensional Burgers equation

Гурбатов¹,

Moshkov²,

Noullez

2010

Phys. Rev. E

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“…A special case when gravitational terms in (33) may cancel exactly relates to the so-called Zeldovich approximation Zel'dovich [65] that assumes a predominantly potential velocity field (∇ × u = 0) such that u = λg, where λ is a constant [66]. Its generalization known as the adhesion model [67,68] relies on multidimensional Burgers' equation in the limit of vanishing viscosity to describe structure formation in a uniform cold gravitationally unstable gas with random initial velocity perturbations [e.g. 69,70].…”

Section: A In Terms Of Two-point Differencesmentioning

confidence: 99%

Exact relations for energy transfer in self-gravitating isothermal turbulence

Banerjee

Kritsuk

2017

Phys. Rev. E

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Self-gravitating isothermal supersonic turbulence is analyzed in the asymptotic limit of large Reynolds numbers. Based on the inviscid invariance of total energy, an exact relation is derived for homogeneous, (not necessarily isotropic) turbulence. A modified definition for the two-point energy correlation functions is used to comply with the requirement of detailed energy equipartition in the acoustic limit. In contrast to the previous relations (Galtier and Banerjee, Phys. Rev. Lett., 107, 134501, 2011; Banerjee and Galtier, Phys. Rev. E, 87, 013019, 2013), the current exact relation shows that the pressure dilatation terms plays practically no role in the energy cascade. Both the flux and source terms are written in terms of two-point differences. Sources enter the relation in a form of mixed second-order structure functions. Unlike kinetic and thermodynamic potential energy, gravitational contribution is absent from the flux term. An estimate shows that for the isotropic case, the correlation between density and gravitational acceleration may play an important role in modifying the energy transfer in self-gravitating turbulence. The exact relation is also written in an alternative form in terms of two-point correlation functions, which is then used to describe scale-by-scale energy budget in spectral space.

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“…Furthermore,Burgers equation is studying in directed polymers [24,3] and has found interesting applications in cosmology, such as "Zel'dovich approximation" [46] and "adhesionmodel" [16]. Another application of Burgers equation is in the theory of turbulence and field [34,37,15,31].…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of Burgers equation with nonlinear damping using non-polynomial tension spline

Shekarabi¹

2016

HJMS

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Numerical solution of Burgers equation with nonlinear damping term has been investigated.We developed new approach based on nonpolynomial cubic tension spline approximation.The proposed approach depends on the parameters involving in tension spline.By choosing suitable values of such parameters the optimal local truncation error of the scheme can be obtained.Convergence analysis of presented method has been discussed in details and we have shown under appropriate condition the method convergence.The method tested on two problems,numerical results have been compared with the exact solution to justify the usefulness and accurate nature of proposed method.

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Probability distribution and spectra of potential hydrodynamic turbulence

Cited by 43 publications

References 8 publications

Evolution of anisotropic structures and turbulence in the multidimensional Burgers equation

Evolution of anisotropic structures and turbulence in the multidimensional Burgers equation

Exact relations for energy transfer in self-gravitating isothermal turbulence

Numerical solution of Burgers equation with nonlinear damping using non-polynomial tension spline

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