Approximate equations of turbulent incompressible fluid flow

Иевлев, В. М.

doi:10.1007/bf01015004

Cited by 6 publications

(16 citation statements)

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“…In other words, only due to the fact that the LMN equations go along with additional physical constraints, they constitute in contrast to the MPC equations a formally closed system, and thus also a more physical system, as it was already recognized by Ievlev (1970): "However, the equations for the probability distributions [the LMN equations] yield a more complete and compact statistical description of turbulence than do the usual moment equations [the MPC or Friedman-Keller equations] and apparently permit an easier formulation of the approximate conditions closing the equations. "…”

Section: Unclosed Hierarchy Of Mpc Equationsmentioning

confidence: 99%

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A critical examination of the statistical symmetries admitted by the Lundgren-Monin-Novikov hierarchy of unconfined turbulence

Frewer,

Khujadze,

Foysi

2014

Preprint

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We present a critical examination of the recent article by Wac lawczyk et al. (2014) which proposes two new statistical symmetries in the classical theory for turbulent hydrodynamic flows. We first show that both symmetries are unphysical in that they induce inconsistencies due to violating the principle of causality. In addition, they must get broken in order to be consistent with all physical constraints naturally arising in the statistical Lundgren-Monin-Novikov (LMN) description of turbulence. As a result, we state that besides the well-known classical symmetries of the LMN equations no new statistical symmetries exist. Yet, aside from this particular issue, the article by Wac lawczyk et al. ( 2014) is flawed in more than one respect, ranging from an incomplete proof, to a self-contradicting statement up to an incorrect claim. All these aspects will be listed, discussed and corrected, thus obtaining a completely opposite conclusion in our study than the article by Wac lawczyk et al. (2014) is proposing.

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Section: Unclosed Hierarchy Of Mpc Equationsmentioning

confidence: 99%

“…Monin (1967)), the reverse cannot be established. In other words, the LMN equations cannot be uniquely determined from the MPC equations, which was shown in Ievlev (1970) (see also Monin & Yaglom (1975); Frewer et al (2014)). Hence, the MPC equations are not equivalent to the LMN equations.…”

Section: Unclosed Hierarchy Of Mpc Equationsmentioning

confidence: 99%

A critical examination of the statistical symmetries admitted by the Lundgren-Monin-Novikov hierarchy of unconfined turbulence

Frewer,

Khujadze,

Foysi

2014

Preprint

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“…(47) be equal to 1.9, it is necessary to choose h ~ 1.815. It is clear, however, that the correct expression for ~o can only be obtained as a result of some variational calculation in the spirit of [6].…”

Section: Gj Dmentioning

confidence: 99%

“…The guiding principles in choosing a closure scheme were considerations of relative simplicity and some experimental indications. The use of more complicated closure schemes, e.g., the scheme proposed in [6], or the choice of the form of the function q~, taking into account nonzero excess in the probability distribution, requires much more calculation than necessary for realizing the goals of the present work.…”

Section: Gj Dmentioning

confidence: 99%

“…The initial, i.e., strongly depending on the time argument, values of the functions are realized for t -z -1 --* 0. , then it is always possible to choose t such that the steady state condition (5) be satisfied for z = z m, Indeed, the right side in the equality 1 ) (6) t>tr+a(+)/ m+k----~ is always finite is a bounded flow, since rL where L is the size of the system; ~,2 is the mean-square value of the fluctuating velocity.…”

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Equation for the structure function of a turbulent stationary isotropic velocity field and its solution in the inertial scale interval

Sosinovich

1981

Journal of Engineering Physics

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Raison d'être and general formulation of two-point statistical description of turbulent premixed combustion

Burluka

2006

Comptes Rendus. Mécanique

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This work undertakes an analysis of parameters defining the rate of chemical reactions in turbulent premixed combustion with particular emphasis on the strong turbulence case. Experimental data show that not only the laminar flame speed and rms turbulent velocity but also both the details of chemical kinetics and the molecular transport coefficients are important in this case. Determination of the molecular transport rates inside a turbulent flame requires a two-point statistical description. In order to construct such a description the transport equation for the two-point joint velocity and scalars probability density function is considered. It proved possible to achieve a closure of the unclosed terms in this equation, including the micromixing terms, following Ievlev's method.

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Approximate equations of turbulent incompressible fluid flow

Cited by 6 publications

References 1 publication

A critical examination of the statistical symmetries admitted by the Lundgren-Monin-Novikov hierarchy of unconfined turbulence

A critical examination of the statistical symmetries admitted by the Lundgren-Monin-Novikov hierarchy of unconfined turbulence

Equation for the structure function of a turbulent stationary isotropic velocity field and its solution in the inertial scale interval

Raison d'être and general formulation of two-point statistical description of turbulent premixed combustion

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