Equivalence of measures and stochastic equations for turbulent flows

Dmitrenko, A. V.

doi:10.1134/s1028335813060098

Cited by 24 publications

(17 citation statements)

References 5 publications

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“…In [1], for the transfer of substantial values F (the mass (the density-ρ), the momentum (ρU r ), the energy (E)) of deterministic (laminar) motion into random (turbulent) motion ( for the area 1) the beginning of the generation of turbulence, the pair (N, M) =…”

Section: The Formulation Of the Problemmentioning

confidence: 99%

“…In according to [1][2][3] considered the physical process is represented as a nonequilibrium thermodynamic system with i -subsets, which is characterized The phenomenological law of conservation and transformation of energy during the evolution of a random system -the first law of thermodynamics -is written as ( )…”

Section: The Formulation Of the Problemmentioning

confidence: 99%

“…Also in [1][2][3], subject to analysis [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], the equivalence of measures and the correlation function for an interaction between deterministic (laminar) and chaotic (turbulent) movement were obtained. This correlation function in the critical point of space-time …”

Section: The Formulation Of the Problemmentioning

confidence: 99%

“…This regularity was installed theoretically and was called as an equivalence of measures between deterministic movement and random movement. The new results for an incompressible fluid were obtained for critical Reynolds number [1], for profiles of the velocity and for correlation of the second order in function of initial turbulence for the flow in the tube [2,3], on the flat plate, in the plane jet, around a circular cylinder, near the rotating disk [3]. Here the regular pattern of the equivalence of measures and new systems of the stochastic equations for non -isothermal flow are presented.…”

Section: Introductionmentioning

confidence: 99%

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Some analytical results of the theory of equivalence measures and stochastic theory of turbulence for non-isothermal flows

Dmitrenko¹

2014

astp

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Fundamentals of the new theory for the processes of transition from deterministic state to the chaos state (turbulence) for non-isothermal flows are presented. According to this theory, systems of stochastic equations of energy, momentum and mass are applied for non-isothermal flows. Then the analytical dependence for estimation of the value of the critical Reynolds number and the value of the critical point of regime change for non-isothermal and compressible flows are written. As an example, consider the classic flow of a Newtonian medium in the circular smooth tube. The values of the critical point of the beginning of the transition from laminar (deterministic) to turbulent motion for non-isothermal flows in the pipe are predicated. It is shown, that predicated values of the critical Reynolds numbers are in satisfactory agreement with the classical data.

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Section: The Formulation Of the Problemmentioning

confidence: 99%

Section: The Formulation Of the Problemmentioning

confidence: 99%

Section: The Formulation Of the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Some analytical results of the theory of equivalence measures and stochastic theory of turbulence for non-isothermal flows

Dmitrenko¹

2014

astp

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“…A new system of stochastic equations is presented, which was obtained on the basis of the equivalence relations of measures between the deterministic and random components [3]. The flow of a liquid or a homogeneous gas in a pipe was considered.…”

Section: Introductionmentioning

confidence: 99%

Euler’s Equation of Continuity: Additional Terms of High Order of Smallness—An Overview

Ovsyannikov

2021

Fluids

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Professor N.E. Zhukovsky was a famous Russian mechanic and engineer. In 1876 he defended his master’s thesis at Moscow University. At a careful reading of N.E. Zhukovsky’s master’s thesis in 1997, V.A. Bubnov—a professor at the Moscow City Pedagogical University—discovered terms of the second order of smallness in the continuity equation for an incompressible fluid. Zhukovsky calculated them, but did not use the amount of substance in the balance. Ten years later, the author found high-order terms in Euler’s derivation of the 1752 continuity equation for an incompressible fluid. The physical meaning of the additional terms became clear after the derivation in 2006 of the continuity equation with terms of high order of smallness for a compressible gas. The higher order terms of the smallness of the continuity equation penetrate into the inhomogeneous part of the wave equation and lead to the generation of self-oscillations, vibrations, sound, and the initial stage of turbulent pulsations. The stochastic approach ensured success in modeling turbulent flows. The use of high-order terms of smallness of the Euler continuity equation makes it possible to transfer the description of some part of the motions from the stochastic part of the equation to the deterministic part. The article contains a review of works with the derivation of the inhomogeneous wave equation. These works use additional terms of a high order of smallness in the continuity equation.

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Stochastic equations for continuum and determination of hydraulic drag coefficients for smooth flat plate and smooth round tube with taking into account intensity and scale of turbulent flow

Dmitrenko

2016

Continuum Mech. Thermodyn.

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Equivalence of measures and stochastic equations for turbulent flows

Cited by 24 publications

References 5 publications

Some analytical results of the theory of equivalence measures and stochastic theory of turbulence for non-isothermal flows

Some analytical results of the theory of equivalence measures and stochastic theory of turbulence for non-isothermal flows

Euler’s Equation of Continuity: Additional Terms of High Order of Smallness—An Overview

Stochastic equations for continuum and determination of hydraulic drag coefficients for smooth flat plate and smooth round tube with taking into account intensity and scale of turbulent flow

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