New Turbulent Scaling Laws From the Multi-Point Correlation Equations

Rosteck, Andreas; Oberlack, Martin

doi:10.1615/tsfp9.1080

Cited by 1 publication

(5 citation statements)

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“…where b 0 1 ( ) is an arbitrary solution of the continuity equation (7). This completes the solution of the first determining equation (27). Summarizing the obtained results we have…”

Section: Solution Of the First Normalization Condition (27)supporting

confidence: 65%

“…The inversion is a nonlinear transformation which breaks when a nonlocal determining equation is solved. In our case at least equation (27) will later lead to breaking of the special conformal group. (25) and (26) Let us now consider the algebraic relations (25) for i = 1, 2, 3.…”

Section: Appendix Lie Group Analysis Of the Considered Systemmentioning

confidence: 84%

“…Such solutions were derived for turbulence statistics in various flow configurations e.g. in [11,27,28]. A plethora of groupinvariant solutions for pdf's is presented in [29] for the FP equation and e.g.…”

Section: Discussion Of the Symmetriesmentioning

confidence: 99%

“…Solution of the second normalization condition (27) Consider the normalization condition . To sum up the obtained results, ξ k 1 ( ) does not depend on v 2 ( ) for = … k 0, , 9.…”

Section: Solution Of the Continuity Equation (28)mentioning

confidence: 99%

“…37) and the corresponding determining equation(27), which, after introducing the forms (21) and (A.2) for κ 0 , 6 as follows from equation (A.25). First, we use equation(10) in the form RHS term.…”

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confidence: 99%

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Lie symmetry analysis of the Lundgren–Monin–Novikov equations for multi-point probability density functions of turbulent flow

Wacławczyk

Grebenev

Oberlack

2017

J. Phys. A: Math. Theor.

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The problem of turbulence statistics described by the Lundgren–Monin–Novikov (LMN) hierarchy of integro-differential equations is studied in terms of its group properties. For this we perform a Lie group analysis of a truncated LMN chain which presents the first two equations in an infinite set of integro-differential equations for the multi-point probability density functions (pdf’s) of velocity. A complete set of point transformations is derived for the one-point pdf’s and the independent variables: sample space of velocity, space and time. For this purpose we use a direct method based on the canonical Lie–Bäcklund operator. Due to the one-way coupling of correlation equations, the present results are complete in the sense that no additional symmetries exist for the first leading equation, even if the full infinite hierarchy is considered.

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“…where b 0 1 ( ) is an arbitrary solution of the continuity equation (7). This completes the solution of the first determining equation (27). Summarizing the obtained results we have…”

Section: Solution Of the First Normalization Condition (27)supporting

confidence: 65%

Section: Appendix Lie Group Analysis Of the Considered Systemmentioning

confidence: 84%

Section: Discussion Of the Symmetriesmentioning

confidence: 99%

“…Solution of the second normalization condition (27) Consider the normalization condition . To sum up the obtained results, ξ k 1 ( ) does not depend on v 2 ( ) for = … k 0, , 9.…”

Section: Solution Of the Continuity Equation (28)mentioning

confidence: 99%

mentioning

confidence: 99%

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