Geodesic
On a Preserving Loitsyansky Invariant into Millionshtchikov Closure Model of Homogeneous Isotropic Turbulent Dynamics
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 9 (2009) no. 4, pp. 23-37 Cet article a éte moissonné depuis la source Math-Net.Ru

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The existence of a solution to an initial-boundary value problem for Millionshtchikov closure model of the von Kármán–Howarth equation is proven. The behavior of the solution obtained is investigated in the limit of viscosity $\nu$ to zero. We establish the asymptotic stability of the Millionshtchikov selfsimilar solution as $t\to\infty$. Moreover, we prove that Loitsyansky integral plays the role of a conservation law for Millionshtchikov closure model of homogeneous isotropic turbulent dynamics.
Keywords: von Karman-Howarth equation, Millionshtchikov model, solvability of initial-boundary value problem, Trotter–Kato product formula.
Mots-clés : Loitsyansky invariant 
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     title = {On a {Preserving} {Loitsyansky} {Invariant} into {Millionshtchikov} {Closure} {Model} of {Homogeneous} {Isotropic} {Turbulent} {Dynamics}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
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V. N. Grebenev; M. Yu. Filimonov. On a Preserving Loitsyansky Invariant into Millionshtchikov Closure Model of Homogeneous Isotropic Turbulent Dynamics. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 9 (2009) no. 4, pp. 23-37. http://geodesic.mathdoc.fr/item/VNGU_2009_9_4_a2/

[1] Kostomakha V. A., “Eksperimentalnoe modelirovanie izotropnoi turbulentnosti”, Dinamika sploshnoi sredy, 70 (1985), 92–104

[2] Khintse I. O., Turbulentnost, Fizmatgiz, M., 1963

[3] Chernykh G. G., Korobitsina Z. L., Kostomakha V. A., “Numerical Simulation of Isotropic Dynamics”, IJCFD, 10 (1998), 173–182 | MR | Zbl

[4] Loitsyanskii L. G., Nekotorye osnovnye zakonomernosti izotropnogo potoka, Trudy TsAGI, 440, 1939

[5] Millionschikov M. D., “Izotropnaya turbulentnost v pole turbulentnoi vyazkosti”, Pisma v ZhETF, 10 (1969), 406–411

[6] Millionschikov M. D., “O strukture koeffitsienta turbulentnoi vyazkosti dlya izotropnoi turbulentnosti”, Pisma v ZhETF, 11 (1970), 203–206

[7] Lytkin Yu. M., Chernykh G. G., “Ob odnom sposobe zamykaniya uravneniya Karmana–Khovarta”, Dinamika sploshnoi sredy, 27 (1976), 124–130 | MR

[8] Oberlack M., Peters N., “Closure of the Two-Point Correlation Equation as a Basis for Reynolds Stress Models”, Appl. Sci. Res., 55 (1993), 533–538 | DOI

[9] Oberlack M., “On the Decay Exponent of Isotropic Turbulence”, PAMM, 1 (2000), 101–104

[10] Grebenev V. N., Oberlack M., “A Geometric Interpretation of the Second-Order Structure Function Arising in Turbulence”, Math. Phys. Anal. Geom., 12:1 (2009), 1–18 | DOI | MR | Zbl

[11] Marsden J., Applications of Global Analysis in Mathematical Physisc, Publish or Perish Inc., Berkely, 1974 | MR | Zbl

[12] Arena O., “On a Singular Parabolic Equations Related to Axially Symmetric Heat Potentials”, Analli. Mat. Pura. Appl. Ser. IV, 105 (1975), 347–393 | DOI | MR | Zbl

[13] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1968

[14] Tersenov S. A., Parabolicheskie uravneniya s menyayuschimsya napravleniem vremeni, Novosibirsk, 1985 | MR

[15] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki, v. 2, Garmonicheskii analiz. Samosopryazhennost, Mir, M., 1978 | MR

[16] Ebin D. G., Marsden J., “Groups of Diffeoemorphism and the Motion of an Incompressible Fluid”, Ann. Math., 92:1 (1970), 102–163 | DOI | MR | Zbl