Structurization of chaos

O. M. Belotserkovskii   ; A. V. Konyukhov   ; A. M. Oparin   ; O. V. Troshkin   ; S. V. Fortova

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 2, pp. 237-250

Résumé

Vortex cascades of instabilities forming a core are studied. Large-scale linear waves in a fluctuating medium are described.

Bibliographie

[1] Belotserkovskii O. M., “Computational experiment: direct numerical simulations of complex gas-dynamics flows on the basis of Euler, Navier–Stokes and Boltzmann models”, Brussel. Numer. Methods in Fluid Dynamics, Karman's Lect., von Karman Inst. Fluid Dynamics (March 15–19, 1976), Hermisphere, Washington, London, 1978, 339–387

[2] Belotserkovskii O. M., “Pryamoe chislennoe modelirovanie svobodnoi razvitoi turbulentnosti”, Zh. vychisl. matem. i matem. fiz., 25:12 (1985), 1856–1882 | MR

[3] Belotserkovskii O. M., Constructive modeling of structural turbulence and hydrodynamic instabilities, World Scient. Publ. Co., Singapore, 2009 | MR | Zbl

[4] Fortova S. V., “Numerical simulation of cascade development of instability in the shear layer”, Phys. Extreme States Matter., IPCP RAS, Chernogolovka, 2009, 117–120

[5] Belotserkovskii O. M., Fortova S. V., “Makroparametry prostranstvennykh techenii v svobodnoi sdvigovoi turbulentnosti”, Zh. vychisl. matem. i matem. fiz., 50:6 (2010), 1126–1139 | MR

[6] Troshkin O. V., “O rasprostranenii malykh vozmuschenii v idealnoi turbulentnoi srede”, Dokl. AN SSSR, 307:5 (1989), 1072–1076 | MR | Zbl

[7] Troshkin O. V., “Volny vozmuschenii turbulentnykh sred”, Zh. vychisl. matem. i matem. fiz., 33:12 (1993), 1844–1863 | MR | Zbl

[8] Troshkin O. V., Nontraditional methods in mathematical hydrodynamics, Trans. Math. Monographs., 144, AMS, Providence, RI, USA, 1995 | MR | Zbl

[9] Kolmogorov A. N., “Lokalnaya struktura turbulentnosti v neszhimaemoi zhidkosti pri ochen bolshikh chislakh Reinoldsa”, Dokl. AN SSSR, 30:4 (1941), 299–303

[10] Obukhov A. M., “O raspredelenii energii v spektre turbulentnogo potoka”, Izv. AN SSSR. Ser. geogr. i geofiz., 5:4 (1941), 453–466

[11] Richardson L. F., “The supply of energy from and to atmospheric eddies”, Proc. Roy. Soc. London A, 97 (1920), 354–373 | DOI

[12] Canuto V. M., “Turbulence and laminar structures: can they co-exist?”, Mon. Not. R. Astron. Soc., 317 (2000), 985–988 | DOI

[13] Troshkin O. V., Yanitskii V. E., Peremezhaemost v odnoi zadache svobodnoi turbulentnosti, VTs AN SSSR, M., 1988

[14] Thomson W., “On the propagation of laminar motion through a turbulentcy moving inviscid liquid”, Philos. Mag. Ser. 5, 24:149 (1887), 342–353

[15] Reynolds O., “On the dynamical theory of incompressible viscous fluids and the determination of the criterion”, Philos. Trans. Roy. Soc. London A, 186 (1895), 123–164 | DOI

[16] Monin A. S., Yaglom A. M., Staticheskaya gidromekhanika, Ch. 1, Nauka, M., 1965

[17] Arnold V. I., Meshalkin A. D., “Seminar A.N. Kolmogorova po izbrannym voprosam analiza (1958–1959)”, Uspekhi matem. nauk, 15:1 (1960), 247–250

[18] Meshalkin L. D., Sinai Ya. G., “Issledovanie ustoichivosti statsionarnogo resheniya odnoi sistemy uravnenii ploskogo dvizheniya neszhimaemoi vyazkoi zhidkosti”, Prikl. matem. i mekhan., 25:6 (1961), 1140–1143 | Zbl

[19] Troshkin O. V., “Algebraicheskaya struktura dvumernykh statsionarnykh uravnenii Nave–Stoksa i nelokalnye teoremy edinstvennosti”, Dokl. AN SSSR, 298:6 (1988), 1372–1376 | MR | Zbl

[20] Oparina E. I., Troshkin O. V., “Ustoichivost techeniya Kolmogorova v kanale s tverdymi stenkami”, Dokl. RAN, 398:4 (2004), 487–491 | MR

[21] Yudovich V. I., “Ob avtokolebaniyakh, voznikayuschikh pri potere ustoichivosti parallelnykh techenii vyazkoi zhidkosti otnositelno dlinnovolnovykh periodicheskikh vozmuschenii”, Izv. AN SSSR. Mekhan. zhidkosti i gaza, 1973, no. 1, 32–35

[22] Gledzer E. B., Dolzhanskii F. V., Obukhov A. M., Sistemy gidrodinamicheskogo tipa i ikh primenenie, Nauka, M., 1981 | MR | Zbl

[23] Belotserkovskii S. O., Modelirovanie techenii vyazkoi neszhimaemoi zhidkosti na osnove uravnenii Nave–Stoksa, Dis. $\dots$ kand. fiz.-matem. nauk, MFTI, M., 1979

[24] Krylov A. L., “Ob ustoichivosti techeniya Puazeilya v ploskom kanale”, Dokl. AN SSSR, 159:5 (1964), 978–981 | MR

[25] Rozhdestvenskii B. L., Simakin I. N., “Modelirovanie turbulentnykh techenii v ploskom kanale”, Zh. vychisl. matem. i matem. fiz., 25:1 (1985), 96–121 | MR

[26] Zubarev D. N., Morozov V. G., Troshkin O. V., “Bifurkatsionnaya model turbulentnogo techeniya v kanale”, Dokl. AN SSSR, 290:2 (1986), 313–317 | MR | Zbl

[27] Patel V. C., Head M. R., “Some observations on skin friction and velocity profiles in fully developed pipe and channel flows”, J. Fluid Mech., 38, Pt. 1 (1969), 181–201 | DOI

[28] Beavers G. S., Sparrow E. M., “Low Reynolds number turbulent flow in large aspect ratio rectangular ducts”, J. Basic Engng., 93 (1971), 296–299 | DOI

[29] Kont-Bello Zh., Turbulentnoe techenie v kanale s parallelnymi stenkami, Mir, M., 1968

[30] Zubarev D. N., Morozov V. G., Troshkin O. V., Danilenko A. Yu., Bifurkatsionnaya model prostykh turbulentnykh techenii, MIAN CCCP, M., 1988

[31] Zubarev D. N., Morozov V. G., Troshkin O. V., “Turbulentnost kak neravnovesnyi fazovyi perekhod”, Teor. i matem. fiz., 92:2 (1992), 293–311 | MR | Zbl

[32] Belotserkovskii O. M., Oparin A. M., Chislennyi eksperiment v turbulentnosti: ot poryadka k khaosu, Nauka, M., 2000 | MR

[33] Dzhozef D., Ustoichivost dvizhenii zhidkosti, Mir, M., 1981

[34] Hoffman J., Johnson C., Computational turbulent incompressible flow, Springer, Berlin etc., 2007 | MR

[35] Landau L. D., Lifshits E. M., Teoreticheskaya fizika, v. VI, Gidrodinamika, Nauka, M., 1988

[36] Abramovich G. N., Teoriya svobodnoi strui i ee prilozheniya, Trudy TsAGI, 293, TsAGI, M., 1936

[37] Loitsyanskii L. G., Mekhanika zhidkostei i gazov, Drofa, M., 2003

[38] Joule J. P., “On the mechanical equivalent of heat”, Philos. Trans., 140, Pt. 1 (1850), 61–82 | DOI