Abstract
The basic propositions of the theory of dispersion turbulence — the principles of quasi‐one‐dimensionality, independence, and isotropy, random velocity fields, and local laws and coefficients of transfer — are presented.
Similar content being viewed by others
REFERENCES
G. I. Taylor, Proc. Roy. Soc., A219, No. 1133, 186–203 (1953).
G. I. Taylor, Proc. Roy. Soc., A223, No. 1155, 446–468 (1954).
G. I. Taylor, Proc. Roy. Soc., A225, No. 1163, 473–477 (1954).
R. Aris, Proc. Roy. Soc., A235, No. 1200, 67–77 (1956).
P. G. Saffman, J. Fluid Mech., 6, No. 3, 321–349 (1959).
A. E. Scheidegger, The Physics of Flow through Porous Media, Toronto (1957).
Development of Research in Filtration Theory in the USSR (1917–1967) [in Russian], Moscow (1969).
V. N. Nikolaevskii, Prikl. Mat. Mekh., 23, No. 6, 1042–1050 (1959).
V. N. Nikolaevskii, Mechanics of Porous and Cracked Media [in Russian], Moscow (1984).
R. A. Greenkorn and D. P. Kessler, Ind. Eng. Chem., 61, No. 9, 14–32 (1969).
R. E. Haring and R. A. Greenkorn, AIChE J., 16, No. 3, 477–483 (1970).
L. I. Kheifets and A. V. Neimark, Multiphase Processes in Porous Media [in Russian], Moscow (1982).
A. M. Yaglom, Usp. Mat. Nauk, 7, Issue 5 (51), 3–168 (1952).
A. S. Monin and A. M. Yaglom, Statistical Hydromechanics [in Russian], Pts. 1 and 2, Moscow (1967).
M. M. Mendel'son and M. I. Shvidler, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 6, 181–184 (1967).
M. I. Shvidler, Izv. Vyssh. Uchebn. Zaved., Geologiya Razvedka, No. 5, 66–83 (1983).
M. I. Shvidler, Statistical Hydrodynamics of Porous Media [in Russian], Moscow (1985).
Yu. A. Buevich and A. I. Leonov, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 6, 167–175 (1967).
Yu. A. Buevich, Yu. A. Korneev, and I. N. Shchelchkova, Inzh.-Fiz. Zh., 30, No. 6, 979–985 (1976).
Yu. A. Buevich, Inzh.-Fiz. Zh., 51, No. 3, 450–458 (1986).
Yu. A. Buevich and V. A. Ustinov, Inzh.-Fiz. Zh., 62, No. 3, 396–403 (1992).
O. G. Martynenko and N. V. Pavlyukevich, Inzh.-Fiz. Zh., 71, No. 1, 5–18 (1998). 380
Yu. A. Kovalenko, in: Proc. All-Union Seminar "Heat Transfer and Thermophysical Properties of Porous Materials" [in Russian], Novosibirsk (1992), pp. 3–26.
R. I. Nigmatulin, Fundamentals of the Mechanics of Heterogeneous Media [in Russian], Moscow (1978).
R. I. Nigmatulin, Dynamics of Multiphase Media [in Russian], Pt. 1, Moscow (1987).
Problems of Averaging and Construction of Continuous Models in the Mechanics of a Continuous Medium [in Russian], Moscow (1980).
I. M. Lifshits, S. A. Grodeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems [in Russian], Moscow (1982).
N. S. Bakhvalov and G. P. Panasenko, Averaging of the Processes in Periodic Media [in Russian], Moscow (1984).
S. M. Kozlov, Dokl. Akad. Nauk SSSR, 241, No. 5, 1016–1023 (1987).
M. I. Shvidler, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 5, 69–78 (1986).
V. I. Arnol'd and A. Avets, Ergodic Problems of Classical Mechanics [in Russian], Izhevsk (1999).
M. A. Gol'dshtik, Transport Processes in a Granular Bed [in Russian], Novosibirsk (1984).
A. V. Luikov, Heat and Mass Transfer [in Russian], Moscow (1972).
D. A. G. Bruggeman, Ann. Phys. (Leipzig), 24, F. 5, No. 7, 636–664 (1935).
P. Ramon, Field Theory: A Modern Primer [Russian translation], Moscow (1984).
L. Raider, Quantum Field Theory [Russian translation], Moscow (1987).
R. J. Elliott, J. A. Krumhansl, and R. L. Leath, Rev. Mod. Phys., 46, No. 3, 18–34 (1974).
S. Kirkpatrik, Rev. Mod. Phys., 45, No. 4, 574–588 (1973).
B. I. Shklovskii and A. L. Éfros, Electronic Properties of Doped Semiconductors [in Russian], Moscow (1979).
D. S. Gaunt and M. F. Sykes, J. Phys. A, 16, No. 4, 783–800 (1983).
I. M. Sokolov, Usp. Fiz. Nauk, 150, Issue 2, 221–256 (1986).
A. V. Neimark, Zh. Tekh. Fiz., 56, No. 11, 834–842 (1981).
P. S. Grinchuk and N. V. Pavlyukevich, in: Proc. IVth Minsk Int. Forum "Heat and Mass Transfer—MIF-2000," Minsk, May 22–26, 2000 [in Russian], Vol. 8, Minsk (2000), pp. 49–59.
O. Wiener, Abh. Math.-Phys. Kl. Konigl-Sachs, Ges. D. Wiss., 32, No. 6, 509–603 (1912).
R. Hill, J. Mech. Phys. Solids, 11, No. 5, 357–362 (1963).
R. Hill, J. Mech. Phys. Solids, 12, No. 4, 199–211 (1964).
A. M. Dykhne, Zh. Ékp. Teor. Fiz., 52, Issue 1, 264–270 (1967).
Z. Haschin and S. Strikman, J. Appl. Phys., 33, No. 10, 112–120 (1962).
K. A. Lur'e and A. V. Cherkaev, Dokl. Akad. Nauk SSSR, 264, No. 5, 230–241 (1982).
G. N. Dul'nev and V. V. Novikov, Inzh.-Fiz. Zh., 36, No. 5, 901–910 (1979).
G. N. Dul'nev, Coefficients of Transfer in Inhomogeneous Media [in Russian], Leningrad (1979).
G. N. Dul'nev and Yu. P. Zarichnyak, Heat Conduction of Mixtures and Composite Materials [in Russian], Leningrad (1974).
G. N. Dul'nev and V. V. Novikov, Inzh.-Fiz. Zh., 45, No. 3, 443–451 (1983).
G. N. Dul'nev, D. P. Volkov, and V. I. Malarev, Inzh.-Fiz. Zh., 56, No. 2, 281–291 (1989).
G. N. Dul'nev and V. I. Malarev, Inzh.-Fiz. Zh., 56, No. 1, 141 (1989).
N. R. Dul'nev, Yu. P. Zarichnyak, and B. L. Muratov, Inzh.-Fiz. Zh., 31, No. 2, 278–283 (1976).
G. N. Dul'nev and V. I. Malarev, Inzh.-Fiz. Zh., 59, No. 3, 522–539 (1990).
G. N. Dul'nev, I. K. Meshkaskii, V. V. Novikov, and I. A. Sokolov, Inzh.-Fiz. Zh., 37, No. 2, 229–235 (1979).
G. R. Dul'nev, Yu. P. Zarichnyak, and V. V. Novikov, Inzh.-Fiz. Zh., 32, No. 1, 150–171 (1976).
V. I. Odelevskii, Zh. Tekh. Fiz., 21, Issue 6, 667–685 (1951).
A. M. Dykhne, Zh. Éksp. Teor. Fiz., 59, Issue 7, 110–119 (1970).
Yu. A. Buevich, Prikl. Mat. Tekh. Fiz., No. 4, 57–66 (1973).
Yu. A. Buevich and Yu. A. Korneev, Inzh.-Fiz. Zh., 31, No. 4, 607–612 (1976).
Yu. A. Buevich and V. G. Markov, Inzh.-Fiz. Zh., 36, No. 5, 829–834 (1979).
M. I. Shvidler, Zh. Éksp. Teor. Fiz., 80, Issue 2, 34–42 (1981).
M. I. Shvidler, Zh. Éksp. Teor. Fiz., 84, Issue 3, 112–120 (1983).
A. F. Chudnovskii, Thermophysical Characteristics of Disperse Materials [in Russian], Moscow (1962). 381
L. L. Vasil'ev and S. A. Tanaeva, Thermophysical Properties of Porous Materials [in Russian], Minsk (1971).
A. V. Gorin and Yu. A. Kovalenko (eds.), Proc. All-Union Seminar "Heat Transfer and Thermophysical Properties of Porous Materials" [in Russian], Novosibirsk (1992).
V. V. Mandelbrot, The Fractal Geometry of Nature, Freeman, San Francisco (1982).
Ya. B. Zel'dovich and D. D. Sokolov, Usp. Fiz. Nauk, 146, No. 3, 493–506 (1985).
B. M. Smirnov, Usp. Fiz. Nauk, 149, No. 2, 177–219 (1986).
E. Feder, Fractals [Russian translation], Moscow (1991).
M. Barnsley, Fractals Everywhere, Academic Press, Boston (1988).
Fractals in Physics, Proc. 6th Int. Symp. on Fractals in Physics [in Russian], Moscow (1988).
A. Yu. Turygin and V. R. Chechetkin, Zh. Éksp. Teor. Fiz., 98, No. 1, 146–161 (1990).
V. V. Zosimov and L. M. Lyamshev, Akust. Zh., 40, No. 5, 709–736 (1994).
K. O. Sabdenov, Fiz. Goren. Vzryva, 31, No. 6, 106–112 (1995).
H.-O. Peitgen and P. H. Richter, The Beauty of Fractals: Images of Complex Dynamical Systems [Russian translation], Moscow (1993).
M. Schroeder, Fractals, Chaos, Power Laws [Russian translation], Izhevsk (2000).
G. A. Edgar, Measure, Topology, and Fractal Geometry, Springer-Verlag, New York (1990).
S. V. Ostakh, in: Proc. 2nd Russ. Nat. Conf. on Heat Transfer [in Russian], Vol. 5, Moscow (1998), pp. 64–66.
R. M. Kronover, Fractals and Chaos in Dynamic Systems. Fundamentals of the Theory [in Russian], Moscow (2000).
R. R. Nigmatullin and N. N. Sutugin, Inzh.-Fiz. Zh., 57, No. 2, 291–298 (1989).
Yu. A. Kovalenko, V. A. Gruzdev, and Yu. A. Veslogzov, Teplofiz. Vys. Temp., 33, No. 3, 373–377 (1995).
Heat-Transfer Processes in Power and Mechanical Engineering, Abstracts of the Regional Interuniversity Seminar [in Russian], Voronezh (1995).
V. V. Shitov, in: V. V. Faleev (ed.), Thermal-Power Engineering, Collected Papers [in Russian], Voronezh (1995), pp. 71–74.
V. V. Shitov, in: V. V. Faleev (ed.), Thermal-Power Engineering, Collected Papers [in Russian], Voronezh (1996), pp. 15–20.
A. V. Mal'shakov, Inzh.-Fiz. Zh., 62, No. 3, 405–410 (1992).
L. S. Kokorev, V. I. Subbotin. V. N. Fedoseev, V. V. Kharitonov, and V. V. Voskoboinikov, Teplofiz. Vys. Temp., 25, No. 1, 92–97 (1987).
V. N. Fedoseev, V. I. Subbotin, and V. V. Kharitonov, Teploénergetika, No. 6, 61–64 (1987).
L. S. Kokorev, V. N. Fedoseev, V. V. Kharitonov, and V. V. Voskoboinikov, New Approach to Calculation of Heat Transfer in Porous Media, Preprint No. 024 of the Moscow Engineering Physics Institute [in Russian], Moscow (1986).
V. V. Atamanov, V. V. Kharitonov, and N. V. Yakutin, Teplofiz. Vys. Temp., 34, No. 4, 590–595 (1996).
D. Montgomery, Res. Rept. Inst. Plasma Phys., Nagoya Univ., No. 670, 1–38 (1984).
A. P. Mirabel and A. S. Monin, Usp. Mekh., 2, Issue 3, 47–95 (1979).
Turbulence Bidimentional, J. de Mec., numero special, No. 2 (1988).
A. G. Bershadskii, Prikl. Mat. Tekh. Fiz., No. 5, 109–115 (1988).
A. G. Bershadskii, Zh. Éksp. Teor. Fiz., 96, Issue 2, 625–631 (1989).
A. G. Bershadskii, Prikl. Mat. Tekh. Fiz., No. 3, 49–51 (1990).
D. Palladin and A. Vul'piani, in: Fractals in Physics [in Russian], Moscow (1988), pp. 624–631.
M. É. Aérov, O. M. Todes, and D. A. Narinskii, Apparatuses with a Stationary Granular Bed [in Russian], Leningrad (1979).
B. M. Galitseiskii, Yu. N. Lapushkin, A. L. Lozhkin, and A. N. Ushakov, in: Heat and Mass Transfer in Interaction of a Flow with a Surface, Collected Scientific Papers of the Moscow Aviation Institute [in Russian], Moscow (1981), pp. 34–137.
A. L. Lozhkin and A. N. Ushakov, in: Heat Transfer in Aviation Technology, Collected Scientific Papers of the Moscow Aviation Institute [in Russian], Moscow (1984), pp. 19–22.
B. M. Galitseiskii, A. L. Lozhkin, and A. N. Ushakov, in: Book of Abstr. of the Minsk Int. Forum "Heat and Mass Transfer—MIF-88" [in Russian], Session 7, Minsk (1988), pp. 16–18. 382
A. L. Lozhkin, in: Some Problems in Heat and Mass Exchange between Flows and Surfaces, Collected Scientific Papers of the Moscow Aviation Institute [in Russian], Moscow (1986), pp. 69–70.
B. M. Galitseiskii, A. L. Lozhkin, and G. É. Solokhina, in: Heat and Mass Transfer in Aircraft Engines, Collected Scientific Papers of the Moscow Aviation Institute [in Russian], Moscow (1991), pp. 12–17.
B. M. Galitseiskii, A. L. Lozhkin, G. É. Solokhina, and A. N. Ushakov, in: Heat Exchangers of Gas-Turbine Engines [in Russian], Tr. TsIAM, No. 1282, Moscow (1991), pp. 22–28.
B. M. Galitseiskii, A. L. Lozhkin, and A. N. Ushakov, Prom. Teplotekh., 13, No. 1, 22–28 (1991).
B. M. Galitseiskii and A. L. Lozhkin, in: Proc. 1st Russ. Nat. Conf. on Heat Transfer [in Russian], Vol. 7, Moscow (1994), pp. 47–52.
B. M. Galitseiskii and A. L. Lozhkin, in: Proc. IVth Minsk Int. Forum "Heat and Mass Transfer—MIF-2000," Minsk, May 22–26, 2000 [in Russian], Vol. 8, Minsk (2000), pp. 14–23.
B. M. Galitseisky and A. P. Mozhaev, in: Proc. 3rd World Conf. Exp. Heat Transfer, Fluid Mechanics, and Thermodynamics, Vol. 2, Honolulu, USA (1993), pp. 1569–1576.
V. M. Polyaev and A. P. Mozhaev, in: Proc. Int. Symp. Turbulence, Heat and Mass Transfer, Vol. 2, Lisbon, Portugal (1994), pp. 12.6.1–12.6.5.
V. M. Polyaev, B. M. Galitseiskii, and A. P. Mozhaev, Vestn. MGTU, Mashinostroenie, No. 3, 109–120 (1995).
A. P. Mozhaev and V. M. Polyaev, in: Proc. 3rd Minsk Int. Forum "Heat and Mass Transfer—MIF-96," Minsk, May 20–24, 1996 [in Russian], Vol. 7, Minsk (1996), pp. 164–168.
V. M. Polyaev, A. P. Mozhaev, B. M. Galitseysky, and A. L. Lozhkin, Exp. Thermal Fluid Sci., 12, No. 4 (1996), pp. 426–432.
A. P. Mozhaev, in: Proc. IVth Minsk Int. Forum "Heat and Mass Transfer—MIF-2000," Minsk, May 22–26, 2000 [in Russian], Vol. 8, Minsk (2000), pp. 3–13.
A. P. Mozhaev, Inzh.-Fiz. Zh., 74, No. 5, 196–200 (2001).
Yu. V. Polezhaev and A. A. Shishkov, Gasdynamic Tests of a Thermal Shield. Handbook [in Russian], Moscow (1992).
Yu. V. Polezhaev and F. B. Yurevich, Thermal Protection [in Russian], Moscow (1976).
S. A. Druzhinin and A. I. Leont'ev, Inzh.-Fiz. Zh., 10, No. 4, 479–481 (1966).
A. I. Leont'ev, B. P. Mironov, and P. P. Lugovskoi, Inzh.-Fiz. Zh., 10, No. 4, 447–451 (1966).
A. I. Leont'ev, B. P. Mironov, and A. V. Fafurin, Teplofiz. Vys. Temp., 7, No. 6, 1134–1140 (1969).
S. S. Kutateladze, I. G. Malenkov, and S. L. Vitkovskii, Teplofiz. Vys. Temp., 17, No. 2, 333–336 (1979).
S. S. Kutateladze and A. I. Leont'ev, Turbulent Boundary Layer of an Incompressible Gas [in Russian], Novosibirsk (1962).
S. S. Kutateladze and A. I. Leont'ev, Heat and Mass Transfer and Friction in a Turbulent Boundary Layer [in Russian], Moscow (1985).
R. G. Bogoyavlenskii, Hydrodynamics and Heat Transfer in High-Temperature Nuclear Reactors with Spherical Fuel Elements [in Russian], Moscow (1978).
A. V. Afanas'ev, L. L. Kalishevskii, and V. G. Krapivtsev, in: Current Problems of Hydrodynamics and Heat Transfer in the Elements of Power Plants and Cryogenic Technology, Collected Scientific Papers [in Russian], Moscow (1988), pp. 10–16.
A. V. Afanas'ev, L. L. Kalishevskii, and V. G. Krapivtsev, in: Book of Abstr. of the Minsk Int. Forum "Heat and Mass Transfer—MIF-98" [in Russian], Session 5, Minsk (1998), pp. 7–9.
A. V. Afanas'ev, A. V. Istomin, and V. G. Krapivtsev, in: Current Problems of Hydrodynamics and Heat Transfer in the Elements of Power Plants and Cryogenic Technology, Collected Scientific Papers [in Russian] (989), pp. 92–97.
R. E. Collins, Flow of Fluids through Porous Materials, Reinhold, New York (1961).
I. Z. Fisher, Statistical Theory of a Liquid [in Russian], Moscow (1961).
I. V. Savel'ev, A Course in General Physics [in Russian], Vol. 1, Moscow (1966).
V. F. Nozdrev and A. A. Senkevich, A Course in Statistical Physics [in Russian], Moscow (1969).
A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis [in Russian], Moscow (1976). 383
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mozhaev, A.P. Chaotic Homogeneous Porous Media. 2. Theory of Dispersion Turbulence: Basic Propositions. Journal of Engineering Physics and Thermophysics 75, 371–383 (2002). https://doi.org/10.1023/A:1015641605365
Issue Date:
DOI: https://doi.org/10.1023/A:1015641605365