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Rev. Mod. Phys. 61, 185–220 (1989)

The large-scale structure of the universe: Turbulence, intermittency, structures in a self-gravitating medium

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S. F. Shandarin
Institute for Physical Problems, Academy of Sciences of the USSR, 117 334 Moscow, Union of Soviet Socialist Republics and Max-Planck-Institut für Physik und Astrophysik, Institut für Astrophysik, 8046 Garching bei München, Federal Republic of Germany

Ya. B. Zeldovich*
Institute for Physical Problems, Academy of Sciences of the USSR, 117 334 Moscow, Union of Soviet Socialist Republics

The density distribution arising at the nonlinear stage of gravitational instability is similar to intermittency phenomena in acoustic turbulence. Initially small-amplitude density fluctuations of Gaussian type transform into thin dense pancakes, filaments, and compact clumps of matter. It is perhaps surprising that the motion of self-gravitating matter in the expanding universe is like that of noninteracting matter moving by inertia. A similar process is the distribution of light reflected or refracted from rippled water. The similarity of gravitational instability to acoustic turbulence is highlighted by the fact that late nonlinear stages of density perturbation growth can be described by the Burgers equation, which is well known in the theory of turbulence. The phenomena discussed in this article are closely related to the problem of the formation of large-scale structure of the universe, which is also discussed.

© 1989 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/RevModPhys.61.185
DOI:
10.1103/RevModPhys.61.185
PACS:

*Deceased. The Russian version of this review was finished in the summer of 1987. By the tragic death of Ya. B. Zeldovich on December 2, 1987, about four-fifths of the paper had been translated into English. Professor Zeldovich would have been 75 years old on March 8, 1989 and was vivid and creative until his last day. The theory of the structure of the universe was one of his favorite subjects, to which he made many note-worthy contributions over the last 20 years.