Singularities of the Equations of Fluid Motion

K. R. Sreenivasan and C. Meneveau*
Mason Laboratory | Yale University | New Haven, CT 06520
*Present Address: Department of Mechanical Engineering
The Johns Hopkins University | Baltimore, MD 21218

ABSTRACT: We explore some implications of the observed multifractal nature of the turbulent energy-dissipation field and of velocity derivatives of increasing order on the near-singularities of the Navier-Stokes equations and the singularities of Euler equations. Although these singularities occur on fractal sets of dimension close to (and only marginally less than) 3, it is shown that most of the energy dissipation is concentrated on a subset of fractal dimension about 2.87 and volume zero. Similar statements can be made with respect to velocity derivatives. In particular, it is shown that the higher the order of the velocity derivative, the less space filling the corresponding singularities become.

Phys. Rev. A, 38, pp. 6287-6295

DOI:10.1103/PhysRevA.38.6287 | Full PDF
Copyright © 1988 by The American Physical Society. All rights reserved.

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Charles Meneveau, Department of Mechanical Engineering, Johns Hopkins University, 3400 N. Charles Street, Baltimore MD 21218, USA, Phone: 1-410-516-7802, Fax: 1-(410) 516-7254, email:

Last update: 04/18/2011