Singularities of the equations of fluid motion

Details Singularities of the equations of fluid motion Singularities of the equations of fluid motion

Dec 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988phrva..38.6287s&link_type=abstract

Physical Review A - General Physics, 3rd Series (ISSN 0556-2791), vol. 38, Dec. 15, 1988, p. 6287-6295. Research supported by NS

Mathematics

69

Energy Dissipation, Euler Equations Of Motion, Flow Equations, Navier-Stokes Equation, Singularity (Mathematics), Flow Distribution, Fractals, High Reynolds Number, Turbulent Boundary Layer, Turbulent Flow

Scientific paper

This paper explores some implications of the observed multifractal nature of the turbulent energy-dissipation field and of velocity derivatives of increasing order for 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) three, 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.

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