Journal article
Functional Calculus Theory for Incompressible Fluid Turbulence
Journal of mathematical physics, v 12(5), pp 812-820
May 1971
Abstract
A functional integral representation for the space‐time Hopf characteristic functional is derived from the probability theory for a statistical ensemble of velocity fields that satisfy the Navier‐Stokes equation for boundary‐free incompressible fluid flow. The functional integral representation involves a pair of real vector field integration variables denoted by u and v, and the evaluation of the integral is performed in two steps. First, the integration over the field variable u is effected exactly in the general case by applying methods of explicit functional integration. Second, the resulting functional integral over the field variable v is reduced to a form amenable to specialized analysis by applying a suitable transformation of the integration field variable v → z. Specializing to mathematically defined ``C‐dominant turbulence,'' the final functional integration over the field variable z is effected exactly and yields a characteristic functional of Gaussian form. The two‐point velocity correlation tensor for C‐dominant turbulence is then obtained from the characteristic functional.
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Details
- Title
- Functional Calculus Theory for Incompressible Fluid Turbulence
- Creators
- Gerald Rosen - Drexel University
- Publication Details
- Journal of mathematical physics, v 12(5), pp 812-820
- Publisher
- American Institute of Physics (AIP)
- Number of pages
- 9
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Physics
- Web of Science ID
- WOS:A1971J543200007
- Scopus ID
- 2-s2.0-36849110240
- Other Identifier
- 991019173860404721