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Zeitschrift für Physik B Condensed Matter
ISSN: 0722-3277 (printed version)
ISSN: 1431-584X (electronic version)
Abstract Volume 100 Issue 3 (1996) pp 461-468
On a Fourier space master equation for Navier-Stokes turbulence
Heinz-Peter Breuer, Francesco Petruccione, Frithjof Weber
Fakultät für Physik, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany (Tel.: (+49) 761-203-5828, Fax: (+49) 761-203-5821)
Received: 26 June 1995 / Revised version: 10 August 1995
Abstract. Three-dimensional homogeneous isotropic turbulence is formulated in terms of a discrete stochastic process in Fourier space. The time-dependent joint probability distribution of the stochastic Fourier modes is governed by a multivariate master equation. It is demonstrated that the characteristic functional of the stochastic process obeys the Hopf functional equation. As a first application of the method stochastic simulations of the Burgers's turbulence model are performed and shown to yield the expected energy spectrum.
PACS: 47.11.+j; 47.27.Gs; 02.70.Lq
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