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Functional integrals in Navier–Stokes incompressible fluid turbulence
Journal article   Peer reviewed

Functional integrals in Navier–Stokes incompressible fluid turbulence

Gerald Rosen
Journal of mathematical physics, v 24(1), pp 193-195
Jan 1983

Abstract

variational methods incompressible flow navier−stokes equations integrals tensors functionals velocity correlations Turbulence
A variational principle is formulated for the dynamical evolution of the Hopf characteristic functional Φ=Φ[y(x),t] by employing an appropriate functional integral over all parameter fields y(x). It follows that the ratio of functional integrals Γ≡∫Φ*Φ̇D ( y)/∫‖Φ‖2 D(y) is an e x a c t c o n s t a n t o f t h e m o t i o n during the decay of boundary‐free Navier–Stokes incompressible fluid turbulence. Bearing the physical dimensions of inverse time, the constant of the motion Γ is a scalar function of the multipoint velocity correlation tensors embodied in Φ. For statistical situations such that the probability measure over the velocity‐field ensemble is semi‐Gaussian (i.e., the real part of ln Φ is a quadratic functional of y), Γ is evaluated explicitly in terms of the two‐point velocity correlation tensor.

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Web of Science research areas
Physics, Mathematical
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