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A probabilistic method for Navier-Stokes vortices

Part of: Incompressible inviscid fluids Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Xinyu He
Xinyu He*
Affiliation:
University of Warwick
*
∗ Postal address: Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK. Email address: xinyu@maths.warwick.ac.uk
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Abstract

Consider a Navier-Stokes incompressible turbulent fluid in R2. Let x(t) denote the position coordinate of a moving vortex with initial circulation Γ0 > 0 in the fluid, subject to a force F. Define x(t) as a stochastic process with continuous sample paths described by a stochastic differential equation. Assuming a suitable notion of weak rotationality, it is shown that the stochastic equation is equivalent to a linear partial differential equation for the complex function ψ, i∂ψ/∂t = [-Γ0Δ + F] ψ, where |ψ|2 = ρ(x,t), ρ being the probability density function of finding the vortex centre in position x at time t.

Keywords

Vortex flowsNavier-Stokes

MSC classification

Primary: 76B47: Vortex flows
Secondary: 60G35: Signal detection and filtering
Type
Short Communications
Information
Journal of Applied Probability , Volume 38 , Issue 4 , December 2001 , pp. 1059 - 1066
Copyright
Copyright © by the Applied Probability Trust 2001 

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