PMID: 11308572Apr 20, 2001Paper

Transport and entropy production due to chaos or turbulence

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
H Mori, Hirokazu Fujisaka

Abstract

A projection-operator method is developed for the statistical-mechanical formulation of chaotic or turbulent transport, such as chaos-induced friction in a forced damped pendulum and turbulent viscosity in a turbulent fluid. Then the nonlinear deterministic equations of motion for these dynamical systems are transformed into linear stochastic equations with chaotic or turbulent fluctuating forces. This leads to a fluctuation-dissipation formula which relates the chaotic or turbulent transport coefficients to the time correlation of the fluctuating forces. Applying this theory to the forced damped pendulum, we explore the chaos-induced friction and the power spectra of chaotic orbits. Applying it to the fluid turbulence governed by the Navier-Stokes equation, we find that the turbulent viscosity in the inertial subrange depends on wave number k as k(-beta) with beta=4 / 3+1 / 2/micro(2/3)/, micro (q) being the intermittency exponent of order q.

Citations

Dec 13, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Makoto Okamura
Jun 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Makoto Okamura, Hazime Mori
Nov 15, 2016·Physical Review. E·Takayuki NarumiYoshiki Hidaka
Mar 15, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hirokazu Fujisaka, Yasuya Nakayama
Aug 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Misato IinoKazuhiro Hara
Dec 17, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Youichi Kitahara, Makoto Okamura
Feb 1, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hazime Mori, Makoto Okamura
Feb 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Takayuki NarumiShoichi Kai

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