title: Response function of turbulence computed via fluctuation-response relation of a Langevin system with vanishing noise.
abstract: For a shell model of the fully developed turbulence and the incompressible Navier-Stokes equations in the Fourier space, when a Gaussian white noise is artificially added to the equation of each mode, an expression of the mean linear response function in terms of the velocity correlation functions is derived by applying the method developed for nonequilibrium Langevin systems [Harada and Sasa, Phys. Rev. Lett. 95, 130602 (2005)]. We verify numerically for the shell-model case that the derived expression of the response function, as the noise tends to zero, converges to the response function of the noiseless shell model.
authors.affiliation: Division of Physics and Astronomy, Graduate School of Science, Kyoto University, Kyoto, 606-8502, Japan.
authors.forename: Takeshi
authors.initials: T
authors.lastname: Matsumoto
authors.affiliation: Department of Materials Science, Shimane University, Matsue 690-8504, Japan.
authors.forename: Michio
authors.initials: M
authors.lastname: Otsuki
authors.affiliation: Department of Mechanical and Aerospace Engineering, Tottori University, Tottori 680-8552, Japan.
authors.forename: Ooshida
authors.initials: O
authors.lastname: Takeshi
authors.affiliation: Graduate School of Engineering Science, Osaka University, Toyonaka 560-8531, Japan.
authors.forename: Susumu
authors.initials: S
authors.lastname: Goto
authors.affiliation: Laboratory of Physics, College of Science and Technology, Nihon University, Funabashi 274-8501, Japan.
authors.forename: Akio
authors.initials: A
authors.lastname: Nakahara
mesh_terms: D003198:Computer Simulation; D008962:Models, Theoretical