Matsumoto Takeshi, Otsuki Michio, Takeshi Ooshida, Goto Susumu, Nakahara Akio
Division of Physics and Astronomy, Graduate School of Science, Kyoto University, Kyoto, 606-8502, Japan.
Department of Materials Science, Shimane University, Matsue 690-8504, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jun;89(6):061002. doi: 10.1103/PhysRevE.89.061002. Epub 2014 Jun 18.
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.
