Eulerian spectral closures for isotropic turbulence using a time-ordered fluctuation-dissipation relation.
Procedures for time-ordering the covariance function, as given in a previous paper [K. Kiyani and W. D. McComb, Phys. Rev. E 70, 066303 (2004)], are extended and used to show that the response function associated at second order with the Kraichnan-Wyld perturbation series can be determined by a local (in wave number) energy balance. These time-ordering procedures also allow the two-time formulation to be reduced to time-independent form by means of exponential approximations and it is verified that the response equation does not have an infrared divergence at infinite Reynolds number. Last, single-time Markovianized closure equations (stated in our previous paper) are derived and shown to be compatible with the Kolmogorov distribution without the need to introduce an ad hoc constant.
McComb
W D
WD
School of Physics, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, United Kingdom. w.d.mccomb@ed.ac.uk
Kiyani
K
K