Statistics of the Inertial Energy Transfer Range in d-Dimensional Turbulence (2 ≤ d ≤ 3) in a Lagrangian Renormalized Approximation

Statistics in the inertial energy transfer range (IETR) of d-dimensional turbulence ( 2≤d≤3) are studied using a Lagrangian renormalized approximation (LRA). The LRA suggests that spectrum IETR is given by Kd|ε¯|2/3k−5/3, where Kd constant and ε¯ flux across wave-number k; forward for dc<d≤3 but inverse 2≤d<dc, dc≈2.065; at d=dc, diverges skewness longitudinal velocity difference vanishes; d-dependence two-time correlation spectra under appropriate normalization weak IETR.