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 the energy spectrum in the IETR is given by K-d vertical bar(epsilon) over bar vertical bar(2/3)k(-5/3), where K-d is a constant and (epsilon) over bar is the energy flux across wave-number k; the energy transfer is forward for d(c) < d <= 3 but inverse for 2 <= d < d(c), where d(c) approximate to 2.065; at d = d(c), K-d diverges and the skewness of the longitudinal velocity difference vanishes; and the d-dependence of the two-time Lagrangian velocity correlation spectra under appropriate normalization is weak in the IETR.