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

Abstract

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 Kd|ε¯|2/3k−5/3, where Kd is a constant and ε¯ is the energy flux across wave-number k; the energy transfer is forward for dcd≤3 but inverse for 2≤ddc, where dc≈2.065; at d=dc, Kd 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.

Keywords

• <i>d</i>-dimensional turbulence
• inertial energy transfer range
• Lagrangian renormalized approximation