A note on Kolmogorov's −5/3 scaling law in a non-inertial frame of reference

This note presents a theoretical study on Kolmogorov's −5/3 scaling law under a change of frame of reference and, in particular, its corresponding form in a non-inertial frame of reference. First, we show that the Kolmogorov scales in the universal equilibrium range and the turbulent kinetic energy spectrum function E(κ, t) are not frame-indifferent, i.e., frame-dependent, in the sense of Truesdell and Noll (1965). Moreover, we investigate the aspects of the scaling coefficient C K under a change of frame of reference and arrive at a generalized Kolmogorov's −5/3 scaling law in a non-inertial frame of reference, which is frame-dependent and in an inertial frame of reference reduces to the form stemming from Kolmogorov's 1941 paper.