Energy transfer in spectra of the d-dimensional past grid turbulence

Free decay theory of the homogeneous and isotropic developed turbulence is considered in the d-dimensional case. The basic quantities under our consideration are the kinetic energy spectrum E(k, t) and energy transfer spectrum T(k, t) as functions of wave number k and decay time t. Starting point for studying E and T represents their adaptation from the stationary model which predicts the Kolmogorov spectrum which is multiplicatively dependent on an unknown scaling function F. In order to study the spectra of decaying turbulence both parameters I and E are supposed to be dependent on t. Formerly derived basic integro-differential equation for F (by Adzhemyan et al., 1998) has been here solved numerically in the dimension interval d is an element of (2, 3) for two cases of the Saffman invariant and the Loitsyansky integral fixing an arbitrary theory parameter alpha (alpha = 2 and 4, correspondingly). ne energy transfer spectrum T(k) has been analyzed for several dimensions d <= 3 showing the presence of integration regions in the wavenumber space where an inverse energy cascade can occur.