MODIFIED SELF-SCALING RELATION FOR THE INERTIAL AND LOW-ENERGY CONTAINING SCALES OF DECAYING TURBULENCE

The limits of a new form of scaling, named Extended Self Similarity (E SS) originally suggested [R. Benzi ct al., Phys. Rev. E48 (1993), 29] for the inertial, dissipation and transition scales are discussed. A m odification of the ESS concept is put forward using the model of decay ing turbulence at high Reynolds numbers [L. Ts. Adzhemyan et al., Czec h. J. Phys. 45 (1995), 517]. In this model the statistical description is simplified by the hypotheses of homogeneity, isotropy, incompressi bility and self-similarity, for the power law stage of decay the prese nce of a single scaling length - Karman scale - is assumed within the energy containing range. The second and third structure functions of t he velocity field [S-2(r) and S-3(r)] have been calculated using the w ell-known connections between the mean energy spectrum and S-2(r), and between mean spectral transfer and third structure function S-3(r) Bo th structure functions have been investigated in the inertial and low enery containing ranges, then expressed in the form involving the lead ing Kolmogorov's K41 asymptotics [S-2(r) proportional to r(2/3), S-3(r ) proportional to r] and its asymptotical corrections. These correctio ns allow to determine corrections to the original ESS form S-2 proport ional to S-3(2/3) (for K41) and to find out the modified variant of th e ESS.