The advancement in the numerical methods of the scaling function calculation in problem of decaying turbulence

The problem of the calculation of the energy spectrum of velocity modes is studied in the case where the homogeneous and isotropic turbulence evolves near the state of its strong development. The Karman scale is considered to be the principal spectral scale and Saffman's invariant is assumed to be conserved during the power time decay. In the past, the physical problem was formulated by means of complicated system of a integro-differential equations. The deficiency of the preliminary approximations has led us to the development of a novel principal computational scheme based on the function optimization approach.