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In this paper, we have investigated the decay process of the kinetic energy density spectrum in a homogeneous isotropic turbulence. It has been shown that the spectral equation for the energy density spectrum E(k) with modified form of energy transfer spectrum due to Obukhov (Compt. Rend. Acad. Sci. U. R. S. S 32:22–24, 1941) and as restricted to early-period decay process, admits of a class of self-preserving...