Abstract
This paper is an extension of our earlier work of solving the whole problem of homogeneous isotropic turbulence from the initial period to the final period of decay. An expansion method has been developed to obtain an axially symmetrical solution of the Navier-Stokes equations of motion in the form of an infinite set of nonlinear partial differential equations of the second order. For the present we solve the zeroth order approximation. By using the method of the Fourier transform, we get a nonlinear integro-differential equation for the amplitude function in the wave number space. It is also the dynamical equation for the energy spectrum.
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