On the solutions of NavierStokes equations and the theory of homogeneous isotropic turbulence
Abstract
The expansion method used here has been developed to obtain an axially symmetrical solution to the NavierStokes equations of motion in the form of an infinite set of nonlinear partial differential equations of the second order. For the present, the zeroth order approximation is solved. By using the method of the Fourier transform, a nonlinear integrodifferential equation is obtained for the amplitude function in the wave number space. This is also the dynamical equation for the energy spectrum. By choosing a suitable initial condition, this equation is solved numerically. The energy spectrum function and the energy transfer spectrum function thereby calculated satisfy the spectrum form of the KarmanHowarth equation exactly. Computations are made of the energy spectrum function, the energy transfer function, the decay of turbulent energy, the integral scale, the Taylor microscale, and the double and triple velocity correlations on the whole range from the initial period to the final period of decay.
 Publication:

NASA STI/Recon Technical Report A
 Pub Date:
 August 1981
 Bibcode:
 1981STIA...8221694H
 Keywords:

 Computational Fluid Dynamics;
 Energy Spectra;
 Energy Transfer;
 Homogeneous Turbulence;
 Isotropic Turbulence;
 NavierStokes Equation;
 Flow Velocity;
 Fourier Transformation;
 Nonlinear Equations;
 Fluid Mechanics and Heat Transfer