Turbulence Spectrum in Chandrasekhar's Theory

Abstract

The results of Chandrasekhar's recent theory of turbulence are transformed in this paper from ordinary space (used exclusively in his paper) to wave-number space. Consideration is limited to the case of stationary, homogeneous, and isotropic turbulence. A "time-dependent spectrum" is defined in terms of the scalar product of eddy velocities at two different times; this spectrum is related to Chandrasekhar's time-dependent correlation function by a Fourier transform, as in the conventional, time-independent case. For infinite Reynolds number the spectrum is obtained directly by transforming the correlation function into wavenumber space; the spectrum is given by a much simpler expression than is the corresponding correlation function.