The Transformation Equations between One- and n-Dimensional Spectra in the n-Dimensional Isotropic Vector or Scalar Fluctuation Field

Abstract

The transformation equations between one- and n-dimensional spectra in the n-dimensional isotropic vector or scalar fluctuation field are derived, the well-known equations for three-dimensional fluctuation field being included as a special case. It is found that the transformation equation for n-dimensional vector fluctuation is of the same form as that for (n+2)-dimensional scalar fluctuation except for the constant coefficient. The spectrum equations for n-dimensional isotropic turbulence and for n-dimensional isotropic temperature fluctuations in the n-dimensional isotropic turbulence are also derived. It is shown that the spectrum equations for any n-dimensional isotropic fluctuations have the same form.