Spectral transfer of scalar and velocity fields in heated-grid turbulence

Abstract

For locally isotropic, homogeneous fluid turbulence, a digital Fourier analysis method of measuring directly the net scalar and velocity spectral transfer Tn(k) of scalar and kinetic energy to a pa;rticular wavenumber from all other wave-numbers is described and applied to heated-grid turbulence. The technique uses the imaginary part of a particular cross-spectrum to obtain the one-dimensional net spectral transfer function Ln(k1) of velocity and scalar turbulence, and is a refinement of that used previously by Van Atta & Chen for measuring the velocity kinetic energy transfer.The detailed spectral transfer Tn(k, k′) from one wavenumber to any other is related to the imaginary part of a particular three-dimensional bispectrum. Tn(k, k′) can be, in principle, computed from a particular two-dimensional triple correlation. Unlike Tn(k), which can be obtained from Ln(k1), Tn(k, k′) cannot be determined from the measurable one-dimensional bippectrum B1, n, n (k1, k1′) nor the one-dimensional transfer spectrum Ln(k1, k1′).The measured net transfer spectra Tn(k) have been used to determine the extent of validity for heated-grid turbulence of the dynamical equations for the three-dimensional power spectra of temperature and velocity in locally isotropic turbulence. The measured temperature transfer spectrum is also compared with those obtained from the power spectra of velocity and temperature by using various simple hypotheses.