Spectral characteristics of velocity and vorticity fluxes in an unstratified turbulent boundary layer

Abstract

Wavenumber spectral characteristics of the velocity and vorticity fluxes in an unstratified turbulent boundary layer are presented. The observed vertical and streamwise velocity spectra agree with empirical forms found in the atmospheric boundary layer. Spectral ratios of 4/3 between the vertical and streamwise velocity spectra and the agreement between the observed vorticity flux quad spectrum and that of isotropic turbulence suggest local isotropy at scales smaller than Z. The normalized cospectrum of the momentum flux agrees remarkably well with the empirical form found in the atmospheric boundary layer. In the inertial subrange the momentum flux cospectrum shows a clear spectral slope of −7/3. The observed composite vorticity flux cospectrum has most of its variance at the streamwise wavenumber kx = (1–10) Z−1 and has a spectral slope of −7/3 in the inertial subrange. The −7/3 spectral slope is consistent with a dimensional argument, assuming that the vorticity flux cospectrum is proportional to the gradient of the mean vorticity, and depends on the turbulence kinetic energy dissipation rate ϵ and the wavenumber. A model turbulent vorticity flux cospectrum is constructed based on the shape of observed spectra, a −7/3 spectral slope in the inertial subrange, and the similarity scaling of the vorticity flux in an unstratified turbulent boundary layer. The turbulence vorticity flux is directly related to the divergence of turbulence momentum flux, the force exerted by turbulence on the mean flow. Therefore our proposed empirical cospectral form of the vorticity fluxes might be useful for turbulence parameterization in numerical models.