Spectral characteristics of surface‐layer turbulence

TLDR

Spectra and cospectra of surface‑layer turbulence are examined using similarity theory and 1968 AFCRL Kansas wind and temperature data. The study compares the derived spectra and cospectra with data from other land and water experiments. With appropriate normalization, the spectra and cospectra collapse onto a universal curve in the inertial subrange, where velocity spectra follow a −5/3 law, temperature spectra −5/2, and cospectra uω and ωθ follow −7/3; high‑frequency behavior matches local isotropy, spectral constants are quantified, and a 4/3 ratio between transverse and longitudinal levels is observed at scales comparable to the height or L/10, with the isotropic limit controlled by shear and buoyancy.

Abstract

Abstract The behaviour of spectra and cospectra of turbulence in the surface layer is described within the framework of similarity theory using wind and temperature fluctuation data obtained in the 1968 AFCRL Kansas experiments. With appropriate normalization, the spectra and cospectra are each reduced to a family of curves which spread out according to z/L at low frequencies but converge to a single universal curve in the inertial subrange. The paper compares these results with data obtained by other investigators over both land and water. Spectral constants for velocity and temperature are determined and the variability in the recent estimates of the constants is discussed. The high‐frequency behaviour is consistent with local isotropy. In the inertial subrange, where the spectra fall as n −5/3 , the cospectra fall faster: uω and ωθ as n −7/3 , and u θ, on the average, as n −5/2 . The 4/3 ratio between the transverse and longitudinal spectral levels is observed at wavelengths of the order of the height above ground under unstable conditions and at wavelengths of the order of L/10 under stable conditions. This lower isotropic limit is shown to be governed by the combined effects of shear and buoyancy on small‐scale eddies.