The influence of stable stratification on small‐scale anisotropy and dissipation in turbulence

Abstract

Small‐scale turbulence measurements in stably stratified grid‐generated turbulence show that strong stable stratification induces large anisotropies in the mean‐square strain rates ∂v/∂x and ∂w/∂x, relative to ∂u/∂x. This effect is magnified with increased strength of stratification. Froude number scaling is partially successful in collapsing the data. Anisotropies of the strain rates associated with the small scales are found to develop relatively faster than the anisotropy of the large‐scale energy containing eddies. The mean‐square magnitude of the ∂w/∂x strain rate is up to 4 times lower than the level predicted from ∂u/∂x based on isotropy. These results cast doubt on the accuracy of employing conventional dissipation estimates based on the assumption of local isotropy in stratified turbulence, at least for the low Reynolds numbers characterizing these experiments. These results are especially relevant to ocean microscale measurements, as buoyancy affected turbulence with similar dynamical character, i.e., ε/νN2 of similar magnitudes, has been observed in the thermocline (see Gregg and Sanford, 1988; Yamazaki, 1990). Estimates of dissipation rates based on the formulations of Stillinger et al. (1983) and Yamazaki and Osborn (1990) are shown to disagree by as large as a factor of 2. The measurements also show that stable stratification induces anisotropy in the lateral horizontal rms velocity component in addition to the well‐known vertical anisotropy. The lateral anisotropy is about half of the vertical anisotropy. Measured spectral relations between the stream wise and lateral velocity components in the horizontal plane were compared with relations predicted by the two‐ and three‐dimensional (2‐D and 3‐D) isotropic theories. Comparison of measured and calculated lateral spectra indicate no tendency toward the development of 2‐D turbulence in the range of Froude numbers studied.