Spectra and energy transfer in stably stratified turbulence

Abstract

The influence of stabilizing buoyancy forces on the spectral characteristics and spectral energy transfer of grid-generated turbulence was studied in a ten-layer closed-loop stratified water channel. The results are compared to the limiting ideal cases of the three-dimensional turbulence and two-dimensional turbulence theories. The velocity power spectra evolve from a classical isotropic shape to a shape of almost k⁻² after the suppression of the net vertical mixing. This final spectral shape is rather different from the k⁻³ to k⁻⁴ predicted by the theory of two-dimensional turbulence and could result from the interaction between small-scale internal waves and quasi-two-dimensional turbulent structures as well as some Doppler shift of advected waves. Several lengthscales are derived from the cospectra of the vertical velocity and density fluctuations and compared with the buoyancy, overturning and viscous lengthscales measured in previous studies, e.g. Stillinger, Helland & Van Atta (1983) and Itsweire, Helland & Van Atta (1986). The smallest turbulent scale, defined when the buoyancy flux goes to zero, can be related to the peak of the cospectra of the buoyancy flux. This new relationship can be used to provide a measure of the smallest turbulent scale in cases where the buoyancy flux never goes to zero, i.e. a growing turbulent stratified shear flow. Finally, the one-dimensional energy transfer term computed from the bispectra shows evidence of a reverse energy cascade from the small scales to the large scales far from the grid where buoyancy forces dominate inertial forces. The observed reverse energy transfer could be produced by the development of quasi-two-dimensional eddies as the original three-dimensional turbulence collapses.