Local isotropy and the decay of turbulence in a stratified fluid

Abstract

The validity of the assumption of local isotropy is investigated using measurements of three orthogonal components of the turbulent velocity fields associated with initially high-Reynolds-number geophysical turbulence. The turbulent fields, generated by various large-scale internal motions caused by tidal flows over an estuarine sill, decay under the influence of stable mean density gradients. With measurements from sensors mounted on a submersible, we examine the evolution of spectral shapes and of ratios of cross-stream to streamwise components, as well as the degree of high-wavenumber universality, for the observational range of the parameterI≡ks/kb=lb/ls. This ratio is a measure of separation between the Kolmogoroff wavenumberks≡ (ε/ν3)¼≡ 2π/lstypical of scales by which turbulent kinetic energy has been dissipated (at rate ε), and the buoyancy wavenumberkb≡ (N3/ε)½≡ 2π/lbtypical of scales at which the ambient stratification parameterN≡ (−gρz/ρ0)½becomes important. For values of I larger than ∼ 3000, inertial subranges are observed in all spectra, and the spectral ratio ϕ22/ϕ11of cross-stream to streamwise spectral densities reaches the isotropic value of 4/3 for about a decade in wavenumber. As ks/kbdecreases, inertial subranges vanish, but spectra of the cross-stream and streamwise components continue to satisfy isotropic relationships at dissipation wavenumbers. We provide a criterion for when ε may safely be estimated from a single measured component of the dissipation tensor, and also explore questions of appropriate low-wavenumber normalization for buoyancy-modified turbulence.