Local isotropy and the decay of turbulence in a stratified fluid

TLDR

Turbulent fields generated by tidal flows over an estuarine sill decay under stable density gradients, with the ratio I quantifying the separation between Kolmogorov and buoyancy scales. The study tests the local isotropy assumption in high‑Reynolds‑number geophysical turbulence and develops a criterion for estimating dissipation from a single velocity component while addressing low‑wavenumber normalization in buoyancy‑modified turbulence. Using submersible‑mounted sensors, the authors measured three velocity components to analyze spectral shapes, cross‑stream to stream.

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 parameter I ≡ k s / k b = l b / l s . This ratio is a measure of separation between the Kolmogoroff wavenumber k s ≡ (ε/ν 3 ) ¼ ≡ 2π/ l s typical of scales by which turbulent kinetic energy has been dissipated (at rate ε), and the buoyancy wavenumber k b ≡ ( N 3 /ε) ½ ≡ 2π/ l b typical of scales at which the ambient stratification parameter N ≡ (− g ρ z /ρ 0 ) ½ becomes important. For values of I larger than ∼ 3000, inertial subranges are observed in all spectra, and the spectral ratio ϕ 22 /ϕ 11 of cross-stream to streamwise spectral densities reaches the isotropic value of 4/3 for about a decade in wavenumber. As k s /k b decreases, 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.