Turbulence decay in stratified and homogeneous marine layers

Abstract

A spectral approach is applied to shear-induced turbulence in stratified layers. A system of spectral equations for stationary balance of turbulent energy and temperature variances was deduced in the vicinity of the local shear scale LU = (ϵ/UZ3)12. At wavenumbers between the inertial-convective (k−53) and wak turbulence (k−3) subranges, additional narrow spectral intervals—‘production’ subranges—may appear (E ∽ k−1, ET ∽ k−2). The upper boundary of these subranges is determined as LU, and the lower boundaries as LR ∽ (ϵ/UZN2)12(χ/TZ2). It is shown that the scale LU is a unique spectral scale that is uniform up to a constant value for every hydrophysical field. It appears that the spectral scale LU is equivalent to the Thorpe scale LTh for the active turbulence model. Therefore, if turbulent patches are generated in a background of permanent mean shear, a linear relation between temperature and mass diffusivities exists. In spectral terms, the fossil turbulence model corresponds to the regime of the Boldgiano-Obukhov buoyancy subrange (E ∽ k−115, ET ∽ k−75). During decay the buoyancy subrange is expanded to lower and higher wavenumbers. At lower wavenumbers the buoyancy subrange is bounded by L∗∗ = 3(χ12/N12TZ), which is equivalent to the Thorpe scale LTh. In such a transition regime only, when the viscous dissipation rate is removed from the set of main turbulence parameters, the Thorpe scale does not correlate with the buoyancy scale LN ∽ ϵ12/N32 and fossil turbulence is realized. Oceanic turbulence measurements in the equatorial Pacific near Baker Island confirm the main ideas of the active and fossil turbulence models.