Turbulence spectra and local similarity scaling in a strongly stratified oceanic bottom boundary layer

Abstract

In the turbulence inertial subrange, wavenumber spectra of vertical velocity and streamwise velocity in a strongly stratified oceanic bottom boundary layer agree with the local similarity scaling laws found previously in the stable atmospheric boundary layer. At scales greater than the turbulence inertial subrange, oceanic velocity spectra exceed the universal spectra. This additional energy at large scales could be due either to internal waves, inappropriate estimates of turbulence parameters, or non-stationarity of the data. Providing that the energy containing eddies in the stratified boundary layer have a scale close to the Ozmidov scale, ε 1/2 N −3/2, where ε is the turbulence kinetic energy dissipation rate and N is the buoyancy frequency, the universal model spectrum leads to a turbulent scaling ε= βNσ w 2, where β is a dimensionless constant 0.6–1.5 and σ w 2 is the vertical velocity variance. This scaling law of ε has been found in free shear flows in the ocean and atmosphere. The turbulence Reynolds stress is related to the vertical velocity variance as −〈 u′ w′〉=1/4 σ w 2. The strong stratification in the observed tidal bottom boundary layer is maintained by the advective density gradient. Results reported here include the effects of horizontal advection.