Abstract
We study in this paper the correlation between the buoyancy flux, the efficiency of energy dissipation and the linear and nonlinear components of potential vorticity, PV, a point-wise invariant of the Boussinesq equations, contrasting the three identified regimes of rotating stratified turbulence, namely wave-dominated, wave–eddy interactions and eddy-dominated. After recalling some of the main novel features of these flows compared to homogeneous isotropic turbulence, we specifically analyze three direct numerical simulations in the absence of forcing and performed on grids of 10243 points, one in each of these physical regimes. We focus in particular on the link between the point-wise buoyancy flux and the amount of kinetic energy dissipation and of linear and nonlinear PV. For flows dominated by waves, we find that the highest joint probability is for minimal kinetic energy dissipation (compared to the buoyancy flux), low dissipation efficiency and low nonlinear PV, whereas for flows dominated by nonlinear eddies, the highest correlation between dissipation and buoyancy flux occurs for weak flux and high localized nonlinear PV. We also show that the nonlinear potential vorticity is strongly correlated with high dissipation efficiency in the turbulent regime, corresponding to intermittent events, as observed in the atmosphere and oceans.
Highlights
We examine the link between kinetic energy dissipation, buoyancy flux and the magnitude of both the linear and nonlinear part of potential vorticity through the analysis of joint Probability Distribution Functions (PDFs)
We focus on three runs that are characteristic of the three regimes encountered in rotating stratified turbulence (RST), namely regime I dominated by quasilinear inertia-gravity waves, regime II in which there is a competition between these waves and nonlinear eddies due to the advection terms of the hydrodynamics and regime III dominated by the nonlinear eddies which can at times be faster than the waves
The results presented in this paper show in particular that the nonlinear part of potential vorticity, Π NL = ω · ∇θ, which is weak initially for initial conditions centered on large scales, comes to dominate small-scale dynamics and is strongly correlated with highly efficient local dissipation involving local instabilities
Summary
The competition between rotation leading to the energy moving to large scales, at a rate eUP and stratification transferring energy to the (small) dissipative scales at a rate edown , has been analyzed recently [14,15]. Oceanographic measurements in the vicinity of the Hawaiian ridge indicate the presence of patches of strong dissipation: with N = 10−3 s−1 and urms ≈ 0.1 ms−1 the rms velocity, the measured kinetic energy dissipation is eV ≈ 10−6 W [16] These data correspond to the dimensional evaluation of dissipation for a length scale of 1 km, which is typical of the tidal excitation due to the bathymetry.
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