Intermittency of vertical density gradients at finescale and link with mixing processes

Nonlinear interactions among internal gravity waves lead to intermittent breaking events with density overturning and vertical turbulent mixing. We analyze the statistics of density fluctuations generated in this process, using direct numerical simulations. We then check the relevance of these results for in situ density profiles measured during the ARCANE experiment on the continental slope west of the Iberian peninsula, a region with strong internal tides. We focus the analysis in the depth range [400-1000 m] for which the temperature is uniform, and the density stratification is due mainly to salinity. We verify in the numerical simulations that the histograms of vertical density gradients become strongly skewed at small vertical scales. This intermittency of density fluctuations can be attributed to the formation of sheets with strong stable density gradients. These sheets result from convergent motion produced by surrounding breaking events. We check that the vertical density gradients at finescale can be represented by a model of layers and sheets distributed with a Poisson statistics, with a mean number of sheets per unit length, $\mu$. We next show that the mean sheet spacing $\mu^{-1}$ is proportional to the Ozmidov scale (proportional to the square root of the energy dissipation). Using the classical link between energy dissipation and vertical eddy diffusivity $K_d$, we deduce a link between the statistics of vertical density gradients and the vertical mixing, namely $K_d$ is proportional to $N \mu^{-2}$. For in situ measurements, we find a similar statistics of vertical density gradients, confirming earlier results obtained by Hayes et al. and Pinkel and Anderson in the open ocean thermocline. This allows us to estimate a rate of total energy dissipation and a vertical eddy diffusivity . Comparisons with other estimates of energy dissipation or vertical mixing would be required to validate this method