South Adriatic Recipes: Estimating the Vertical Mixing in the Deep Pit

It is shown that the evolution of the vertical temperature structure in the deep South Adriatic Pit (dSAP), below Otranto Strait the sill depth (780m), is well described by a continuous vertical diffusion, a continuous forcing by heat fluxes at the upper boundary (Otranto Strait sill depth) and an intermittent forcing by rare (a few per decade) deep convective and gravity-current events. The analysis is based on two types of data: (i) a 13 years observational data time-series (2006--2019) at 750m, 900m, 1000m and 1200m depth of the temperature from the E2M3A Observatory and (ii) 55 vertical profiles (1985--2019) in the dSAP. The analytical solution of the gravest mode of the heat equation compares well to the temperature profiles and numerical integration of the resulting forced heat-equation compare favourably to the temporal evolution of the time-series data. The vertical mixing coefficient is obtained with three independent methods. The first is based on a best fit of the long term evolution by the numerical diffusion-injection model to the 13-years temperature time-series in the dSAP. The second is obtained by short time (daily) turbulent fluctuations, and a Prandtl mixing length approximation. The third is base on the zero and first mode of an EOF analysis of the time series between (2014--2019). All three methods give a vertical diffusivity of around \kappa = 5 10^{-4}m^{2}s^{-1}. Eigenmodes of the homogeneous heat equation subject to the present boundary conditions are sine functions. It is shown that the gravest mode allows for explaining typically 99.5% of the vertical temperature variability (the first three modes typically explain 99.85%) of the vertical temperature profiles at 1m resolution. The longest time scale of the dissipative dynamics in the dSAP is found to be around 5 years. The first mode of the EOF analysis (85%) represents a constant heating over the entire depth and the zero mode is close to the parabolic profile predicted by the heat equation for such forcing. It is shown that the temperature structure is governed by the continuous warming at the sill depth and deep convective and gravity current events play a less important role.