Direct observations of general geothermal convection in deep Mediterranean waters

Abstract

Like elsewhere in the deep sea, life in the deep Mediterranean depends on turbulent exchange across the stable vertical density stratification for supply of nutrients and oxygen. Commonly modelled, turbulent exchange is inversely proportional to the stratification rate. However, this proportionality depends on the particular turbulence type, whether it is driven by vertical current differences (shear) or by buoyancy (convection). While shear turbulence is well observed in stratified seas, direct observations of convection turbulence are limited. In this paper, high-resolution moored temperature observations show that Mediterranean Sea waters are not stagnant in the lower 109 m above the seafloor at 2480 m, although variations are in the range of only 0.0001–0.001 °C. In winter, convection turbulence is regularly observed. Fortnightly averaged spectra show a collapse to the inertial-subrange scaling of dominant shear turbulence for data from about 100 m above the seafloor, and to the buoyancy-subrange scaling of dominant convection turbulence at about 10 m above the seafloor. Time-depth images reveal details of convection turbulence driven from below, which is considered primarily due to general geothermal heating through the Earth crust not related to volcanic vents. When its observation is not masked by (sub-)mesoscale eddies that advect warmer, stratified waters from above, the geothermal heat flux matches the deep-sea turbulence dissipation rate, if in the calculations a mixing efficiency of 0.5 is taken typical for natural convection, integration is over 250 m above the seafloor as confirmed from shipborne CTD, and if maximum 2-m-scale buoyancy frequency replaces its 100-m-scale mean equivalent.

Appendix. Moored T-sensor turbulence values

Over the vertical range of moored T-sensors, the conservative temperature-density anomaly (Θ-σ₂) consistent relationship amounts,

$${\delta \sigma }_{2}/\delta\Theta =-0.85\pm 0.05\mathrm{kg }{\mathrm{m}}^{-3}{^\circ{\rm C} }^{-1}.$$

(A1)

The relatively tight relationship (A1) implies the T-sensor data may be used as a proxy for density variations and in which salinity contributions are implicitly incorporated. The relationship is useful for inferring turbulence values using the method of reordering unstable data-points to monotonously stable vertical profiles (Thorpe 1977). Turbulent overturns follow reordering every 2 s the 109-m-high (for corner lines) potential density profile σ₂(z), which may contain inversions, into a stable monotonic profile σ₂(z_s) without inversions. After comparing observed and reordered profiles, displacements d = min(|z − z_s|)⋅sgn(z − z_s) are calculated necessary for generating the reordered stable profile. Then, the turbulence kinetic energy dissipation rate reads,

$$\upvarepsilon =0.64{\mathrm{d}}^{2}{\mathrm{N}}^{3},$$

(A2)

where buoyancy frequency N is computed from each of the reordered, essentially statically stable, vertical density profiles.

The numerical constant follows from empirically relating the root-mean-square (rms) overturning scale d_rms = (Σd²/n)^0.5 over n samples with rms-Ozmidov scale

$${\mathrm{L}}_{\mathrm{O}}={\left({\upvarepsilon /\mathrm{N}}^{3}\right)}_{\mathrm{rms}}$$

(A3)

of largest isotropic turbulence overturns in a stratified fluid as an average over many realizations via the ratio: L_O/d_rms = 0.8 (Dillon 1982). This ratio reflects turbulence in any high Reynolds number stably stratified environment like the deep sea, in which shear-driven and convection turbulence intermingle at small and large scales and are difficult to separate. In all cases, the mechanical turbulence must work against the stratification that follows from the reordering. It has thus successfully been applied for mainly convection turbulence (e.g. Chalamalla and Sarkar 2015; Kumar et al. 2021) while first used for mainly shear turbulence (Thorpe 1977). Comparison between calculated turbulence values using shear measurements and using Thorpe overturning scales with above constant led to ‘consistent results’ (Nash et al. 2007).

Likewise, using a constant mixing efficiency of Γ = 0.2 after substantial and suitable averaging (Osborn 1980; Oakey 1982; Gregg et al. 2018), vertical turbulent diffusivity is computed as,

$${\mathrm{K}}_{\mathrm{Z}}=\mathrm{\Gamma \varepsilon }{\mathrm{N}}^{-2}.$$

(A4)

In (A2), and thus (A4), individual d are used rather than taking their rms-value across a single overturn as originally proposed by Thorpe (1977). The reason is that individual overturns cannot easily be distinguished, first, because they are found at various scales with small ones overprinting larger overturns, and second, because some overturns exceed the range of T-sensors. ‘Sufficient’ averaging is required, also to include various turbulence types of different scales and different age with potentially different L_O/d_rms-ratio (Chalamalla and Sarkar 2015) during a turbulent overturn lifetime. While shipborne vertical profiling instruments limit to vertical data averaging, the advantage of a densely instrumented mooring line is also averaging data over time.