notes_01.md

\chapter{Experimental investigation of mixing in stratified turbulence}

{#fig:thermohaline-global width=80%}

The meridional overturning circulation (MOC) is a global circuit of ocean currents spanning all ocean basins in depth and breadth. This circulation is responsible for the bulk of heat transport from the equator to the poles across the globe. Without this global conveyor belt, shown in @fig:thermohaline-global, the temperatures at latitudes away from the equator would be considerably lesser [@bryden_slowing_2005]. It is also responsible for replenishing the surface water with nutrients and critical to the sustenance of marine life.

{#fig:moc}

The MOC was also known as the thermohaline circulation, due to the misconception that heat and salinity fluxes due to melting of ice near the polar region and evaporation elsewhere as shown in @fig:thermohaline-global. Today, the MOC is thought to be driven by a combination of wind forcing, changes in buoyancy and diapycnal mixing, as shown in @fig:moc, a simplified sketch of the Atlantic MOC. The exact contribution of these three forces remain an open question [see chapter 21 in @vallis_atmospheric_2017]. It should be noted that the circulation happens within a ocean with varying degrees of stable stratification in both temperature and salinity. For illustrating this the time averaged temperature and salinity in the Atlantic ocean [calculated from @carton_soda3_2018] are plotted in @fig:atlantic-salt-temp. It is understood that through mixing, kinetic energy is converted into available potential energy which allows the streamlines to overturn and thus allowing bottom water from great depths to resurface.

{#fig:atlantic-salt width=100%}

{#fig:atlantic-temp width=100%}

Stratification in the Atlantic Ocean along a meridional cross-section at 26.2$^{\circ}$ W, plotted from reanalysis data spanning years 2000-2010.

In the strongly stratified regime, mixing coefficient values have been found to be in the range, $\Gamma \in [0.26, 0.51]$ [@BrethouwerLindborg2009;@maffioli_mixing_2016], thus significantly larger than the canonical value of $\Gamma = 0.2$. In @maffioli_mixing_2016, high resolution DNS of Boussinesq equation suggested that the mixing coefficient peaks at an intermediate $Fr \approx 0.29$ with $\Gamma \approx 0.51$ and then for stronger stratifications a declining trend up to $Fr \approx 0.02$ with $\Gamma \approx 0.33$ was recorded. Also note that, as shown in @fig:stratified-regime, oceans measurements are considerably more stratified [@gargett_composite_1981].

The question of what value the mixing coefficient would tend to at higher levels of stratification, is at the heart of the project titled Mixing and Length Scales in Stratified Turbulence (MILESTONE) [@ISSF2016].

Preliminary results

In M16, the carriage is accelerated over a length of 0.25 cm and moved at constant speed over 5.5m. The constant speed is varied from 2 cm/s to 16 cm/s in different runs. In M17, the carriage is accelerated over 0.5 cm and travels at constant speed over 5m. The constant speed is varied from 1 cm/s up to 24 cm/s.