Efficient mixing in stratified flows: experimental study of a Rayleigh–Taylor unstable interface within an otherwise stable stratification

Abstract

Boussinesq salt-water laboratory experiments of Rayleigh-Taylor instability (RTI) can achieve mixing efficiencies greater than 0.75 when the unstable interface is confined between two stable stratifications. This is much greater than that found when RTI occurs between two homogeneous layers when the mixing efficiency has been found to approach 0.5. Here, the mixing efficiency is defined as the ratio of energy used in mixing compared with the energy available for mixing. If the initial and final states are quiescent then the mixing efficiency can be calculated from experiments by comparison of the corresponding density profiles. Varying the functional form of the confining stratifications has a strong effect on the mixing efficiency. We derive a buoyancy-diffusion model for the rate of growth of the turbulent mixing region, h = 2 √ αAgh (where A = A(h) is the Atwood number across the mixing region when it extends a height h, g is acceleration due to gravity and α is a constant). This model shows good agreement with experiments when the value of the constant α is set to 0.07, the value found in experiments of RTI between two homogeneous layers (where the height of the turbulent mixing region increases as h = αAgt 2 , an expression which is equivalent to that derived forḣ).

Inclined gravity currents filling basins: The influence of Reynolds number on entrainment into gravity currents

“…This non-dimensionalisation did not successfully collapse the data onto the theoretical curve given by (13). The high flow rate experiments filled more quickly than the theoretical curve and the low flow rate experiments filled more slowly than the theoretical curve.…”

“…The experimental apparatus is shown in figure 1 The position of the front of the fluid ponding at the bottom of the basin (shown diagrammatically in figure 2) was found from an aspirated conductivity probe on a belt-driven linear traverse 13 . The traverse was oriented perpendicular to the base of the tank.…”

On the meaning of mixing efficiency for buoyancy-driven mixing in stratified turbulent flows

“…The reason that this class of flows is so useful is that they have a well-defined final density profile, observed in both laboratory experiments (Lawrie & Dalziel 2011b;Davies Wykes & Dalziel 2014) and numerical simulations (Lawrie & Dalziel 2011b). Specifically, laboratory experiments (with a fluid assumed to be miscible with a linear equation of state) have a final density profile very close to the one that we will refer to as the perfect mixing profile.…”

Vortex-ring-induced stratified mixing

“…By attaching a fast response thermistor (P25 NTC type, General Electric) to the conductivity probe, we measured both the conductivity and temperature of the water and, assuming no other solute in the fluid volume, we can back out the fluid density. This methodology is similar to that preformed in Davies Wykes & Dalziel (2014), and the reader is referred there for further information. The relative error in the point density measurements in this method has been shown to be O(0.1 %) of the density range with which it has been calibrated.…”

“…Mixing efficiency measurements are complicated owing to the large number of variables that must be measured in the system. A number of experimentally (Prastowo et al 2008(Prastowo et al , 2009Davies Wykes & Dalziel 2014) and numerically (Peltier & Caulfield 2003;Scotti & White 2011;Gayen, Hughes & Griffiths 2013) measured mixing efficiencies have been reported. However, these results are typically measurements for internally mixed problems (Turner 1979), where the mixing mechanism is generated near the mixing location.…”