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

AbstractBoussinesq 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, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\dot{h} = 2 \sqrt{\alpha A g h}$ (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 $\alpha$ is a constant). This model shows good agreement with experiments when the value of the constant $\alpha$ 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 $h =\alpha A g t^2$, an expression which is equivalent to that derived for $\dot{h}$).This work was funded by EPSRC (grant number EP/P505445/1) and an AWE CASE award (AWE contract number 30174006).This is the accepted manuscript. The final version is available from CUP at http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9346643&fileId=S0022112014003085. This work is © British Crown Copyright 2014/AWE

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

The concept of a mixing efficiency is widely used to relate the amount of irreversible diabatic mixing in a stratified flow to the amount of energy available to support mixing. This common measure of mixing in a flow is based on the change in the background potential energy, which is the minimum gravitational potential energy of the fluid that can be achieved by an adiabatic rearrangement of the instantaneous density field. However, this paper highlights examples of mixing that is primarily ‘buoyancy-driven’ (i.e. energy is released to the flow predominantly from a source of available potential energy) to demonstrate that the mixing efficiency depends not only on the specific characteristics of the turbulence in the region of the flow that is mixing, but also on the density profile in regions remote from where mixing physically occurs. We show that this behaviour is due to the irreversible and direct conversion of available potential energy into background potential energy in those remote regions (a mechanism not previously described). This process (here termed ‘relabelling’) occurs without requiring either a local flow or local mixing, or any other process that affects the internal energy of that fluid. Relabelling is caused by initially available potential energy, associated with identifiable parcels of fluid, becoming dynamically inaccessible to the flow due to mixing elsewhere. These results have wider relevance to characterising mixing in stratified turbulent flows, including those involving an external supply of kinetic energy.G.O.H. was supported by Australian Research Council Future Fellowship FT100100869 and was hosted by DAMTP during this work. M.S.D.W. was funded by EPSRC (grant number EP/P505445/1) and an AWE CASE award (AWE contract number 30174006).This is the author accepted manuscript. The final version is available from Cambridge University Press via http://dx.doi.org/10.1017/jfm.2015.46

The effect of an indoor-outdoor temperature difference on transient cross-ventilation

We examine the effect of an indoor-outdoor temperature difference on the transient wind-driven cross-ventilation of a room. Laboratory experiments are performed in a water flume using a reduced-scale model room. For solely wind-driven cross-ventilation with no initial temperature difference between the room and the external fluid, the ventilation rate is constant. In experiments, the mean dye concentration decays exponentially, which is expected when the room remains well-mixed. When there is an initial temperature difference but no wind, the buoyancy-driven exchange-ventilation results lie between a model that assumes the room is well-mixed and a new model that assumes no mixing between the incoming flow and the room. When both wind and buoyancy drive the flow, the relative importance of these two effects can be described by a Froude number, Fr. For buoyancy-dominated ventilation (Fr1), a temperature difference slightly reduces the ventilation rate, but only by up to 6%, a change that can be neglected in most applications. Two processes compete to ventilate the room in combined cases: the removal of fluid from a lower layer by flow through the windows and the erosion of an upper layer by entrainment into the jet that crosses the room. The relative rates of these two processes depend on the geometry of the room.This work is supported by the Engineering and Physical Sciences Research Council (EPSRC) Grand Challenge grant Managing Air for Green Inner Cities (MAGIC) [grant number EP/N010221/1]

Shaping of melting and dissolving solids under natural convection

How quickly does an ice cube melt or a lump of sugar dissolve? We address the open problem of the shapes of solids left to melt or dissolve in an ambient fluid driven by stable natural convection. The theory forms a convective form of a Stefan problem in which the evolution is controlled by a two-way coupling between the shape of the body and stable convection along its surface. We develop a new model describing the evolution of such bodies in two-dimensional or axisymmetric geometries and analyse it using a combination of numerical and analytical methods. Different initial conditions are found to lead to different fundamental shapes and descent rates. For the cases of initially linear surfaces (wedges or cones), the model admits similarity solutions in which the tip descends from its initial position as t4/5 , where t is time. It is determined that the evolving shape always forms a parabola sufficiently near the tip. For steeply inclined bodies, we establish a general two-tiered asymptotic structure comprising a broad 4/3 -power intermediate near-tip region connected to a deeper parabolic region at the finest scale. The model results apply universally for any given relationship between density, viscosity, diffusivity and concentration, including two-component convection. New laboratory experiments involving the dissolution of cones of sugar candy in water are found to collapse systematically onto our theoretically predicted shapes and descent rates with no adjustable parameters

Energetics of mixing for the filling box and the emptying-filling box

The mixing efficiency of a plume in a filling box and an emptying-filling box is calculated for both transient and steady states. The mixing efficiency of a plume in a filling box in an asymptotic steady state is 1/2, independent of the details of this state or how the plume is modelled. The mixing efficiency of a plume in an emptying-filling box in steady state is 1 - xi, where xi = h/H, the depth of the ambient layer h non-dimensionalised by the height of the box H. A deeper mixed layer therefore corresponds to a higher mixing efficiency

Effects of ventilation on the indoor spread of COVID-19.

Although the relative importance of airborne transmission of the SARS-CoV-2 virus is controversial, increasing evidence suggests that understanding airflows is important for estimation of the risk of contracting COVID-19. The data available so far indicate that indoor transmission of the virus far outstrips outdoor transmission, possibly due to longer exposure times and the decreased turbulence levels (and therefore dispersion) found indoors. In this paper we discuss the role of building ventilation on the possible pathways of airborne particles and examine the fluid mechanics of the processes involved

Guiding microscale swimmers using teardrop-shaped posts.

The swimming direction of biological or artificial microscale swimmers tends to be randomised over long time-scales by thermal fluctuations. Bacteria use various strategies to bias swimming behaviour and achieve directed motion against a flow, maintain alignment with gravity or travel up a chemical gradient. Herein, we explore a purely geometric means of biasing the motion of artificial nanorod swimmers. These artificial swimmers are bimetallic rods, powered by a chemical fuel, which swim on a substrate printed with teardrop-shaped posts. The artificial swimmers are hydrodynamically attracted to the posts, swimming alongside the post perimeter for long times before leaving. The rods experience a higher rate of departure from the higher curvature end of the teardrop shape, thereby introducing a bias into their motion. This bias increases with swimming speed and can be translated into a macroscopic directional motion over long times by using arrays of teardrop-shaped posts aligned along a single direction. This method provides a protocol for concentrating swimmers, sorting swimmers according to different speeds, and could enable artificial swimmers to transport cargo to desired locations

The ventilation of buildings and other mitigating measures for COVID-19: a focus on wintertime.

The year 2020 has seen the emergence of a global pandemic as a result of the disease COVID-19. This report reviews knowledge of the transmission of COVID-19 indoors, examines the evidence for mitigating measures, and considers the implications for wintertime with a focus on ventilation.This work was undertaken as a contribution to the Rapid Assistance in Modelling the Pandemic (RAMP) initiative, coordinated by the Royal Society

The ventilation of buildings and other mitigating measures for COVID-19: a focus on wintertime.

The year 2020 has seen the emergence of a global pandemic as a result of the disease COVID-19. This report reviews knowledge of the transmission of COVID-19 indoors, examines the evidence for mitigating measures, and considers the implications for wintertime with a focus on ventilation

Shaping of melting and dissolving solids under natural convection

How quickly does an ice cube melt or a lump of sugar dissolve? We address the open problem of the shapes of solids left to melt or dissolve in an ambient fluid driven by stable natural convection. The theory forms a convective form of a Stefan problem in which the evolution is controlled by a two-way coupling between the shape of the body and stable convection along its surface. We develop a new model describing the evolution of such bodies in two-dimensional or axisymmetric geometries and analyse it using a combination of numerical and analytical methods. Different initial conditions are found to lead to different fundamental shapes and descent rates. For the cases of initially linear surfaces (wedges or cones), the model admits similarity solutions in which the tip descends from its initial position as, where t is time. It is determined that the evolving shape always forms a parabola sufficiently near the tip. For steeply inclined bodies, we establish a general two-tiered asymptotic structure comprising a broad -power intermediate near-tip region connected to a deeper parabolic region at the finest scale. The model results apply universally for any given relationship between density, viscosity, diffusivity and concentration, including two-component convection. New laboratory experiments involving the dissolution of cones of sugar candy in water are found to collapse systematically onto our theoretically predicted shapes and descent rates with no adjustable parameters