Session E34: Geophysical Fluid Dynamics: Stratified Flows II

Miscible Viscous Gravity Currents

Full- and partial-depth lock-release laboratory experiments are performed examining the evolution of a glycerol solution being released into an ambient fluid of either fresh or salty water. The advance of the current front and the depth of the current from its head back to the lock are tracked over time. While the viscosity of pure glycerol is sufficiently high to retard mixing between the current and ambient fluid, where mixing does occur the viscosity reduces significantly so permitting more turbulent mixing to occur. Meanwhile viscous stresses at the bottom of the current introduces shear within the boundary layer which extends vertically over a significant fraction of the current's depth. Thus, even though there is no evidence of a lubrication layer below the current, the current nonetheless advances initially at speeds close to those of effectively inviscid gravity currents. As the viscous boundary layer depth becomes comparable to the current depth in the tail the fluid slows dramatically while the turbulent front continues to advance, slowing as it becomes depleted of fluid.   

Study of mixing efficiency of a buoyant plume using velocity and density measurements

Experiments were performed to quantify the mixing dynamics of a buoyant plume intruding vertically into a linear stably stratified environment ($N=$ 0.2s$^{\mathrm{-1}})$. Simultaneous measurements of velocity and density fields were achieved using a combination of Particle Image Velocimetry (PIV) and Planar Laser Induced Fluorescence (PLIF). The refractive indices of the ambient and the plume fluid were matched to avoid optical aberrations. The production flux ($P)$, buoyancy flux ($B)$, and dissipation ($\varepsilon )$ in the kinetic energy equation were calculated to understand the energy budget. Along the direction of plume flow, $P$, $B$, and $\varepsilon $ show a gradually decreasing trend. Using the parameterization proposed by \textit{Osborne 1980}, the mixing efficiency ($\gamma )$ was calculated to understand the local mixing dynamics of a buoyant plume.   

Buoyant miscible displacement flow of shear-thinning fluids: Experiments and Simulations

We study displacement flow of two miscible fluids with density and viscosity contrast in an inclined pipe. Our focus is mainly on displacements where transverse mixing is not significant and thus a two-layer, stratified flow develops. Our experiments are carried out in a long pipe, covering a wide range of flow-rates, inclination angles and viscosity ratios. Density and viscosity contrasts are achieved by adding Glycerol and Xanthan gum to water, respectively. At each angle, flow rate and viscosity ratio are varied and density contrast is fixed. We identify and map different flow regimes, instabilities and front dynamics based on $Fr$, $Re/Fr\cos\beta$ and viscosity ratio $m$. The problem is also studied numerically to get a better insight into the flow structure and shear-thinning effects. Numerical simulations are completed using OpenFOAM in both pipe and channel geometries and are compared against the experiments.   

Comparison of the key mechanisms leading to rollovers in Liquefied Natural Gas using Computational Fluid Dynamics

Growing demand for the LNG fosters growth of the number of production sites with varying composition and density. Combining different sources of LNG may result in a stably stratified system, in which heat and mass transfer between the layers is limited. Heating of the LNG due to wall thermal conductivity leads to formation of convection cells confined within the layers. While the upper layer can release the extra energy via preferential methane boil-off, the bottom layer cannot and hence becomes superheated. Gradual density equilibration reduces stratification and may eventually lead to a sudden mixing event called ``rollover'', accompanied by violent evaporation of the superheated LNG. Three phenomena are potentially responsible for density equilibration. The first is the growing difference in thermal expansion of the layers due to the reduced ability of the bottom layer to reject heat. The second is the penetration of the heated near-wall boundary layer into the upper layer. The third is the ``entrainment mixing'' occurring at the contact surface between the two layers. The present study uses CFD to compare these mechanisms. Boussinesq approximation and an extended version of the k-$\varepsilon $ model is used. The code is validated by comparison with a large-scale LNG rollover experiment.   

Effects of Density Stratification in Compressible Polytropic Convection

We study compressible convection in polytropically-stratified atmospheres, exploring the effect of varying the total density stratification. Using the Dedalus pseudospectral framework, we perform 2D and 3D simulations. In these experiments we vary the number of density scale heights, studying atmospheres with little stratification (1 density scale height) and significant stratification (5 density scale heights). We vary the level of convective driving (quantified by the Rayleigh number), and study flows at similar Mach numbers by fixing the initial superadiabaticity. We explore the differences between 2D and 3D simulations, and in particular study the equilibration between different reservoirs of energy (kinetic, potential and internal) in the evolved states.   

The effects of Mach number and rotation on heat transport in stratified convection

We use the Dedalus pseudospectral framework to study fully compressible convection in the context of plane-parallel, polytropically stratified atmospheres. We perform a suite of 2D and 3D simulations in which we vary the initial superadiabaticity and the Rayleigh number (Ra) while fixing the initial density stratification, aspect ratio, and Prandtl number. The evolved value of the Mach number (Ma) is primarily controlled by the superadiabaticity. The evolved heat transport, quantified by the Nusselt number (Nu), follows scaling relationships similar to those found in the well-studied, incompressible Rayleigh-B\'{e}nard problem. This scaling holds up in both 2D and 3D and is not appreciably affected by the magnitude of Ma. First results on rotating atmospheres are presented.