Andrew W. Woods | Searcharxiv

arXiv2018

Dynamical dispersion in turbulent plumes

Experimental observations of turbulent buoyant plumes, produced by a constant source of buoyancy, have been described with great success using a horizontally averaged model for the conservation of mass, momentum and buoyancy flux. However, experimental observations of plumes with time-dependent buoyancy fluxes has proved more challenging for quantitative models. At each level in the plume, the horizontal variation in velocity leads to an along-axis shear and hence dispersive transport relative to the mean. With a time-dependent source, axial dispersion of the dynamic properties of the plume has a key role in the evolution of the flow. Using ideas of mixing length theory, we introduce a model for this axial dispersion, and test the model by comparison with experimental observations of plumes in which the buoyancy flux is suddenly decreased or suddenly increased. In both cases, we show the transition from one buoyancy flux to another is self-similar, and using the data, we find the axial dispersion may be expressed as βUb where β lies in the range 0.70-0.88 and U and b are respectively the horizontally averaged vertical velocity and radius of the plume at height z and time t. Our model also reduces to that of a classical plume when the buoyancy flux is steady.

physics.flu-dyn↗

arXiv2015

CO$_2$ dissolution in a background hydrological flow

We investigate the long time steady-state dissolution of CO$_{2}$ in a deep saline aqquifer in the presence of a background hydrological flow. In steady-state, the distribution of CO$_2$ in the groundwater upstream of the aquifer involves a balance between three competing effects: (i) the buoyancy-driven flow of CO$_2$ saturated water; (ii) the diffusion of CO$_2$ from saturated to under-saturated water; and (iii) the advection associated with the oncoming background flow. This leads to three limiting regimes. In the limit of very slow diffusion, a nearly static intrusion of dense fluid may extend a finite distance upstream, balanced by the pressure gradient associated with the oncoming background flow. In the limit of fast diffusion relative to the flow, a gradient zone may become established in which the along aquifer diffusive flux balances the advection associated with the background flow. However, if the buoyancy-driven flow speed exceeds the background hydrological flow speed, then a third, intermediate regime may become established. In this regime, a convective recirculation develops upstream of the anticline involving the vertical diffusion of CO$_2$ from an upstream propagating flow of dense CO$_2$ saturated water into the downstream propagating flow of CO$_2$ unsaturated water. For each limiting case, we find analytical solutions for the distribution of CO$_2$ upstream of the anticline, and test our analysis with full numerical simulations. A key result is that, although there may be very different controls on the distribution and extent of CO$_2$ bearing water upstream of the anticline, in each case the dissolution rate is given by the product of the background volume flux and the difference in concentration between the CO$_2$ saturated water and the original aquifer water upstream.

physics.flu-dyn↗