Dispersion in two-dimensional turbulent buoyant plumes

Using high-resolution imaging and dye studies, we investigate experimentally the mixing of a tracer by the eddies within a two-dimensional turbulent buoyant plume. Instantaneously, the plume consists of a series of eddies, and at each point along the centreline of the plume, the along-plume speed of the leading edge of the eddies $w_{e}\approx 1.3f^{1/3}$, where $f$ is the buoyancy flux, while the product of the length scale, $A$, and frequency, ${\it\omega}$, of the eddies ${\it\omega}A\approx 0.15f^{1/3}$. The circulation and flow associated with the eddies lead to longitudinal mixing relative to the mean flow. To illustrate this mixing, we analyse the evolution of the horizontally averaged dye front produced by adding a constant flux of dye to a steady plume for times t>0. We show that the centre of mass of the horizontally averaged dye front has an along-plume speed ${\approx}1.04f^{1/3}$. This is consistent with the predictions of a time-averaged model for the evolution of the horizontally averaged mass, momentum and buoyancy flux in the plume. The new data also show that the longitudinal spreading of the horizontally averaged dye front can be described in terms of a dispersivity ${\approx}\,0.02f^{1/3}z$, where $z$ is the vertical distance below the source. This model of longitudinal mixing enables calculation of the residence time distribution of material in the plume, which may be key to modelling the products of a reaction in which the reaction time is comparable to the travel time in the plume.This is the accepted manuscript. The final version is available at http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9740664&fulltextType=RA&fileId=S0022112015002608

Gravity-Driven Reacting Flows in a Confined Porous Aquifer

We develop a model for the dynamics of a reactive gravity-driven flow in a porous layer of finite depth, accounting for the change in permeability and density across the dissolution front. We identify that the two controlling parameters are the mobility ratio across the reaction front and the ratio of the buoyancy-driven flow to the fluid injection rate. We present some numerical solutions for the evolution of a two-dimensional dissolution front, and develop an approximate analytic solution for the limit of large injection rate compared to the buoyancy-driven flow. The model predictions are compared with some new analogue laboratory experiments in which fresh water displaces a saturated aqueous solution initially confined within a two-dimensional reactive permeable matrix composed of salt powder and glass ballotini. We also present self-similar solutions for an axisymmetric gravity-driven reactive current moving through a porous layer of finite depth. The solutions illustrate how the reaction front becomes progressively wider as the ratio of the buoyancy-driven flow to the injection rate increases, and also as the mobility contrast across the front increases

Three-dimensional buoyancy-driven flow along a fractured boundary

We describe the steady motion of a buoyant fluid migrating through a porous layer along a plane, inclined boundary from a localized well. We first describe the transition from an approximately radially spreading current near the source, to a flow which runs upslope, as it spreads in the cross-slope direction. Using the model, we predict the maximum injection rate for which, near the source, the flow does not fully flood the porous layer. We then account for the presence of a fracture on the boundary through which some of the flow can drain upwards, and calculate how the current is partitioned between the fraction that drains and the remainder which continues running upslope. The fraction that drains increases with the permeability of the fracture and also with the distance from the source, as the flow slows and has more time to drain. We introduce new scalings and some asymptotic solutions to describe both the flow near the fracture and the three-dimensional surface of the injected fluid as it spreads upslope. We extend the model to the case of multiple fractures, so that the current eventually drains away as it flows over successive fractures. We calculate the shape of the region that is invaded by the buoyant fluid and we show that this flow, draining through a series of discrete fractures, may be approximated by a flow that continuously drains through its upper boundary. The effective small uniform permeability of this upper boundary is given by \textbackslash{k}_{b} \textbackslashapprox \textbackslashint \textbackslashnolimits {k}_{f} \textbackslashhspace{0.167em} \textbackslashmathrm{d} x/ {D}_{F} \textbackslash, where \textbackslash\textbackslashint \textbackslashnolimits {k}_{f} \textbackslashhspace{0.167em} \textbackslashmathrm{d} x\textbackslash is the integral of permeability across the width of the fracture and \textbackslash{D}_{F} \textbackslash is the inter-fracture spacing. Finally, we discuss the relevance of the work for CO2 sequestration and we compare some simple predictions of the plume shape, volume and volume flux derived from our model with data from the Sleipner project, Norway for the plume of CO2 which developed in Horizon 1

Formalising attack trees to support economic analysis

Attack trees and attack graphs are both examples of what one might term attack modelling techniques. The primary purpose of such techniques is to help establish and enumerate the ways in which a system could be compromised; as such, they play a key role in the (security) risk analysis process. Given their role and the consequent need to ensure that they are correct, there are good reasons for capturing such artefacts in a formal manner. We describe such a formal approach, which has been motivated by a desire to model attacks from the perspectives of attackers, to support economic analysis. As an illustration, we consider exploitation cost

Formalising attack trees to support economic analysis

Attack trees and attack graphs are both examples of what one might term attack modelling techniques. The primary purpose of such techniques is to help establish and enumerate the ways in which a system could be compromised; as such, they play a key role in the (security) risk analysis process. Given their role and the consequent need to ensure that they are correct, there are good reasons for capturing such artefacts in a formal manner. We describe such a formal approach, which has been motivated by a desire to model attacks from the perspectives of attackers, to support economic analysis. As an illustration, we consider exploitation cost