A note on axisymmetric supercritical coning in a porous medium

Abstract

The steady response of a fluid with two layers of different density in a porous medium is considered during extraction through a point sink. Supercritical withdrawal in which both layers are being withdrawn is investigated using a spectral method. We show that for each withdrawal rate, there is a single entry angle of the interface into the point sink.As the flow rate decreases the angle of entry steepens until it becomes almost vertical, at which point the method fails. This limit is shown to correspond to the upper bound on sub-critical (single-layer) flow.2010 Mathematics subject classification: 0103.

Extraction of density-layered fluid from a porous medium

“…List [15] and Yih [16] showed that there is a distinct layering of the flow for linear density stratification. At flow rates higher than the critical coning value, solutions include flows with multiple flowing layers, such as those described in [5,[17][18][19]. These solutions are analogous to similar supercritical flows in surface water hydrodynamics [20,21].…”

“…We now treat (19) as a boundary value problem with the boundary conditions (5) plus dΨ dξ → 0 as ξ → ∞ and 0 < ζ < 1, which dictates the flow becomes horizontal, and solve using the finite difference method.…”

“…Fig 19. Comparison of surface shapes η(r ) with h * s = 0.5, M = 0.05, 0.1, 0.15 (bottom to top) between linear (dashed line) and nonlinear (solid line) computations…”

Spaces of Security and Insecurity

“…3 However, despite the abhorrence and fear it knowingly invokes 4 , the discourse of terrorism "constructs no precise criminal act, rendering terrorism of dubious utility as a legal entity." 5 Notwithstanding this, apart from their condemnatory rhetoric, it is primarily through specialist -and usually draconian -legislation that Western states now constitute acts of violence as terrorism. In other words, apart from the vocabulary of 'terrorism' 6 it is states' use of anti-terrorism legislation to confront specific acts of violence that serves to define these acts as 'terrorism.'…”

A simple model of magnetic fields associated with outflow from a source; new orthogonal polynomials

“…Point source flows have also proved of interest in flows through porous media. Hocking and Zhang [14] studied the selective withdrawal of fluid from an upper layer of fluid, and showed how the interface between the two layers is drawn up towards a sink placed in the upper layer, as the withdrawal rate (Froude number) is increased. For sufficiently high Froude number, the interface is drawn into the sink, after which flow from both fluids takes place simultaneously.…”