2012
DOI: 10.1017/jfm.2012.165
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Flotation and free surface flow in a model for subglacial drainage. Part 1. Distributed drainage

Abstract: We present a continuum model for melt water drainage through a spatially distributed system of connected subglacial cavities, and consider in this context the complications introduced when effective pressure or water pressure drops to zero. Instead of unphysically allowing water pressure to become negative, we model the formation of a partially vapour- or air-filled space between ice and bed. Likewise, instead of allowing sustained negative effective pressures, we allow ice to separate from the bed at zero eff… Show more

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Cited by 73 publications
(145 citation statements)
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“…Physically, the model is based on a conduit whose size evolves due to a combination of dissipation-driven wall melt at a rate c 1 Q , opening due to ice sliding over bed roughness at rate v o (1 − S/S 0 ) (where S 0 is a cut-off due to bed roughness being drowned out; see Schoof et al, 2012) and creep closure at rate c 2 SN n , with discharge in the conduit given by a Darcy-Weisbach or Manning friction law through Eq. (2b).…”
Section: The Modelmentioning
confidence: 99%
See 1 more Smart Citation
“…Physically, the model is based on a conduit whose size evolves due to a combination of dissipation-driven wall melt at a rate c 1 Q , opening due to ice sliding over bed roughness at rate v o (1 − S/S 0 ) (where S 0 is a cut-off due to bed roughness being drowned out; see Schoof et al, 2012) and creep closure at rate c 2 SN n , with discharge in the conduit given by a Darcy-Weisbach or Manning friction law through Eq. (2b).…”
Section: The Modelmentioning
confidence: 99%
“…For computational tractability and in keeping with many other similar drainage models (e.g. Werder et al, 2013), we do not impose the upper and lower bounds on water pressure considered in Schoof et al (2012) and Hewitt et al (2012).…”
Section: The Modelmentioning
confidence: 99%
“…The addition of this sub-model to the Parallel Ice Sheet Model (PISM) accomplishes three specific goals: (a) conservation of the mass of water, (b) simulation of spatially and temporally variable basal shear stress from physical mechanisms based on a minimal number of free parameters, and (c) convergence under grid refinement. The model is a common generalization of four others: (i) the undrained plastic bed model of Tulaczyk et al (2000b), (ii) a standard "routing" model used for identifying locations of subglacial lakes, (iii) the lumped englacial-subglacial model of Bartholomaus et al (2011), and (iv) the elliptic-pressure-equation model of Schoof et al (2012). We preserve physical bounds on the pressure.…”
mentioning
confidence: 99%
“…Current theoretical understanding of GrIS basal hydrology calls on the evolution of the subglacial drainage system from low to high hydraulic efficiency, to accommodate for melt supply variability over the ablation season [19][20][21] , although limited direct observations of the basal environment do not fully verify this model [22][23][24] . Moreover, the representation of an evolving subglacial drainage system in numerical models is challenging, and currently necessitates major simplifications such as reduced spatial dimensions 23,[25][26][27][28] , application on idealized domains 25,29 or disregarding feedbacks on ice flow 30 . Significantly, these dynamic processes are yet to be realistically incorporated into studies aiming to forecast future sea-level rise [31][32][33] .…”
mentioning
confidence: 99%