scholarly journals An experimental and theoretical study of the dynamics of grounding lines

2013 ◽  
Vol 728 ◽  
pp. 5-28 ◽  
Author(s):  
Samuel S. Pegler ◽  
M. Grae Worster
Keyword(s):  
Theoretical Study ◽  
Fluid Layer ◽  
Gravity Current ◽  
Three Dimensional ◽  
Vertical Shear ◽  
Inviscid Fluid ◽  
West Antarctica ◽  
Full Contact ◽  
Grounding Line ◽  
Longitudinal Extension

AbstractWe present an experimental and theoretical study of a thin, viscous fluid layer that flows radially under gravity from a point source into a denser inviscid fluid layer of uniform depth above a rigid horizontal surface. Near the source, the viscous layer lies in full contact with the surface, forming a vertical-shear-dominated viscous gravity current. At a certain distance from the source, the layer detaches from the surface to form a floating current whose dynamics are controlled by the viscous stresses due to longitudinal extension. We describe the dynamics of the grounded and floating components using distinct thin-layer theories. Separating the grounded and floating regions is the freely moving line of detachment, or grounding line, whose evolution we model by balancing the horizontal forces between the two regions. Using numerical and asymptotic analysis, we calculate the evolution of the system from a self-similar form at early times towards a steady state at late times. We use our solutions to illustrate how three-dimensional stresses within marine ice sheets, such as that of West Antarctica, can lead to stabilization of the grounding line. To assess the validity of the assumptions underlying our model, we compare its predictions with data from a series of laboratory experiments.

Lateral controls on grounding-line dynamics

2013 ◽  
Vol 722 ◽  
Author(s):  
Samuel S. Pegler ◽  
Katarzyna N. Kowal ◽  
Leonard Q. Hasenclever ◽  
M. Grae Worster
Keyword(s):  
Fluid Layer ◽  
Finite Depth ◽  
Shear Stresses ◽  
Inviscid Fluid ◽  
Full Contact ◽  
Grounding Line ◽  
Local Shear ◽  
Self Similar ◽  
Flow Transitions ◽  
Viscous Stresses

AbstractWe present a theoretical and experimental study of viscous gravity currents introduced at the surface of a denser inviscid fluid layer of finite depth inside a vertical Hele-Shaw cell. Initially, the viscous fluid floats on the inviscid fluid, forming a self-similar, buoyancy-driven current resisted predominantly by the viscous stresses due to shear across the width of the cell. Once the viscous current contacts the base of the cell, the flow can be considered in two regions: a grounded region in which the current lies in full contact with the base; and a floating region. The subsequent advance of the grounding line separating these regions is shown to be controlled by the thickening of the current associated with balancing the local shear stresses. An understanding of the flow transitions is developed using asymptotic and numerical analysis of a model based on lubrication theory.

scholarly journals Sensitivity of the dynamics of Pine Island Glacier, West Antarctica, to climate forcing for the next 50 years

2014 ◽  
Vol 8 (5) ◽  
pp. 1699-1710 ◽  
Author(s):  
H. Seroussi ◽  
M. Morlighem ◽  
E. Rignot ◽  
J. Mouginot ◽  
E. Larour ◽  
...  
Keyword(s):  
Sea Level Rise ◽  
Sea Level ◽  
Three Dimensional ◽  
Major Contributor ◽  
West Antarctica ◽  
Climatic Impact ◽  
Ice Shelf ◽  
Ice Dynamics ◽  
Surface Mass ◽  
Grounding Line

Abstract. Pine Island Glacier, a major contributor to sea level rise in West Antarctica, has been undergoing significant changes over the last few decades. Here, we employ a three-dimensional, higher-order model to simulate its evolution over the next 50 yr in response to changes in its surface mass balance, the position of its calving front and ocean-induced ice shelf melting. Simulations show that the largest climatic impact on ice dynamics is the rate of ice shelf melting, which rapidly affects the glacier speed over several hundreds of kilometers upstream of the grounding line. Our simulations show that the speedup observed in the 1990s and 2000s is consistent with an increase in sub-ice-shelf melting. According to our modeling results, even if the grounding line stabilizes for a few decades, we find that the glacier reaction can continue for several decades longer. Furthermore, Pine Island Glacier will continue to change rapidly over the coming decades and remain a major contributor to sea level rise, even if ocean-induced melting is reduced.

scholarly journals Dynamics of laterally confined marine ice sheets

2016 ◽  
Vol 790 ◽  
Author(s):  
Katarzyna N. Kowal ◽  
Samuel S. Pegler ◽  
M. Grae Worster
Keyword(s):  
Transition Region ◽  
Gravity Current ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Vertical Shear ◽  
Shear Stresses ◽  
Horizontal Shear ◽  
Ice Shelf ◽  
Slip Boundary ◽  
Grounding Line

We present an experimental and theoretical study of the dynamics of laterally confined marine ice sheets in the natural limit in which the long, narrow channel into which they flow is wider than the depth of the ice. A marine ice sheet comprises a grounded ice sheet in contact with bedrock that floats away from the bedrock at a ‘grounding line’ to form a floating ice shelf. We model the grounded ice sheet as a viscous gravity current resisted dominantly by vertical shear stresses owing to the no-slip boundary condition applied at the bedrock. We model the ice shelf as a floating viscous current resisted dominantly by horizontal shear stresses owing to no-slip boundary conditions applied at the sidewalls of the channel. The two shear-dominated regions are coupled by jump conditions relating force and fluid flux across a short transition region downstream of the grounding line. We find that the influence of the stresses within the transition region becomes negligible at long times and we model the transition region as a singular interface across which the ice thickness and mass flux can be discontinuous. The confined shelf buttresses the sheet, causing the grounding line to advance more than it would otherwise. In the case that the sheet flows on a base of uniform slope, we find asymptotically that the grounding line advances indefinitely as $t^{1/3}$, where $t$ is time. This contrasts with the two-dimensional counterpart, for which the shelf provides no buttressing and the grounding line reaches a steady state (Robison, J. Fluid Mech., vol. 648, 2010, pp. 363–380).

Dynamics of a viscous layer flowing radially over an inviscid ocean

2012 ◽  
Vol 696 ◽  
pp. 152-174 ◽  
Author(s):  
Samuel S. Pegler ◽  
M. Grae Worster
Keyword(s):  
Fluid Layer ◽  
Axisymmetric Flow ◽  
Inviscid Fluid ◽  
Late Time ◽  
West Antarctica ◽  
Ice Shelf ◽  
Compressive Stresses ◽  
Hoop Stresses ◽  
Asymptotic Analyses ◽  
Viscous Stresses

AbstractWe present a theoretical and experimental study of a viscous fluid layer spreading over a deep layer of denser, inviscid fluid. Specifically, we study an axisymmetric flow produced by a vertical line source. Close to the source, the flow is controlled viscously, with a balance between radial compressive stresses and hoop stresses. Further out, the flow is driven by gradients in the buoyancy force and is resisted by viscous extensional and hoop stresses. An understanding of these different fluid-mechanical relationships is developed by asymptotic analyses for early times and for the near and far fields at late times. Confirmation of the late-time, far-field behaviour is obtained from a series of laboratory experiments in which golden syrup was injected into denser solutions of potassium carbonate. We use our mathematical solutions to discuss a physical mechanism by which horizontal viscous stresses in a spreading ice shelf, such as those in West Antarctica, can buttress the grounded ice sheet that supplies it.

Nonlinear interactions between convection, rotation and flows with vertical shear

1986 ◽  
Vol 164 ◽  
pp. 91-105 ◽  
Author(s):  
David H. Hathaway ◽  
Richard C. J. Somerville
Keyword(s):  
Kinetic Energy ◽  
Shear Flow ◽  
Fluid Layer ◽  
Three Dimensional ◽  
Rotation Vector ◽  
Vertical Shear ◽  
Nonlinear Interactions ◽  
Mean Flow ◽  
Rotation Vectors ◽  
Convective Motions

A three-dimensional and time-dependent numerical model is used to study the nonlinear interactions between thermal convective motions, rotation, and imposed flows with vertical shear. All cases have Rayleigh numbers of 104 and Prandtl numbers of 1.0. Rotating cases have Taylor numbers of 104.For the non-rotating cases, the effects of the shear on the convection produce longitudinal rolls aligned with the shear flow and a downgradient flux of momentum. The interaction between the convection and the shear flow decreases the shear in the interior of the fluid layer while adding kinetic energy to the convective motions. For unit Prandtl number the dimensionless flux of momentum is equal to the dimensionless flux of heat.For rotating cases with vertical rotation vectors, the shear flow favours rolls aligned with the shear and produces a downgradient flux of momentum. However, the Coriolis force turns the flow induced by the convection to produce a more complicated shear that changes direction with height. As in the non-rotating cases, the convective motions become more energetic by extracting energy from the mean flow. For Richardson numbers larger than about − 1.0, the dominant source of eddy kinetic energy is the shear flow rather than buoyancy.For rotating cases with tilted rotation vectors the results depend upon the direction of the shear. For weak shear, convective rolls aligned with the rotation vector are favoured. When the shear flow is directed to the east along the top, the rolls become broader and the convection weaker. For large shear in this direction, the convective motions are quenched by the competition between the shear flow and the tilted rotation vector. When the shear flow is directed to the west along the top, strong shear produces rolls aligned with the shear. The heat and momentum fluxes become large and can exceed those found in the absence of a tilted rotation vector. Countergradient fluxes of momentum can also be produced.

scholarly journals Mass balance of the Antarctic ice sheet 1992–2016: reconciling results from GRACE gravimetry with ICESat, ERS1/2 and Envisat altimetry

2021 ◽  
pp. 1-27
Author(s):  
H. Jay Zwally ◽  
John W. Robbins ◽  
Scott B. Luthcke ◽  
Bryant D. Loomis ◽  
Frédérique Rémy
Keyword(s):  
Mass Balance ◽  
Antarctic Peninsula ◽  
East Antarctica ◽  
Mantle Material ◽  
West Antarctica ◽  
Mantle Viscosity ◽  
Grounding Line ◽  
The Antarctic ◽  
Total Gain

Abstract GRACE and ICESat Antarctic mass-balance differences are resolved utilizing their dependencies on corrections for changes in mass and volume of the same underlying mantle material forced by ice-loading changes. Modeled gravimetry corrections are 5.22 times altimetry corrections over East Antarctica (EA) and 4.51 times over West Antarctica (WA), with inferred mantle densities 4.75 and 4.11 g cm−3. Derived sensitivities (Sg, Sa) to bedrock motion enable calculation of motion (δB0) needed to equalize GRACE and ICESat mass changes during 2003–08. For EA, δB0 is −2.2 mm a−1 subsidence with mass matching at 150 Gt a−1, inland WA is −3.5 mm a−1 at 66 Gt a−1, and coastal WA is only −0.35 mm a−1 at −95 Gt a−1. WA subsidence is attributed to low mantle viscosity with faster responses to post-LGM deglaciation and to ice growth during Holocene grounding-line readvance. EA subsidence is attributed to Holocene dynamic thickening. With Antarctic Peninsula loss of −26 Gt a−1, the Antarctic total gain is 95 ± 25 Gt a−1 during 2003–08, compared to 144 ± 61 Gt a−1 from ERS1/2 during 1992–2001. Beginning in 2009, large increases in coastal WA dynamic losses overcame long-term EA and inland WA gains bringing Antarctica close to balance at −12 ± 64 Gt a−1 by 2012–16.

scholarly journals Stokes drift through corals

2021 ◽  
Author(s):  
Joseph J. Webber ◽  
Herbert E. Huppert
Keyword(s):  
Coral Reef ◽  
Coral Reefs ◽  
Porous Layer ◽  
Large Scale ◽  
Fluid Layer ◽  
Ocean Waves ◽  
Stokes Drift ◽  
Inviscid Fluid ◽  
Porous Bed ◽  
Vertical Drift

AbstractMotivated by shallow ocean waves propagating over coral reefs, we investigate the drift velocities due to surface wave motion in an effectively inviscid fluid that overlies a saturated porous bed of finite depth. Previous work in this area either neglects the large-scale flow between layers (Phillips in Flow and reactions in permeable rocks, Cambridge University Press, Cambridge, 1991) or only considers the drift above the porous layer (Monismith in Ann Rev Fluid Mech 39:37–55, 2007). Overcoming these limitations, we propose a model where flow is described by a velocity potential above the porous layer and by Darcy’s law in the porous bed, with derived matching conditions at the interface between the two layers. Both a horizontal and a novel vertical drift effect arise from the damping of the porous bed, which requires the use of a complex wavenumber k. This is in contrast to the purely horizontal second-order drift first derived by Stokes (Trans Camb Philos Soc 8:441–455, 1847) when working with solely a pure fluid layer. Our work provides a physical model for coral reefs in shallow seas, where fluid drift both above and within the reef is vitally important for maintaining a healthy reef ecosystem (Koehl et al. In: Proceedings of the 8th International Coral Reef Symposium, vol 2, pp 1087–1092, 1997; Monismith in Ann Rev Fluid Mech 39:37–55, 2007). We compare our model with field measurements by Koehl and Hadfield (J Mar Syst 49:75–88, 2004) and also explain the vertical drift effects as documented by Koehl et al. (Mar Ecol Prog Ser 335:1–18, 2007), who measured the exchange between a coral reef layer and the (relatively shallow) sea above.

scholarly journals A THREE DIMENSIONAL MODEL OF THE GULF OF ALASKA

1986 ◽  
Vol 1 (20) ◽  
pp. 193 ◽  
Author(s):  
Shiao-Kung Liu ◽  
Jan J. Leendertse
Keyword(s):  
Three Dimensional ◽  
Gulf Of Alaska ◽  
Vertical Shear ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Weather Model ◽  
Closure Scheme ◽  
Vertical Grid ◽  
Northern Pacific ◽  
Horizontal Grid

This paper presents the development of a three dimensional model of the Gulf of Alaska. The model extends between the Vancouver Island and the Aleutian Islands covering approximatedly 1.5 million square kilometers over the northern Pacific Ocean. Formulated on an ellipsoidal horizontal grid and variable vertical grid, the model is schematized over a 81 x 53 x 10 grid structure. The solution scheme is implicit over the vertical and is programmed using one-dimensional dynamic array for the efficient use of machine storage. The turbulence closure scheme for the non-homogeneous vertical shear is formulated so that the potential and kinetic energetics are monitored and transferred in a closed form. The hydrodynamic model is coupled to a two-dimensional stochastic weather model and an oil-spill trajectory/weathering model. The former also simulates stochastically the cyclogenetic/cyclolytic processes within the modeled area. The paper also compares the computed results with the available field data. Good agreements are found in tidal amplitude and phases as well as currents.

scholarly journals Sensitivity of Pine Island Glacier, West Antarctica, to changes in ice-shelf and basal conditions: a model study

2002 ◽  
Vol 48 (163) ◽  
pp. 552-558 ◽  
Author(s):  
Marjorie Schmeltz ◽  
Eric Rignot ◽  
Todd K. Dupont ◽  
Douglas R. MacAyeal
Keyword(s):  
Shear Stress ◽  
Element Model ◽  
Shelf Area ◽  
West Antarctica ◽  
Ice Shelf ◽  
Ice Stream ◽  
Model Study ◽  
Grounding Line ◽  
Glacier Velocity ◽  
Basal Shear

AbstractWe use a finite-element model of coupled ice-stream/ice-shelf flow to study the sensitivity of Pine Island Glacier, West Antarctica, to changes in ice-shelf and basal conditions. By tuning a softening coefficient of the ice along the glacier margins, and a basal friction coefficient controlling the distribution of basal shear stress underneath the ice stream, we are able to match model velocity to that observed with interferometric synthetic aperture radar (InSAR). We use the model to investigate the effect of small perturbations on ice flow. We find that a 5.5–13% reduction in our initial ice-shelf area increases the glacier velocity by 3.5–10% at the grounding line. The removal of the entire ice shelf increases the grounding-line velocity by > 70%. The changes in velocity associated with ice-shelf reduction are felt several tens of km inland. Alternatively, a 5% reduction in basal shear stress increases the glacier velocity by 13% at the grounding line. By contrast, softening of the glacier side margins would have to be increased a lot more to produce a comparable change in ice velocity. Hence, both the ice-shelf buttressing and the basal shear stress contribute significant resistance to the flow of Pine Island Glacier.

scholarly journals Interannual surface velocity variations of Pine Island Glacier, West Antarctica

2003 ◽  
Vol 36 ◽  
pp. 205-214 ◽  
Author(s):  
Bernhard T. Rabus ◽  
Oliver Lang
Keyword(s):  
Feature Tracking ◽  
Surface Velocity ◽  
Synthetic Aperture ◽  
Clear Correlation ◽  
West Antarctica ◽  
Velocity Increase ◽  
Grounding Line ◽  
Velocity Variations ◽  
Independent Confirmation ◽  
Observation Period

AbstractThe surface velocity of Pine Island Glacier, West Antarctica, during the period 1992–2000 is measured with synthetic aperture radar feature-tracking techniques. Over the observation period, we find a monotonic acceleration with a spatially uniform amplitude of about 12% of the surface velocity. The acceleration extends > 80 km inland of the grounding line into a zone of prominent arcuate crevasses.The upper limit of these crevasses has migrated up-glacier by 0.2 km a−1 correlated with a velocity increase of similar size in the crevassed zone. On the other hand, there is no clear correlation between the velocity variations and observations of grounding-line migration. These findings suggest ongoing dynamic thinning of Pine Island Glacier, providing independent confirmation of recent interferometric results obtained by Rignot and others (2002).

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