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.

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 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 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.

A new approach for pre-stressing of rail-end-bolt holes

2016 ◽  
Vol 231 (12) ◽  
pp. 2275-2283 ◽  
Author(s):  
JT Maximov ◽  
GV Duncheva ◽  
IM Amudjev ◽  
AP Anchev ◽  
N Ganev
Keyword(s):  
Fatigue Life ◽  
Fatigue Cracks ◽  
New Technology ◽  
Innovative Technology ◽  
Bolted Joint ◽  
Compressive Stresses ◽  
Process Formation ◽  
Technology Process ◽  
Bolt Holes ◽  
Hoop Stresses

Bolted joint railroad is the subject matter of this paper. Rail joint elements are subjected to cyclic and impact loads as a result of the passage of trains, which causes the origination and growth of fatigue cracks occurring, in most cases, around the bolt holes. Fatigue failure around rail-end-bolt holes is particularly dangerous because it leads to derailment of trains and, consequently, to inevitable accidents. Moreover, the cracking at rail-ends, which starts from bolt hole surface, causes premature rails replacement. The presence of residual compressive hoop stresses around the bolted holes, which is achieved by prestressing of these holes, extends the fatigue life of bolted joint railroads. This article presents an innovative technology for pre-stressing of rail-end-bolt holes, implemented on a vertical machining centre of Revolver vertical (RV) type. Two consecutive operations are involved in the manufacturing technology process: formation of the hole by drilling, reaming and making of a chamfer through a new combined cutting tool; cold hole working by spherical motion cold working through a new tool equipment, which minimizes the axial force on the reverse stroke. The new technology introduces beneficial residual compressive stresses around the bolted holes thereby preventing the fatigue cracks growth and increasing the fatigue life of these openings.

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 Significant submarine ice loss from the Getz Ice Shelf, Antarctica

2018 ◽  
Author(s):  
David M. Rippin
Keyword(s):  
Mass Loss ◽  
West Antarctica ◽  
Ice Shelf ◽  
Ice Streams ◽  
Ice Shelves ◽  
Warming Climate ◽  
Circulation Patterns ◽  
Direct Measurements ◽  
Radio Echo Sounding ◽  
The Impact

Abstract. We present the first direct measurements of changes taking place at the base of the Getz Ice Shelf (GzIS) in West Antarctica. Our analysis is based on repeated airborne radio-echo sounding (RES) survey lines gathered in 2010 and 2014. We reveal that while there is significant variability in ice shelf behaviour, the vast majority of the ice shelf (where data is available) is undergoing basal thinning at a mean rate of nearly 13 m a−1, which is several times greater than recent modelling estimates. In regions of faster flowing ice close to where ice streams and outlet glaciers join the ice shelf, significantly greater rates of mass loss occurred. Since thinning is more pronounced close to faster-flowing ice, we propose that dynamic thinning processes may also contribute to mass loss here. Intricate sub-ice circulation patterns exist beneath the GzIS because of its complex sub-ice topography and the fact that it is fed by numerous ice streams and outlet glaciers. It is this complexity which we suggest is also responsible for the spatially variable patterns of ice-shelf change that we observe. The large changes observed here are also important when considering the likelihood and timing of any potential future collapse of the ice shelf, and the impact this would have on the flow rates of feeder ice streams and glaciers, that transmit ice from inland Antarctica to the coast. We propose that as the ice shelf continues to thin in response to warming ocean waters and climate, the response of the ice shelf will be spatially diverse. Given that these measurements represent changes that are significantly greater than modelling outputs, it is also clear that we still do not fully understand how ice shelves respond to warming ocean waters. As a result, ongoing direct measurements of ice shelf change are vital for understanding the future response of ice shelves under a warming climate.

scholarly journals Mapping ice-shelf flow with interferometric synthetic aperture radar stacking

2012 ◽  
Vol 58 (208) ◽  
pp. 265-277 ◽  
Author(s):  
Malcolm McMillan ◽  
Andrew Shepherd ◽  
Noel Gourmelen ◽  
Jeong-Won Park ◽  
Peter Nienow ◽  
...  
Keyword(s):  
Synthetic Aperture Radar ◽  
Atmospheric Pressure ◽  
Synthetic Aperture ◽  
Ocean Tide ◽  
Interferometric Synthetic Aperture Radar ◽  
West Antarctica ◽  
Ice Shelf ◽  
Flow Displacement ◽  
Shelf Flow ◽  
Aperture Radar

AbstractInterferometric synthetic aperture radar (InSAR) observations of ice-shelf flow contain ocean-tide and atmospheric-pressure signals. A model-based correction can be applied, but this method is limited by its dependency upon model accuracy, which in remote regions can be uncertain. Here we describe a method to determine two-dimensional ice-shelf flow vectors independently of model predictions of tide and atmospheric pressure, by stacking conventional and multiple aperture InSAR (MAI) observations of the Dotson Ice Shelf, West Antarctica. In this way we synthesize a longer observation period, which enhances long-period (flow) displacement signals, relative to rapidly varying (tide and atmospheric pressure) signals and noise. We estimate the error associated with each component of the velocity field to be ~22 ma-1, which could be further reduced if more images were available to stack. With the upcoming launch of several satellite missions, offering the prospect of regular short-repeat SAR acquisitions, this study demonstrates that stacking can improve estimates of ice-shelf flow velocity.

Topographic controls on gravity currents in porous media

2013 ◽  
Vol 734 ◽  
pp. 317-337 ◽  
Author(s):  
Samuel S. Pegler ◽  
Herbert E. Huppert ◽  
Jerome A. Neufeld
Keyword(s):  
Porous Media ◽  
Axisymmetric Flow ◽  
Early Time ◽  
Gravity Currents ◽  
Late Time ◽  
Horizontal Distance ◽  
Topographic Controls ◽  
Time Regime ◽  
Flow Transitions ◽  
Theoretical Results

AbstractWe present a theoretical and experimental study of the propagation of gravity currents in porous media with variations in the topography over which they flow, motivated in part by the sequestration of carbon dioxide in saline aquifers. We consider cases where the height of the topography slopes upwards in the direction of the flow and is proportional to the $n\text{th} $ power of the horizontal distance from a line or point source of a constant volumetric flux. In two-dimensional cases with $n\gt 1/ 2$, the current evolves from a self-similar form at early times, when the effects of variations in topography are negligible, towards a late-time regime that has an approximately horizontal upper surface and whose evolution is dictated entirely by the geometry of the topography. For $n\lt 1/ 2$, the transition between these flow regimes is reversed. We compare our theoretical results in the case $n= 1$ with data from a series of laboratory experiments in which viscous glycerine is injected into an inclined Hele-Shaw cell, obtaining good agreement between the theoretical results and the experimental data. In the case of axisymmetric topography, all topographic exponents $n\gt 0$ result in a transition from an early-time similarity solution towards a topographically controlled regime that has an approximately horizontal free surface. We also analyse the evolution over topography that can vary with different curvatures and topographic exponents between the two horizontal dimensions, finding that the flow transitions towards a horizontally topped regime at a rate which depends strongly on the ratio of the curvatures along the principle axes. Finally, we apply our mathematical solutions to the geophysical setting at the Sleipner field, concluding that topographic influence is unlikely to explain the observed non-axisymmetric flow.

scholarly journals Numerical Simulations of Two-Layer Flow past Topography. Part I: The Leeside Hydraulic Jump

2018 ◽  
Vol 75 (4) ◽  
pp. 1231-1241 ◽  
Author(s):  
Richard Rotunno ◽  
George H. Bryan
Keyword(s):  
Fluid Dynamics ◽  
Hydraulic Jump ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Layer ◽  
Transition To Turbulence ◽  
Height Velocity ◽  
Inviscid Fluid ◽  
Initial Value ◽  
Density Interface

Abstract Laboratory observations of the leeside hydraulic jump indicate it consists of a statistically stationary turbulent motion in an overturning wave. From the point of view of the shallow-water equations (SWE), the hydraulic jump is a discontinuity in fluid-layer depth and velocity at which kinetic energy is dissipated. To provide a deeper understanding of the leeside hydraulic jump, three-dimensional numerical solutions of the Navier–Stokes equations (NSE) are carried out alongside SWE solutions for nearly identical physical initial-value problems. Starting from a constant-height layer flowing over a two-dimensional obstacle at constant speed, it is demonstrated that the SWE solutions form a leeside discontinuity owing to the collision of upstream-moving characteristic curves launched from the obstacle. Consistent with the SWE solution, the NSE solution indicates the leeside hydraulic jump begins as a steepening of the initially horizontal density interface. Subsequently, the NSE solution indicates overturning of the density interface and a transition to turbulence. Analysis of the initial-value problem in these solutions shows that the tendency to form either the leeside height–velocity discontinuity in the SWE or the overturning density interface in the exact NSE is a feature of the inviscid, nonturbulent fluid dynamics. Dissipative turbulent processes associated with the leeside hydraulic jump are a consequence of the inviscid fluid dynamics that initiate and maintain the locally unstable conditions.

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