Flotation and free surface flow in a model for subglacial drainage. Part 1. Distributed drainage

2012 ◽  
Vol 702 ◽  
pp. 126-156 ◽  
Author(s):  
Christian Schoof ◽  
Ian J. Hewitt ◽  
Mauro A. Werder
Keyword(s):  
Water Pressure ◽  
Computing Time ◽  
Potential Gradient ◽  
Coupled System ◽  
Free Surface Flow ◽  
Travelling Wave ◽  
Surface Flow ◽  
Squeeze Film ◽  
Effective Pressure ◽  
Water Drainage

AbstractWe 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 effective pressure. The resulting model is a free boundary problem in which an elliptic obstacle problem determines hydraulic potential, and therefore also determines regions of zero effective pressure and zero water pressure. This is coupled with a transport problem for stored water, and the coupled system bears some similarities with Hele-Shaw and squeeze-film models. We present a numerical method for computing time-dependent solutions, and find close agreement with semi-analytical travelling wave and steady-state solutions. As may be expected, we find that ice–bed separation is favoured by high fluxes and low ice surface slopes and low bed slopes, while partially filled cavities are favoured by low fluxes and high slopes. At the boundaries of regions with zero water or effective pressure, discontinuities in water level are frequently present, either in the form of propagating shocks or as stationary hydraulic jumps accompanied by discontinuities in potential gradient.

scholarly journals Boulder Pickup by Tsunami Surge

2019 ◽  
Vol 13 (05n06) ◽  
pp. 1941006
Author(s):  
Samuel Harry ◽  
Margaret Exton ◽  
Harry Yeh
Keyword(s):  
Pore Water Pressure ◽  
Initial Conditions ◽  
Scale Effects ◽  
Traditional Approach ◽  
Water Pressure ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Flow Conditions ◽  
The Difference ◽  
The Impact

Study of boulder transport by tsunamis is challenging because boulder size, shape, and composition vary greatly; furthermore, flow conditions, topography, and initial conditions are generally unknown. To investigate the mechanism of boulder pickup, experiments of tsunami-like flow past spherical boulders partially buried in a sediment bed are conducted. The experiments are performed in a large centrifuge facility to reduce scale effects and the corresponding dynamic similitude is discussed. The traditional approach to determine boulder pickup is adapted for the case of a half-buried spherical boulder. The adapted model predicts that the boulders are transported, but does not accurately predict the timing of pick up. To investigate the difference in pickup timing, two physical phenomena are discussed: pore-water-pressure dissipation in the soil, and the impact of the free-surface flow on hydrodynamic forces. For a spherical shaped boulder, vertical forces (i.e. buoyant and lift forces) are critical for the initiation of boulder pickup. It was found that spherical boulders that are three-quarter buried in the soil are not transported, even when exposed to flow conditions that would otherwise predict transport.

Numerical Simulation of Free Surface Flows Using STACS-VOF Method

2007 ◽  
Author(s):  
Vedanth Srinivasan ◽  
De Ming Wang
Keyword(s):  
Free Surface ◽  
Stokes Equations ◽  
Current Method ◽  
Coupled System ◽  
Free Surface Flow ◽  
Surface Force ◽  
Free Surface Flows ◽  
Surface Flow ◽  
Air Entrapment ◽  
Simple Strategy

This paper presents a numerical method that couples the incompressible Navier-Stokes equations with the Volume of Fluid method in a Cartesian co-ordinate system for tracking immiscible interfaces in multiple dimensions. The governing equations are discretized based on a finite volume method on a non-staggered fixed grid. The free surface flow problem is solved as a single phase flow system in which the free surface is captured using a Switching Technique for Advection and Capturing of Surfaces (STACS) scheme. The effects of surface tension at the interfaces are treated using a Continuum Surface Force (CSF) model. The pressure velocity coupling is achieved using a SIMPLE strategy. The coupled system, implemented in the commercial CFD software, AVL FIRE/SWIFT, is applied to a two dimensional dam breaking problem. The simulation results reveal a multitude of phenomena such as, free surface vortex generation, air entrapment and splashing of the liquid surge front. The computational results are in good agreement with experimental data, wherever available. The effects of time and grid resolution on the solution behavior are elaborated in detail. Different convection schemes are tested and the current method is compared to another existing interface capturing methodology.

scholarly journals Effects of ice deformation on Röthlisberger channels and implications for transitions in subglacial hydrology

2016 ◽  
Vol 62 (234) ◽  
pp. 750-762 ◽  
Author(s):  
COLIN R. MEYER ◽  
MATHEUS C. FERNANDES ◽  
TIMOTHY T. CREYTS ◽  
JAMES R. RICE
Keyword(s):  
Water Pressure ◽  
Circular Cross Section ◽  
Antiplane Shear ◽  
Shear Strain Rate ◽  
Effective Pressure ◽  
Water Drainage ◽  
Ice Streams ◽  
Turbulent Dissipation ◽  
Creep Flow ◽  
Fixed Radius

ABSTRACTAlong the base of glaciers and ice sheets, the sliding of ice over till depends critically on water drainage. In locations where drainage occurs through Röthlisberger channels, the effective pressure along the base of the ice increases and can lead to a strengthening of the bed, which reduces glacier sliding. The formation of Röthlisberger channels depends on two competing effects: (1) melting from turbulent dissipation opens the channel walls and (2) creep flow driven by the weight of the overlying ice closes the channels radially inward. Variation in downstream ice velocity along the channel axis, referred to as an antiplane shear strain rate, decreases the effective viscosity. The softening of the ice increases creep closure velocities. In this way, even a modest addition of antiplane shear can double the size of the Röthlisberger channels for a fixed water pressure or allow channels of a fixed radius to operate at lower effective pressure, potentially decreasing the strength of the surrounding bed. Furthermore, we show that Röthlisberger channels can be deformed away from a circular cross section under applied antiplane shear. These results can have broad impacts on sliding velocities and potentially affect the total ice flux out of glaciers and ice streams.

Flotation and free surface flow in a model for subglacial drainage. Part 2. Channel flow

2012 ◽  
Vol 702 ◽  
pp. 157-187 ◽  
Author(s):  
I. J. Hewitt ◽  
C. Schoof ◽  
M. A. Werder
Keyword(s):  
Free Surface ◽  
Channel Flow ◽  
Numerical Solutions ◽  
Flow Line ◽  
Water Pressure ◽  
Free Surface Flow ◽  
High Water ◽  
Surface Flow ◽  
Overburden Pressure ◽  
Subglacial Drainage

AbstractWe present a new model of subglacial drainage incorporating flow in a network of channels and a porous sheet, with water exchange between the two determined by pressure gradients. The sheet represents the average effect of many linked cavities, whilst the channels emerge from individual cavities that enlarge due to dissipation-induced melting. The model distinguishes cases when the water pressure drops to zero, in which case it allows for the drainage space to be only partially filled with water (free surface flow), and when the pressure reaches the ice overburden pressure, in which case it allows for uplift of the ice to whatever extent is needed to accommodate the water (flotation). Numerical solutions are found for a one-dimensional flow-line version of the model. The results capture typically observed or inferred features of subglacial drainage systems, including open channel flow at the ice margin, seasonal channel evolution, and high water pressures and uplift of the ice surface driven by rapid changes in water supply.

Analysis of Polygonal Vortex Flows in a Cylinder with a Rotating Bottom

2021 ◽  
Vol 11 (3) ◽  
pp. 1348
Author(s):  
A. Rashkovan ◽  
S.D. Amar ◽  
U. Bieder ◽  
G. Ziskind
Keyword(s):  
Experimental Studies ◽  
Free Surface Flow ◽  
Careful Analysis ◽  
Numerical Approach ◽  
Surface Flow ◽  
Initial Water ◽  
Eddy Simulation ◽  
Disk Rotation ◽  
Inner Radius ◽  
Liquid Flows

The present paper provides a physically sound numerical modeling of liquid flows experimentally observed inside a vertical circular cylinder with a stationary envelope, rotating bottom and open top. In these flows, the resulting vortex depth may be such that the rotating bottom disk becomes partially exposed, and rather peculiar polygon shapes appear. The parameters and features of this work are chosen based on a careful analysis of the literature. Accordingly, the cylinder inner radius is 145 mm and the initial water height is 60 mm. The experiments with bottom disk rotation frequencies of 3.0, 3.4, 4.0 and 4.6 Hz are simulated. The chosen frequency range encompasses the regions of ellipse and triangle shapes as observed in the experimental studies reported in the literature. The free surface flow is expected to be turbulent, with the Reynolds number of O(105). The Large Eddy Simulation (LES) is adopted as the numerical approach, with a localized dynamic Subgrid-Scale Stresses (SGS) model including an energy equation. Since the flow obviously requires a surface tracking or capturing method, a volume-of-fluid (VOF) approach has been chosen based on the findings, where this method provided stable shapes in the ranges of parameters found in the corresponding experiments. Expected ellipse and triangle shapes are revealed and analyzed. A detailed character of the numerical results allows for an in-depth discussion and analysis of the mechanisms and features which accompany the characteristic shapes and their alterations. As a result, a unique insight into the polygon flow structures is provided.

scholarly journals Laminar free-surface flow into a vertical cylinder

1975 ◽  
Vol 3 (1) ◽  
pp. 51-68 ◽  
Author(s):  
Thomas G. Smith ◽  
J.O. Wilkes
Keyword(s):  
Free Surface ◽  
Vertical Cylinder ◽  
Free Surface Flow ◽  
Surface Flow

scholarly journals Dilation of subglacial sediment governs incipient surge motion in glaciers with deformable beds

2020 ◽  
Vol 476 (2238) ◽  
pp. 20200033 ◽  
Author(s):  
B. M. Minchew ◽  
C. R. Meyer
Keyword(s):  
Pore Water ◽  
Flow Model ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Slip Rate ◽  
Effective Pressure ◽  
Ice Flow ◽  
History Of ◽  
Glacier Surges ◽  
Geographical Clustering

Glacier surges are quasi-periodic episodes of rapid ice flow that arise from increases in slip rate at the ice–bed interface. The mechanisms that trigger and sustain surges are not well understood. Here, we develop a new model of incipient surge motion for glaciers underlain by sediments to explore how surges may arise from slip instabilities within a thin layer of saturated, deforming subglacial till. Our model represents the evolution of internal friction, porosity and pore water pressure within the till as functions of the rate and history of shear deformation, and couples the till mechanics to a simple ice-flow model. Changes in pore water pressure govern incipient surge motion, with less permeable till facilitating surging because dilation-driven reductions in pore water pressure slow the rate at which till tends towards a new steady state, thereby allowing time for the glacier to thin dynamically. The reduction of overburden (and thus effective) pressure at the bed caused by dynamic thinning of the glacier sustains surge acceleration in our model. The need for changes in both the hydromechanical properties of the till and the thickness of the glacier creates restrictive conditions for surge motion that are consistent with the rarity of surge-type glaciers and their geographical clustering.

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