scholarly journals Basal-flow characteristics of a non-linear flow sliding frictionless over strongly undulating bedrock

1997 ◽  
Vol 43 (143) ◽  
pp. 80-89 ◽  
Author(s):  
G. Hilmar Gudmundsson
Keyword(s):  
Flow Parameter ◽  
Flow Characteristics ◽  
Critical Value ◽  
Main Flow ◽  
Sliding Velocity ◽  
Flow Circulation ◽  
The Mean ◽  
Glacier Flow ◽  
Basal Shear ◽  
Basal Flow

AbstractThe flow field of a medium sliding without friction over a strongly undulating surface is calculated numerically. The results are used to elucidate the basal-flow characteristics of glacier flow and they are discussed with reference to known analytical solutions. Extrusion flow is found to become increasingly pronounced as the value of n, where n is a parameter in Glen’s flow law, becomes larger. For sinusoidal bedrock undulations, a flow separation occurs if the amplitude-to-wavelength ratio exceeds a critical value of about 0.28. The main flow then sets up a secondary flow circulation within the trough, and the ice participating in this circular motion theoretically never leaves it. The sliding velocity is calculated numerically as a function of the mean basal shear stress, the amplitude-to-wavelength ratio and the flow parameter n. For moderate and high slope fluctuations, the sliding velocity is significantly different from what would be expected from results based on the small-slope approximation.

scholarly journals Basal-flow characteristics of a non-linear flow sliding frictionless over strongly undulating bedrock

1997 ◽  
Vol 43 (143) ◽  
pp. 80-89 ◽  
Author(s):  
G. Hilmar Gudmundsson
Keyword(s):  
Flow Parameter ◽  
Flow Characteristics ◽  
Critical Value ◽  
Main Flow ◽  
Sliding Velocity ◽  
Flow Circulation ◽  
The Mean ◽  
Glacier Flow ◽  
Basal Shear ◽  
Basal Flow

AbstractThe flow field of a medium sliding without friction over a strongly undulating surface is calculated numerically. The results are used to elucidate the basal-flow characteristics of glacier flow and they are discussed with reference to known analytical solutions. Extrusion flow is found to become increasingly pronounced as the value ofn,wherenis a parameter in Glen’s flow law, becomes larger. For sinusoidalbedrockundulations, a flow separation occurs if the amplitude-to-wavelength ratio exceeds a critical value of about 0.28. The main flow then sets up a secondary flow circulation within the trough, and the ice participating in this circular motion theoretically never leaves it. The sliding velocity is calculated numerically as a function of the mean basal shear stress, the amplitude-to-wavelength ratio and the flow parametern.For moderate and high slope fluctuations, the sliding velocity is significantly different from what would be expected from results based on the small-slope approximation.

scholarly journals Basal-flow characteristics of a linear medium sliding frictionless over small bedrock undulations

1997 ◽  
Vol 43 (143) ◽  
pp. 71-79 ◽  
Author(s):  
G. Hilmar Gudmundsson
Keyword(s):  
Flow Characteristics ◽  
Local Maximum ◽  
Critical Value ◽  
Two Dimensions ◽  
Creeping Flow ◽  
Wave Number ◽  
Vertical Position ◽  
Gravity Driven ◽  
The Mean ◽  
Basal Flow

AbstractThe basal deformation of a gravity-driven linear creeping flow sliding frictionless over slowly varying bed undulations in two dimensions is analysed analytically, using results from second-order perturbation theory. One of the key results is that, close to sinusoidal bedrock undulations, up to two different spatial regions of local extrusion flow may arise. The offset and onset of extrusion flow is controlled primarily by the amplitude-to-wavelength ratio. Above the crest of a sinusoidal bed line, a local maximum of the surface-parallel velocity develops for ε : =ak< 0.138, whereais the amplitude andkis the wave number. Asεincreases from zerо to this critical value, the vertical position of the velocity maximum moves fromkz= 1 tokz≈ 1.98, wherezis the vertical distance above the mean bed line. Within and above the trough of a sinusoid, a region of local minimum of the surface-parallel velocity component develops, which shifts fromkz= 1 towards the bed line asεincreases front zero to 1/2. Below this velocity minimum, and for some distance above the velocity maximum, the surface-parallel velocity increases with depth. This type of extrusion flow will cause a reversal of borehole-inclination profiles close to the bedrock.

scholarly journals Basal-flow characteristics of a linear medium sliding frictionless over small bedrock undulations

1997 ◽  
Vol 43 (143) ◽  
pp. 71-79 ◽  
Author(s):  
G. Hilmar Gudmundsson
Keyword(s):  
Flow Characteristics ◽  
Local Maximum ◽  
Critical Value ◽  
Two Dimensions ◽  
Creeping Flow ◽  
Wave Number ◽  
Vertical Position ◽  
Gravity Driven ◽  
The Mean ◽  
Basal Flow

AbstractThe basal deformation of a gravity-driven linear creeping flow sliding frictionless over slowly varying bed undulations in two dimensions is analysed analytically, using results from second-order perturbation theory. One of the key results is that, close to sinusoidal bedrock undulations, up to two different spatial regions of local extrusion flow may arise. The offset and onset of extrusion flow is controlled primarily by the amplitude-to-wavelength ratio. Above the crest of a sinusoidal bed line, a local maximum of the surface-parallel velocity develops for ε : = ak < 0.138, where a is the amplitude and k is the wave number. As ε increases from zerо to this critical value, the vertical position of the velocity maximum moves from kz = 1 to kz ≈ 1.98, where z is the vertical distance above the mean bed line. Within and above the trough of a sinusoid, a region of local minimum of the surface-parallel velocity component develops, which shifts from kz = 1 towards the bed line as ε increases front zero to 1/2. Below this velocity minimum, and for some distance above the velocity maximum, the surface-parallel velocity increases with depth. This type of extrusion flow will cause a reversal of borehole-inclination profiles close to the bedrock.

Numerical analysis of the groove effect on the tip leakage vortex cavitating flow

2019 ◽  
Vol 234 (6) ◽  
pp. 836-847
Author(s):  
Zhaodan Fei ◽  
Rui Zhang ◽  
Hui Xu ◽  
Tong Mu
Keyword(s):  
Flow Pattern ◽  
Flow Characteristics ◽  
Cavitating Flow ◽  
Main Flow ◽  
Leakage Flow ◽  
Tip Leakage Flow ◽  
Tip Leakage Vortex ◽  
Tip Leakage ◽  
Curvature Effects ◽  
The Mean

In this paper, the groove effect on the tip leakage vortex cavitating flow characteristics of a simplified NACA0009 hydrofoil with tip gap is studied. Considering local rotation characteristics and curvature effects of the tip leakage vortex flow, the rotation-curvature corrected shear-stress-transport turbulence model is applied to simulate the time-averaged turbulent flow. The Zwart–Gerber–Belamri cavitation model is used to simulate the cavitating flow. The results show that the groove could affect the tip leakage vortex cavitating flow. The groove enhances the interaction between the tip leakage flow and main flow, and then it affects the cavitation of the tip leakage vortex. Compared with the non-groove case, for groove cases of αgre ≤75°, the tip leakage vortex cavitating flow is suppressed, the flow pattern in the gap is improved, and the mean leakage velocity Vlk < 0.8. The region of high leakage velocity is eliminated and the distribution of the pressure is more uniform. The tip leakage vortex cavitation area is reduced, and the maximum decrease is 72.90%. While for groove cases of αgre≥90°, neither the tip leakage vortex cavitating flow nor flow pattern in the tip gap is ameliorated, the mean leakage velocity Vlk lies the range from 0.90 to 0.96. The region of high leakage velocity still exists and even the tip leakage vortex cavitation area is increased. Based on three-dimensional streamlines and vorticity transport equation, the interaction between the tip leakage flow and main flow leads to the variation of the tip leakage vortex cavitating flow. This paper aims for a useful reference to mitigate the tip leakage vortex cavitation and control the influence of the tip leakage vortex cavitating flow for the hydraulic machinery.

scholarly journals Comparison of Three Contemporary Flow Laws in a Three-Dimensional, Time-Dependent Glacier Model

1973 ◽  
Vol 12 (66) ◽  
pp. 361-373 ◽  
Author(s):  
L. A. Rasmussen ◽  
W. J. Campbell
Keyword(s):  
Shear Stress ◽  
Steady State ◽  
Large Scale ◽  
Three Dimensional ◽  
Time Dependent ◽  
Flow Law ◽  
Glacier Flow ◽  
Basal Shear ◽  
Basal Flow ◽  
Flow Laws

A numerical model for three-dimensional, time-dependent glacier flow (Campbell and Rasmussen, 1970) treated the ice as a Newtonian viscous fluid and related its dynamics to two large-scale bulk parameters: the viscosity v determining the ice-to-ice friction, and a basal friction parameter A determining the ice-to-rock friction. The equations were solved using the relatively simple flow law of Bodvarsson (1955) in which the basal shear stress is proportional to volume transport. Recent research suggests that a more realistic basal flow law is one in which the basal shear stress to some lower power (1–3) is either proportional to the vertically averaged velocity (Glen, 1958; Nye, 1960, 1963[a], [b], [c], 1965[a], [b], [c]) or to the ratio of the vertically averaged velocity to glacier thickness (Budd and Jenssen, in press).In the present study a generalized flow law incorporating all of the above bulk basal flow laws is applied to the Campbell–Rasmussen momentum equation to form a generalized two-dimensional transport equation, which, when combined with the continuity equation, yields a numerically tractable set of equations for three-dimensional, time-dependent glacier flow. Solutions of the model are shown for steady-state flow and surge advance and recovery for a typical valley glacier bed for powers 1, 2, and 3 for each of the basal flow laws for a steady-state climate input and a given ice-to-ice viscosity parameter.

scholarly journals Surging Glaciers—The Dilemma Continues

1979 ◽  
Vol 24 (90) ◽  
pp. 502-503 ◽  
Author(s):  
M. F. Meier
Keyword(s):  
Shear Stress ◽  
Phenomenological Approach ◽  
Sliding Velocity ◽  
Recent Interest ◽  
Normal Behavior ◽  
Rapid Flow ◽  
Basal Sliding ◽  
Ice Velocity ◽  
Glacier Flow ◽  
Basal Shear

AbstractA glacier surge, according to most definitions, is a short-lived phase of unusually rapid glacier flow, after which the glacier returns to more normal behavior, with the surge–non-surge phases recurring on a regular or periodic basis. Recent interest is largely directed toward analyzing the effect of water at the bed on the periodic change in flow regime and on the rapid flow during a surge phase. For instance, study of a local depression of basal shear stress that dependson a “friction lubrication factor” which becomes important as the ice velocity increases, is one promising phenomenological approach. An important physical approach focuses on a water “collection zone” that occurs where and when the longitudinal pressure gradient in the subglacial wtaer film approaches zero. The data necessary for properly verifying these and other similar theories do not yet exist. Computer modeling of rapidly-surging glaciers based on a “friction lubrication factor” has been quite successful in duplicating their major features. Once rapid movement (102–103m a–1) has begun, sufficient water is generated at the bed, from ice melted by heat dissipated in sliding, to produce some decoupling of the glacier from its bed and to maintain the surge, but only if this water is not lost by rapid drainage. Some glaciers exhibit periodic pulses in which the basal sliding velocity during the fastest part of the pulses appears to be in the range for “normal” glaciers (&lt;102m a–1). Some evidence suggests a continuum of behavior from steady (normal) glaciers through these “mini-surges” to classic surges. This continuum and the “mini-surges” seem to be difficult to explain quantitatively by existing theories. A few glaciers flow continuously at surging speeds (&gt;103m a–1) in certain reaches. The up-glacier transition reaches show speeds decreasing to “nonrmal” with no indication of intermediate surging regime, but the down-glacier transition reaches may be areas where surges are triggered.

scholarly journals Subglacial processes on an Antarctic ice stream bed. 2: Can modelled ice dynamics explain the morphology of mega-scale glacial lineations?

2016 ◽  
Vol 62 (232) ◽  
pp. 285-298 ◽  
Author(s):  
STEWART S.R. JAMIESON ◽  
CHRIS R. STOKES ◽  
STEPHEN J. LIVINGSTONE ◽  
ANDREAS VIELI ◽  
COLM Ó COFAIGH ◽  
...  
Keyword(s):  
Shear Stress ◽  
Flow Characteristics ◽  
Stream Velocity ◽  
Ice Dynamics ◽  
Ice Flow ◽  
Basal Ice ◽  
Ice Stream ◽  
Ice Velocity ◽  
The Mean ◽  
Basal Shear

ABSTRACTMega-scale glacial lineations (MSGLs) are highly elongate subglacial bedforms associated with ice streaming. However, the link between MSGLs and rapid ice flow is largely qualitative, and there have been few attempts to quantitatively link their formation to ice flow characteristics (e.g. ice velocity, thickness, basal shear stress). We take measurements of MSGLs from a palaeo-ice stream that once occupied Marguerite Trough, Antarctic Peninsula and explore a range of possible correlations with ice dynamics generated from an ensemble of numerical modelling experiments that reproduce the deglaciation of the ice stream. Our results confirm that high mean ice velocities and a weak bed correlate with longer MSGLs. Furthermore, the height of MSGLs are low (2–3 m) where modelled basal shear stress is low, but their height tends to be higher and more variable where basal shear stress is larger. The mean density of MSGLs decreases as ice flux increases. Our analysis further suggests that the length of MSGLs is a function of basal ice velocity and time. Although our data/model correlations confirm the importance of ice velocity in MSGL formation, a significant challenge remains if we are to employ MSGLs as a quantifiable measure of past ice stream velocity.

scholarly journals Surging Glaciers—The Dilemma Continues

1979 ◽  
Vol 24 (90) ◽  
pp. 502-503
Author(s):  
M. F. Meier
Keyword(s):  
Shear Stress ◽  
Phenomenological Approach ◽  
Sliding Velocity ◽  
Recent Interest ◽  
Normal Behavior ◽  
Rapid Flow ◽  
Basal Sliding ◽  
Ice Velocity ◽  
Glacier Flow ◽  
Basal Shear

AbstractA glacier surge, according to most definitions, is a short-lived phase of unusually rapid glacier flow, after which the glacier returns to more normal behavior, with the surge–non-surge phases recurring on a regular or periodic basis. Recent interest is largely directed toward analyzing the effect of water at the bed on the periodic change in flow regime and on the rapid flow during a surge phase. For instance, study of a local depression of basal shear stress that dependson a “friction lubrication factor” which becomes important as the ice velocity increases, is one promising phenomenological approach. An important physical approach focuses on a water “collection zone” that occurs where and when the longitudinal pressure gradient in the subglacial wtaer film approaches zero. The data necessary for properly verifying these and other similar theories do not yet exist. Computer modeling of rapidly-surging glaciers based on a “friction lubrication factor” has been quite successful in duplicating their major features. Once rapid movement (102–103 m a–1) has begun, sufficient water is generated at the bed, from ice melted by heat dissipated in sliding, to produce some decoupling of the glacier from its bed and to maintain the surge, but only if this water is not lost by rapid drainage. Some glaciers exhibit periodic pulses in which the basal sliding velocity during the fastest part of the pulses appears to be in the range for “normal” glaciers (<102 m a–1). Some evidence suggests a continuum of behavior from steady (normal) glaciers through these “mini-surges” to classic surges. This continuum and the “mini-surges” seem to be difficult to explain quantitatively by existing theories. A few glaciers flow continuously at surging speeds (>103 m a–1) in certain reaches. The up-glacier transition reaches show speeds decreasing to “nonrmal” with no indication of intermediate surging regime, but the down-glacier transition reaches may be areas where surges are triggered.

scholarly journals Comparison of Three Contemporary Flow Laws in a Three-Dimensional, Time-Dependent Glacier Model

1973 ◽  
Vol 12 (66) ◽  
pp. 361-373 ◽  
Author(s):  
L. A. Rasmussen ◽  
W. J. Campbell
Keyword(s):  
Shear Stress ◽  
Steady State ◽  
Large Scale ◽  
Three Dimensional ◽  
Time Dependent ◽  
Flow Law ◽  
Glacier Flow ◽  
Basal Shear ◽  
Basal Flow ◽  
Flow Laws

A numerical model for three-dimensional, time-dependent glacier flow (Campbell and Rasmussen, 1970) treated the ice as a Newtonian viscous fluid and related its dynamics to two large-scale bulk parameters: the viscosity v determining the ice-to-ice friction, and a basal friction parameter A determining the ice-to-rock friction. The equations were solved using the relatively simple flow law of Bodvarsson (1955) in which the basal shear stress is proportional to volume transport. Recent research suggests that a more realistic basal flow law is one in which the basal shear stress to some lower power (1–3) is either proportional to the vertically averaged velocity (Glen, 1958; Nye, 1960, 1963[a], [b], [c], 1965[a], [b], [c]) or to the ratio of the vertically averaged velocity to glacier thickness (Budd and Jenssen, in press). In the present study a generalized flow law incorporating all of the above bulk basal flow laws is applied to the Campbell–Rasmussen momentum equation to form a generalized two-dimensional transport equation, which, when combined with the continuity equation, yields a numerically tractable set of equations for three-dimensional, time-dependent glacier flow. Solutions of the model are shown for steady-state flow and surge advance and recovery for a typical valley glacier bed for powers 1, 2, and 3 for each of the basal flow laws for a steady-state climate input and a given ice-to-ice viscosity parameter.

scholarly journals Experimental study on the mean flow characteristics of a supersonic multiple jet configuration

2021 ◽  
Vol 108 ◽  
pp. 106377
Author(s):  
Mohammed Faheem ◽  
Aqib Khan ◽  
Rakesh Kumar ◽  
Sher Afghan Khan ◽  
Waqar Asrar ◽  
...  
Keyword(s):  
Experimental Study ◽  
Flow Characteristics ◽  
Mean Flow ◽  
The Mean
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