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 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.

The structure of weakly compressible grid-generated turbulence

2001 ◽  
Vol 432 ◽  
pp. 219-283 ◽  
Author(s):  
G. BRIASSULIS ◽  
J. H. AGUI ◽  
Y. ANDREOPOULOS
Keyword(s):  
Mach Number ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Three Dimensional ◽  
High Amplitude ◽  
Time Dependent ◽  
Wide Range ◽  
Dynamical Flow ◽  
Set Up ◽  
Decay Exponent

A decaying compressible nearly homogeneous and nearly isotropic grid-generated turbulent flow has been set up in a large scale shock tube research facility. Experiments have been performed using instrumentation with spatial resolution of the order of 7 to 26 Kolmogorov viscous length scales. A variety of turbulence-generating grids provided a wide range of turbulence scales with bulk flow Mach numbers ranging from 0.3 to 0.6 and turbulent Reynolds numbers up to 700. The decay of Mach number fluctuations was found to follow a power law similar to that describing the decay of incompressible isotropic turbulence. It was also found that the decay coefficient and the decay exponent decrease with increasing Mach number while the virtual origin increases with increasing Mach number. A possible mechanism responsible for these effects appears to be the inherently low growth rate of compressible shear layers emanating from the cylindrical rods of the grid. Measurements of the time-dependent, three dimensional vorticity vectors were attempted for the first time with a 12-wire miniature probe. This also allowed estimates of dilatation, compressible dissipation and dilatational stretching to be obtained. It was found that the fluctuations of these quantities increase with increasing mean Mach number of the flow. The time-dependent signals of enstrophy, vortex stretching/tilting vector and dilatational stretching vector were found to exhibit a rather strong intermittent behaviour which is characterized by high-amplitude bursts with values up to 8 times their r.m.s. within periods of less violent and longer lived events. Several of these bursts are evident in all the signals, suggesting the existence of a dynamical flow phenomenon as a common cause.

scholarly journals Inversion of flow Measurements for Stress and Rheological Parameters in a Valley Glacier

1973 ◽  
Vol 12 (64) ◽  
pp. 19-44
Author(s):  
Charles F. Raymond
Keyword(s):  
Shear Stress ◽  
Power Law ◽  
Measurement Errors ◽  
Effective Viscosity ◽  
Three Dimensional ◽  
Rheological Parameters ◽  
Mean Stress ◽  
Flow Measurements ◽  
Anomalous Zone ◽  
Flow Law

AbstractMethods are developed for determining the distributions of stress and effective viscosity in a glacier, under the assumptions: the ice is quasi-viscous, the flow is time independent, and acceleration forces are negligible. Measurements of the three-dimensional distribution of velocity are needed for their application. The differential equations of mechanical equilibrium, expressed in terms of viscosity, strain-rate components, mean stress, and their gradients, are viewed as equations to be solved for viscosity and mean stress subject to boundary conditions at the free upper surface. For certain rectilinear flow patterns, unique distributions of stress and effective viscosity can always be derived. For more complicated flow this is not necessarily so. However, it is still possible to choose the best values of rheological parameters in any trial flow law based on the requirement that the residuals to the equations of equilibrium be minimized in a mean-square sense. The techniques are applied to measurements of internal deformation made in nine bore holes on the Athabasca Glacier. At the center line the magnitude of the surface-parallel shear stress increases with depth more slowly than would be expected from a standard shape factor correction or the theoretical distribution of Nye. Correspondingly the lateral distribution of lateral shear stress shows the opposite relationships. In the lower one- to two-thirds of the depth corresponding to a range in effective stress from about 0.5 to 1.2 bars, the gross rheology of the ice is not distinguishably different from the experimentally determined flow law of Glen (n = 4.2, T = 0.02° C) as generalized by Nye. The results do not support the conclusion that the effective viscosity is higher than would be expected from Glen’s experiments as indicated by the more limited measurements of Paterson and Savage. Power-law parameters derived for the different bore holes considered separately show a spread, which suggests some rheological inhomogeneity. However, no definite conclusions can be drawn, because of direct measurement errors at the bore holes and less definable uncertainty in the interpolated distribution of velocity between the holes. The upper one- to two-thirds of the glacier constitutes an anomalous zone in which there is either a strong effect from a complex distribution of stress arising from longitudinal stress gradients or more complicated rheology than in a homogeneous power-law material.

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.

Turbulent Vorticity Diffusion in the Stronger Wall Jet Managed by a Flat Plate Wing in the Outer Layer

2015 ◽  
Author(s):  
Takuma Katayama ◽  
Shinsuke Mochizuki
Keyword(s):  
Shear Stress ◽  
Flat Plate ◽  
Outer Layer ◽  
Large Scale ◽  
Reynolds Shear Stress ◽  
Three Dimensional ◽  
Quantitative Relationship ◽  
Wall Jet ◽  
Mean Velocity ◽  
The Mean

The present experiment focuses on the vorticity diffusion in a stronger wall jet managed by a three-dimensional flat plate wing in the outer layer. Measurement of the fluctuating velocities and vorticity correlation has been carried out with 4-wire vorticity probe. The turbulent vorticity diffusion due to the large scale eddies in the outer layer is quantitatively examined by using the 4-wire vorticity probe. Quantitative relationship between vortex structure and Reynolds shear stress is revealed by means of directly measured experimental evidence which explains vorticity diffusion process and influence of the manipulating wing. It is expected that the three-dimensional outer layer manipulator contributes to keep convex profile of the mean velocity, namely, suppression of the turbulent diffusion and entrainment.

scholarly journals Basal shear stress under alpine glaciers: insights from experiments using the iSOSIA and Elmer/Ice models

2016 ◽  
Vol 4 (1) ◽  
pp. 159-174 ◽  
Author(s):  
C. F. Brædstrup ◽  
D. L. Egholm ◽  
S. V. Ugelvig ◽  
V. K. Pedersen
Keyword(s):  
Shear Stress ◽  
Landscape Evolution ◽  
Empirical Studies ◽  
Three Dimensional ◽  
Temporal Distribution ◽  
Higher Order ◽  
Glacial Erosion ◽  
Significant Control ◽  
Basal Sliding ◽  
Basal Shear

Abstract. Shear stress at the base of glaciers exerts a significant control on basal sliding and hence also glacial erosion in arctic and high-altitude areas. However, the inaccessible nature of glacial beds complicates empirical studies of basal shear stress, and little is therefore known of its spatial and temporal distribution. In this study we seek to improve our understanding of basal shear stress using a higher-order numerical ice model (iSOSIA). In order to test the validity of the higher-order model, we first compare the detailed distribution of basal shear stress in iSOSIA and in a three-dimensional full-Stokes model (Elmer/Ice). We find that iSOSIA and Elmer/Ice predict similar first-order stress and velocity patterns, and that differences are restricted to local variations at length scales of the order of the grid resolution. In addition, we find that subglacial shear stress is relatively uniform and insensitive to subtle changes in local topographic relief. Following the initial comparison studies, we use iSOSIA to investigate changes in basal shear stress as a result of landscape evolution by glacial erosion. The experiments with landscape evolution show that subglacial shear stress decreases as glacial erosion transforms preglacial V-shaped valleys into U-shaped troughs. These findings support the hypothesis that glacial erosion is most efficient in the early stages of glacial landscape development.

scholarly journals A Glacier Flow Model Incorporating Longitudinal Deviatoric Stresses

1984 ◽  
Vol 30 (106) ◽  
pp. 334-340 ◽  
Author(s):  
E. M. Shoemaker ◽  
L. W. Morland
Keyword(s):  
Steady State ◽  
Deviatoric Stress ◽  
Shear Stresses ◽  
Field Equations ◽  
Plane Flow ◽  
Steady State Model ◽  
Glacier Flow ◽  
Basal Shear ◽  
Deviatoric Stresses ◽  
Proper Generalization

AbstractA model for glacier flow is developed which incorporates longitudinal deviatoric stress contributions to the field equations. The underlying assumptions may be applied to develop models for various situations. Here, they are developed for steady-state and non-steady-state sliding glaciers in plane flow. The models reduce to a proper generalization of plane-flow pseudo-hydrostatic theory if longitudinal deviatoric stresses are neglected in comparison to basal shear stresses. Solution of this simpler reduced model allows an estimate to be made of the magnitude of the longitudinal deviatoric stress to test if it is negligible or, more generally, investigate under what conditions it can be neglected. The steady-state model predicts that longitudinal deviatoric stresses are negligible for very arbitrary non-uniform sliding-law distributions provided that the following conditions exist: the region must be distant from an ice divide or terminus and subject to normal (not extreme) accumulation or ablation. On the other hand, examples are produced where, under non-steady conditions, longitudinal deviatoric stresses are important and even dominant.

Analysis of a LPT Rotor Blade for a Geared Engine: Part II — Characterization of the Time-Varying Flow Field in a Single Stage Research Turbine

2016 ◽  
Author(s):  
Daniele Infantino ◽  
Francesca Satta ◽  
Daniele Simoni ◽  
Marina Ubaldi ◽  
Pietro Zunino ◽  
...  
Keyword(s):  
Flow Field ◽  
Rotor Blade ◽  
Large Scale ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Single Stage ◽  
Tip Vortex ◽  
Time Dependent ◽  
Exit Plane ◽  
Open Rotor

The present paper is the second part of a two-part paper focused on the design and the analysis of an optimized rotor blade for a geared open rotor engine. This part is focused on the experimental investigation of the three-dimensional unsteady flow field at the exit plane of a rotor row installed in a large scale single-stage low speed research turbine. The investigation is aimed at in depth characterizing the wake-boundary layer and the vortex-vortex interaction processes induced by the rotor-stator relative motion. Measurements have been carried out at a typical aeroengine cruise condition Reynolds number. The rotor blade aerodynamic loadings at different blade spans have been measured. A five-hole probe has been used to assess the row efficiency and detailed hot-wire phase-locked ensemble-averaged data have been analyzed to characterize the three-dimensional time-dependent flow field at the rotor exit plane. Results clearly highlight a significant distortion of the rotor blade wake and tip vortex during the migration of the high turbulence regions (wake and secondary flows) associated with the upstream stator. The unsteady interaction between the stator secondary flows and the rotor passage vortex provokes a time dependent movement of the low momentum area at the hub surface, sensibly modifying the penetration of the rotor secondary flows in an incoming stator wake passage period. The comparison of deterministic and random velocity fluctuations also allows the distinction between the structures generated by the stator and those due to the rotor.

scholarly journals In search of ice-stream sticky spots

1993 ◽  
Vol 39 (133) ◽  
pp. 447-454 ◽  
Author(s):  
Richard B. Alley
Keyword(s):  
Shear Stress ◽  
Large Scale ◽  
Water Pressure ◽  
Pressure Measurements ◽  
West Antarctica ◽  
Ice Surface ◽  
Ice Stream ◽  
Bed Roughness ◽  
Basal Shear

AbstractThe basal shear stress of an ice stream may be supported disproportionately on localized regions or “sticky spots”. The drag induced by large bedrock bumps sticking into the base of an ice stream is the most likely cause of sticky spots. Discontinuity of lubricating till can cause sticky spots, but they will collect lubricating water and therefore are unlikely to support a shear stress of more than a few tenths of a bar unless they contain abundant large bumps. Raised regions on the ice-air surface can also cause moderate increases in the shear stress supported on the bed beneath. Surveys of large-scale bed roughness would identify sticky spots caused by bedrock bumps, water-pressure measurements in regions of thin or zero till might reveal whether they were sticky spots, and strain grids across the margins of ice-surface highs would show whether the highs were causing sticky spots. Sticky spots probably are not dominant in controlling Ice Stream Β near the Upstream Β camp, West Antarctica.

Very-large-scale motions in a turbulent boundary layer

2011 ◽  
Vol 673 ◽  
pp. 80-120 ◽  
Author(s):  
JAE HWA LEE ◽  
HYUNG JIN SUNG
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Spatial Organization ◽  
Reynolds Shear Stress ◽  
Three Dimensional ◽  
Hairpin Vortices ◽  
Extraction Algorithm ◽  
Normal Distance

Direct numerical simulation of a turbulent boundary layer was performed to investigate the spatially coherent structures associated with very-large-scale motions (VLSMs). The Reynolds number was varied in the range Reθ = 570–2560. The main simulation was conducted by using a computational box greater than 50δo in the streamwise domain, where δo is the boundary layer thickness at the inlet, and inflow data was obtained from a separate inflow simulation based on Lund's method. Inspection of the three-dimensional instantaneous fields showed that groups of hairpin vortices are coherently arranged in the streamwise direction and that these groups create significantly elongated low- and high-momentum regions with large amounts of Reynolds shear stress. Adjacent packet-type structures combine to form the VLSMs; this formation process is attributed to continuous stretching of the hairpins coupled with lifting-up and backward curling of the vortices. The growth of the spanwise scale of the hairpin packets occurs continuously, so it increases rapidly to double that of the original width of the packets. We employed the modified feature extraction algorithm developed by Ganapathisubramani, Longmire & Marusic (J. Fluid Mech., vol. 478, 2003, p. 35) to identify the properties of the VLSMs of hairpin vortices. In the log layer, patches with the length greater than 3δ–4δ account for more than 40% of all the patches and these VLSMs contribute approximately 45% of the total Reynolds shear stress included in all the patches. The VLSMs have a statistical streamwise coherence of the order of ~6δ; the spatial organization and coherence decrease away from the wall, but the spanwise width increases monotonically with the wall-normal distance. Finally, the application of linear stochastic estimation demonstrated the presence of packet organization in the form of a train of packets in the log layer.

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