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An experimental programme has been carried out for studying temperate-ice sliding over rock surfaces with a wide range of roughnesses, for normal and shear stresses comparable to those expected under real ice masses. The limiting static shear stress for acceleration has been found to be directly proportional to the normal load giving a constant limiting coefficient of static friction characteristic of the surface. For a constant applied normal stress N and shear stress τ b, well below the limiting static shear, a steady velocity Vb results which increases approximately proportionally to τ b and decreases with increasing N and the roughness of the surface. For high normal stress the velocity becomes approximately proportional to the shear stress cubed and inversely proportional to the normal stress. As the shear stress increases acceleration sets in, which, for different roughness and normal loads, tends to occur for a constant value of the product τ b Vb . For some surfaces at high normal loads this acceleration was retarded by erosion. For constant-applied-velocity tests a steady shear stress resulted, which tended to become constant with high velocities, and which increased with increasing normal stress but with a reduced coefficient of sliding friction. The relevance of the results to the sliding of real ice masses is discussed with particular reference to the importance of the effect of the relative normal stress, above basal water pressure, to the sliding rate.

A BSTRACT. An experimental progra mme has been carried out for studying te mperate-i ce sliding over r ock surfaces with a wide ra nge of r oughnesses, for n ormal and shear stresses comparable to those expected und er real ice masses. The limiting stati c shear stress for acceleration has been found to be directly proporti onal to the normal load giving a constant limiting coeffici e nt of stat ic fri ctio n characteristic of the surface.Fo r a consta nt applied normal stress N and shear stress Tb, well below the limiting static shear, a steady velocity Vb results whi ch increases a pproxima tely proportionally to Tb and d ecr eases with in creas ing Nand the roughness of the surface. For high norma l stress the veloc ity becomes a pproximately proportiona l to the shear stress cubed and inversely prop o rtio na l to the normal stress . As the shea r stress increases a ccele ra tion sets in, whi ch, for different roughn ess a nd norm al loads, te nds to occur for a co nsta nt value of the produ ct Tb Vb. F o r some surfaces at high norm al loads this acceleration was reta rded by erosio n. For consta nt-a ppliedvelocity tests a steady shear stress res ulted, which tend ed to become co nsta nt with hig h velocities, a nd whi ch in creased with increa sing norma l stress but w ith a redu ced coeffi cient of sliding fri ction. The rel evan ce of the results to the sliding of real ice m asses is discussed with particula r referen ce to the importa nce of the effect of the rel ati ve no rmal stress, a bove b asal water pressure, to the sliding ra te.R ESUME. E ludes empiriques du glissemen t de la glace. On a mis a u point un progra mme experi menta l pour e tudier la gl ace te mpe ree est so n glisse m e nt sur des surfaces r ocheuses de ru gos ite varian t d a ns d e g ra ndes proportions, pour d es etTorts norm a ux o u un cisa illeme nt compa rables a ceu x qu e l'on peut a tte indre d a ns d es masses reell es d e glace. On a trou ve que la contra inte d e cisa ill ement sta tiqu e limite pou r a boutir a u ne acceleration est directe ment proporti o nn ell e a la cha rge n o rm a le ce qui donn e un e valeur limi te constante du coeffi cient d e fri ction stati que qui est un e ca racteristique d ' u ne surface. P o ur un effort norma l co nsta nt Net une co ntra inte d e cisa ill ement Tb , bie n inferieure a u c isa illemen t sta tiqu e limite, une vitesse d 'equilibre V b s'eta blit qui cro it a pprox ima ti vem e nt co mm e T b et d en'o it qua nd croisse nt N e t la rugosit e de la surface. P o ur un effort n o rm a l importa nt la v itesse dev ient approximat ivement propo r t io nn ell e au cube du cisaill ement et in verse m e nt proportionn ell e a l'effo rt norma l. Lorsque le cisaill ement c ro it, l' accelerati on commence qui, pour d iffe re ntes rugosites, et diffe re ntes charges no rm ales tend a ma inte nir co nsta nt le p roduit T b V b. Pour certa ines surfaces a fortes cha rges no rm a les, cette accelera tion est reta rd ee par l'eros ion. P our d es essa is it vitesse co nsta nte, on obti...

A simple computer scheme developed by Budd and Smith (1985) and modified by D. Jenssen has been further developed to provide a rapid computation of steady-state balance fluxes over arbitrary ice masses, given the surface elevations and net accumulation distribution. The scheme provides a powerful diagnostic tool to examine the flux and state of balance over whole ice masses or limited regions to interpret field observations for dynamics or the state of balance.In many cases the uncertainty in the state of balance may be much less than the uncertainty in the deformation and sliding properties of the ice and so the flux and velocities derived from balance could provide a useful guide for the dynamics where direct observations are sparse.The scheme assumes that, on a horizontal scale of many ice thicknesses, the ice-flow direction is approximately down the steepest surface slope. The continuity equation is used to compute steady-state implied downslope fluxes at each grid point from integrations of the net accumulation over the area from the summits to the edges. The algorithm ensures the exact integral balance of the surface net flux over the area with flow through boundaries.Applications are demonstrated for the whole of Antarctica and for regional areas. Comparisons are made between fluxes computed from observed ice thicknesses and velocities and those computed from balance. The observed ice thicknesses can also be used to compute surface velocities from assumed column-to-surface velocity ratios. The combined fluxes from observations and balance can be used to compute rates of change of elevation with time.

ABSTRACT. The generalized (Glen) flow relation for ice, involving the second invariants of the stress deviator and strain-rate tensors, is only expected to hold for isotropic polycrystalline ice. Previous single-stress experiments have shown that for the steady-state flow, which develops at large strains, the tertiary strain rate is greater than the minimum (secondary creep) value by an enhancement factor which is larger for shear than compression. Previous experiments combining shear with compression normal to the shear plane have shown that enhancement of the tertiary octahedral strain rate increases monotonically from compression alone to shear alone. Additional experiments and analyses presented here were conducted to further investigate how the separate tertiary shear and compression strain-rate components are related in combined stress situations. It is found that tertiary compression rates are more strongly influenced by the addition of shear than is given by a Glen-type flow relation, whereas shear is less influenced by additional compression. A scalar function formulation of the flow relation is proposed, which fits the tertiary creep data well and is readily adapted to a generalized form that can be extended to other stress configurations and applied in ice mass modelling. BACKGROUNDIn natural ice masses the most important and common state of deformation is arguably a combination of approximately bed-parallel shear and vertical compression. For deformational flow with a stationary boundary, a region of simple shear is associated in an essential way with bulk transport of ice in glaciers, ice sheets and ice shelves, and this is generally accompanied by normal deformations associated with increasing velocities along the flow and divergence or convergence transverse to the flow.For a coordinate system with x and y horizontal and z vertical, and corresponding component velocities (u, v, w), simple shear deformation in the x direction can be characterized by du/dz = c where we note that the horizontal planes on which the forces generating shear deformation act do not rotate, while compression normal to these planes is described by dw/dz = k, where c/2 and k are the respective shear and vertical compressive strain rates. The compressive flow may be confined or unconfined, and quite generally the accompanying horizontal normal strain rates are du dx ¼ ð À 1Þk and dv dy ¼ Àk where the factors involving indicate the proportions of the deformations in the horizontal directions, relative to the rate of vertical compression. Note that = 1/2 corresponds to uniaxial compression in the z direction, while = 1 corresponds to longitudinally confined compression in the experiments reported here (Fig. 1).The generalized flow relation for ice involving the second invariants of the stress deviator and strain-rate tensors (Nye, 1953;Glen, 1958) provides a useful formulation for the interactions between the individual stress and strain-rate components for isotropic ice. This relation is not expected to apply for anisotropic i...

ABSTRACT. A 345 m deep bore hol e in ice about 385 m thick, near the edge of Law Dome, Antarctica, was drilled in 1974 about 3 km up-slream from the site of a previous bore hole, nearly reaching the bed, obtained in 1969. The core from this n ew bore hole has b een studied comprehe nsively, particularly with regard to the ice-crystal orienta tion fabri cs. Sa mpl es of the ice core were subj ected to simple shear at temperatures and deviatoric stresses whi ch match the ill situ conditions of the ice sh eet.Similar studies of randomly-oriented la boratory-made polycrystalline ice we re undertaken. Long-term tests, lasting for up to two years, were required to determine minimum strain-ra tes. The flow law for the anisotropic ice was thus determined as a fun ction of that for the isotropic ice to ge ther with a measure of c-axis fabri c strength perpendicular to the shear plane.Core studies indicate that the uppe r part of the ice shee t has a polycrystalline structure appropriate to the surface longitudinal stress. Deep e r in the core a strong concentration of n ea r-vertical c-axes develops. Ice having very large crystals with multipl e max ima fa bri cs w as found in the lower quarter of the ice thickness.Shear measurements in the bore hole in dicate the exist e n ce of high strain-rates in the zone of vertical c-axes, and oflower shear-rates below tha t level. The low va lues of shear-rates in the basal region cannot be explained in terms of crystallographic ch a nges alone, a nd the refore it is inferred tha t the shear stress decreases in this layer-a result whi ch also provides a possible explanation for the developme nt of the observed basal crystal structure. On a entrepris des etudes semblabl es sur de la glace polycristalline a orientation quel conque fabriquee en labo ratoire. Les essais a long terme s'etendant sur plus de deux ans, etaien t necessaires pour determiner les vitesses de deformation minimum. L a loi d' ecouleme nt pour un e glace anisotrope a alors ete determinee comme une fonction de celle s'appliquant a la glace isotrope associee a une m esure de I'abondance des cristaux a axes-c p e rpendiculaires a u pla n d e cisa illement. REsuME. Proprietis de I' ecoulement des calottes glaciaires deduites des mesures de cisaille1llent dans des forages c01llbilleeSLes etudes de carottes indiquent que la partie superieure des calottes glaciaires ont une structure polycristalline adaptee aux efforts longitudinaux en surface. Plus profond dans la carotte une forte concentration d'axes-c presque verticaux se manifeste . D e la glace a tres grands cristaux et de multiples maximums d'orientations d'axes a ete trouve dans le dernier quart de I'epaisseur de la glace.Les mesures de cisaill ement dans le forage sont I' indi ce de I' existence d'une forte vitesse de deformation dans la zone a axe-c verticaux et d ' un plus faibl e cisai ll em e nt sous ce niveau. Les faibles valeurs des vitesses de cisaillement dans la region du fond ne peuvent s'expliquer seulement par des changements cristallographiques et ...

High rates of sea ice growth and brine rejection in the Mertz Glacier Polynya drive the production of dense continental shelf waters in the Adélie Depression. We consider the rate of outflow of waters having sufficient density to sink into the neighboring abyssal ocean and form Adélie Land Bottom Water (ALBW). Along with Weddell and Ross Sea Bottom Waters, the ALBW is an important source of Antarctic Bottom Water. The relevant processes are modeled using a variant of the Max Planck Institute Ocean Model (MPIOM) under daily NCEP‐NCAR reanalysis forcing for the period 1991–2000. The orthogonal curvilinear horizontal grid allows for the construction of a global domain with high resolution in our region of interest. The modeled Mertz Glacier Polynya is realistic in location and extent, exhibiting low ice thickness (<0.4 m) and low ice fraction (<50%). The net surface ocean to atmosphere heat flux exceeds 200 W m2 and is dominated by sensible heat exchange. In wintertime (May through September inclusive), 7.5 m of sea ice forms over the Adélie Depression at a rate of 4.9 cm d−1: this results in annual average volumetric production of 99 km3 of sea ice. The associated brine release drives dense shelf water formation. The off‐shelf flow of dense water exhibits strong interannual variability in response to variability in both atmospheric forcing and ocean preconditioning. Averaged over the period 1991–2000 the off shelf flow of dense water is 0.15 Sv: for a period of strong outflow (1993–1997), this increases to 0.24 Sv. Most of the outflow occurs during July through October, at a rate of 0.40 (0.63) Sv over the period 1991–2000 (1993–1997). The peak mean monthly outflow can exceed 1 Sv.

The use of well known simple periodic solutions of the two-dimensional biharmonic stress equation for studying the flow over undulations of an ice mass of small surface slope is examined. The model considered is one in which most of the shear (deformation or. sliding) takes place near the base and the upper part moves largely as a block, with longitudinal strain-rates varying linearly with the longitudinal stress deviations. For bedrock perturbations of a given wavelength the steady-state surface shape consists of similar waves but out of phase by ½π, such that the steepest slope occurs over the highest bedrock; and the amplitude is reduced by a “damping factor”, depending on the speed, viscosity, ice thickness and wavelength.Minimum damping occurs forλm≈ 3.3 times the ice thickness, while waves much longer or much shorter than this are almost completely damped out. The energy dissipation and the resistance to the ice flow is also a maximum for an undulation scale of several times the ice thickness, whereas the effects of small basal irregularities die out exponentially with distance into the ice, and only have an effect in so far as the average basal stress is related to the average surface slope. As a result of this a revision of present glacier sliding theories becomes possible.Various predictions of the theory have been confirmed from spectral analysis of surface and bedrock profiles of ice caps.