Glacial motion is the motion of glaciers, which can be likened to rivers of ice. It has played an important role in sculpting many landscapes. Most lakes in the world occupy basins scoured out by glaciers. Glacial motion can be fast (up to 30 metres per day (98 ft/d), observed on Jakobshavn Isbræ in Greenland) or slow (0.5 metres per year (20 in/year) on small glaciers or in the center of ice sheets), but is typically around 25 centimetres per day (9.8 in/d).
Processes of motion Glacier motion occurs from four processes, all driven by gravity: basal sliding, glacial quakes generating fractional movements of large sections of ice, bed deformation, and internal deformation.
In the case of basal sliding, the entire glacier slides over its bed. This type of motion is enhanced if the bed is soft sediment, if the glacier bed is thawed and if meltwater is prevalent. Bed deformation is thus usually limited to areas of sliding. Seasonal melt ponding and penetrating under glaciers shows seasonal acceleration and deceleration of ice flows affecting whole icesheets. Some glaciers experience glacial quakes—glaciers "as large as Manhattan and as tall as the Empire State Building, can move 10 meters in less than a minute, a jolt that is sufficient to generate moderate seismic waves." There has been an increasing pattern of these ice quakes - "Quakes ranged from six to 15 per year from 1993 to 2002, then jumped to 20 in 2003, 23 in 2004, and 32 in the first 10 months of 2005." A glacier that is frozen up to its bed does not experience basal sliding. Internal deformation occurs when the weight of the ice causes the deformation of ice crystals. This takes place most readily near the glacier bed, where pressures are highest. There are glaciers that primarily move via sliding, glacial quakes, and others that move almost entirely through deformation.
Governing physical principles Glaciers move and flow downslope due to either deformation or sliding. The flow of material through a glacier is generally not constant at various points within the glacier itself, but is rather faster or slower depending on a plethora of contributing factors. One way to describe these factors is by describing their impact on glacier stresses. One may distinguish between two kinds of stresses: driving stresses (for which gravity causes the glacier to flow downslope) or resistive stresses (which prevent the glacier's downslope acceleration). Stress is a vector quantity with units of force per unit area. It is a useful quantity for describing glacial movement because the efficacy of a force (such as gravity or friction) is emphasized or weakened depending on the area over which it is distributed. For the purposes of describing glacial motion, we can classify all stresses as either (a) normal stresses which act perpendicular to a surface of interest or (b) shear stresses which act transversely to a surface of interest. Glacial ice experiences a driving stress due to basal shear stresses, which are shear stresses on the glacial bed. For a basic model of basal shear stress, we may say that:
τ = ρ g h sin ( α ) {\displaystyle \tau =\rho gh\sin(\alpha )}
Where α is the slope of the glacial bed, ρ is the ice density, g is the acceleration of gravity, and h is the ice thickness. Also note that:
σ = ρ g h {\displaystyle \sigma =\rho gh}
Where sigma is the normal stress experienced by the glacial bed due to the weight of the glacial ice. (Note that the expression ρgh is equivalent to the expression for hydrostatic pressure, i.e. the static stress exerted on some point under the weight of a fluid column). As such, the shear stress is simply the downslope component of the glacial ice's weight. It is thus evident that the stress state of the glacier is not constant through the thickness of the glacier, because the normal stress increases closer to the glacial bed due to higher weight being carried on lower layers (indeed the stress varies ~linearly with depth). Regardless, under this driving shear stress, the glacial ice will deform, experiencing non-linear viscous flow. The relationship for the amount of deformation and driving shear stress can be modeled using the Glen-Nye Flow Law which is a constitutive law to describe the rheology of glacial ice and states that:
ϵ ˙ e = A τ e n {\displaystyle {\dot {\epsilon }}_{e}=A\tau _{e}^{n}}
In essence, the rate of strain (deformation per unit length of the glacier) is proportional to a constant A times the basal shear stress to the power of n, another constant. Typically,
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