Driving stress#
Ice-sheet flow is driven by gravity. Specifically it is a quantity called the driving stress that drives flow:
where
Derivation.#
Consider a column of ice that extends from the ice-sheet bed to the surface and has length
where
(todo: replace this figure, add figure caption)
To calculate the force acting on one side of the ice column (blue arrow), with thickness
Note that in this calculation, we have assumed constant
The more relevant quantity to consider here is not just the force acting on one side of the ice column, but rather the difference between the forces on either side. If we imagine that the ice column is part of an ice sheet with a surface slope of
We can now invoke the chain rule to rewrite this as
This is the stres imbalance integrated over the is ice thickness and across a width
This makes sense intuitively; there is more driving stress where the ice is thicker (higher
We can generalize this to two dimensions as follows:
The driving stress field will point in the direction in which the slope changes the fastest.
We can also generalize this to account for cases when the be topography is not flat:
where