Ice shelf

An ice shelf is the floating extension of a grounded ice sheet. Hydrostatic flotation makes its surface slope and horizontal driving stress depend on the density contrast between ice and seawater.

The grounding line is the transition where an ice sheet detaches from its bed and begins to float as an ice shelf. Ice thickness there obeys the hydrostatic flotation condition.

A shelfy stream is a grounded, rapidly sliding ice stream whose internal resistance is dominated by longitudinal extension, as in an ice shelf, but which retains a basal drag. It is described by the shallow-shelf approximation.

The shallow-shelf approximation treats horizontal velocity as nearly depth-independent and balances membrane stress, hydrostatic driving stress, and basal traction. For Newtonian ice of thickness $h$ and speed $u$, the extensional resultant is $4\mu h{u}_x$.

Short-wavelength corrugations on the underside of a highly viscous ice shelf relax through local Stokes flow. For a wavelength much smaller than the shelf thickness, the deformation occupies a depth of order the inverse wavenumber and the ice may be treated as a viscous half-space.