Newtonian shallow-ice flux ($q=-g{h}^3{h}_x/(3\nu )$)

For a two-dimensional Newtonian ice sheet of thickness $h$ on a flat no-slip bed, hydrostatic pressure and vertical shear give the depth-integrated fluxwhere $\nu$ is the kinematic viscosity. Mass conservation is $h_t+q_x=a$ for accumulation rate $a$.