The Motion of a Viscous Fluid Under a Surface Load. Part II

Abstract

Following up previous work on the subsidence of a circular load on the surface of a highly viscous fluid, the same problem is treated for the case of a load in the form of an infinitely long strip with parallel sides. Simple expressions are derived for the limiting displacements as the system approaches hydrostatic equilibrium and for the form taken by the surface of the fluid at any time during the motion. Curves illustrating these quantities are plotted. It is pointed out that the subsidence of a load on the earth's surface having a span comparable to that of a continental ice sheet must produce appreciable flow at great depth. Using the previously derived figure for the mean viscosity of the earth it is found that with a load 2000 km wide equilibrium would be very nearly reached in about 18,000 years, and that loads of smaller span would require proportionately greater time to reach the same stage.