Viscosity of the upper mantle as non-Newtonian fluid.

The problem of isostatic recovery of incompressible and highly viscous fluid is considered for the case of non-Newtonian fluid which satisfies the following relation between the strain rate ε and the stress difference τ:ε∝τn (n>1). Because of nonlinearity of the equations of motion, it is impossible to solve them analytically. In this paper, therefore, the variational method is applied and a relation between the relaxation time of isostatic recovery τr and the wave length λ is obtained approximately. The case when the top surface is free and the bottom surface is rigid is considered. From the theoretical results and the postglacial uplife data of Fennoscandia and Laurentide, the upper mantle can be understood as a non-Newtonian fluid in which the strain rate is approximately proportional to the third power of the stress difference (n=3). This is in accordance with the results of WEERTMAN (1970), STOCKER and ASHBY (1973) and so on. The effective viscosity of the upper mantle is found to be η=5×1011ε-2/3 poises, where the unit of ε is sec-1. For the geological strain rate, say 10-15sec-1, the apparent viscosity is 5×1021 poises. This value is of the same order as the results of previous workers.