Solution to the Stokes´ First Problem for the Earthquake-Induced Flow

The classical Stokes´ problems are of great importance in many theoretical studies and practical applications. There are two kinds of Stokes´ problems [1] referred to the flow induced by a moving plate with constant speed and the oscillating plate, respectively. For geophysicists interested in the flow induced by earthquakes, fracture of ice sheets and other related problems, the extension of the classical Stokes´ problems is required to calculate practical geophysical flows. Hence, in present study, the Stokes´ first problem is modified to calculate the flow driven by a moving half-infinite plate (see Fig.l). The significant application of present study is to simulate the fluid motion motivated by the earthquake. Different from the existing results given by Zeng and Weinbaum [2], by using some mathematical techniques and integral transforms associated with the concept of symmetrical space, the velocity profile is obtained in a much easier way. At both far ends, present solution is reduced to that of the classical Stokes´ first problem which implies the effect of discontinuity at z=0 does not affect the far- field flow. In conclusion, present study provides a basis for predicting the flow while the earthquake occurs..