Acceleration of shear flow ina viscoplastic half-plane with a depth-varying yield stress

The problem of acceleration from a state of rest of a shear flow in a viscoplastic half-plane is studied analytically when a tangential stress is specified at the boundary. It is assumed that the dynamic viscosity and density of the medium are constant, and the yield stress can change in a continuous or discontinuous manner depending on the depth. The entire half-plane at any moment of time consists of previously unknown layers where shear flow occurs and rigid zones. The latter can move as a rigid whole, or they can be motionless, such as, for example, a half-plane, to which disturbances caused by the action of tangential forces have not yet reached. To find the stress and velocity fields, a method is developed based on quasi-self-similar diffusion-vortex solutions of parabolic problems in areas with moving boundaries. The question of what conclusions about the depth distribution of the yield stress can be drawn from available measurements of the velocity of the half-plane boundary is discussed.