Transverse waves in a viscous fluid induced by rotating oscillations of a porous sphere

Background. The studying of the fluid motion through porous media is of a significant interest for investigation of natural phenomena and technological processes. The paper considers the motion of a viscous fluid induced by rotating oscillations of a porous sphere in the fluid that is immersed in a nonpermeable concentric spherical shell. Materials and methods. We used the methods of mathematical physics and vector analysis. The problem was solved in a spherical coordinate system. For graphs constructing we used numerical methods. Results. The study has determined the motion of viscous fluid inside and outside of the porous sphere. Exact solutions have been obtained for the nonsteady Brinkman equations inside of the porous sphere and for Navier-Stokes equations outside one. Conclusions. The work proves the existence of intrinsic transverse waves, the velocity of which is perpendicular to the direction of their propagation. Inside of the porous sphere the velocity is changing from zero in the centre to a certain value at the surface. Outside the sphere the velocity is changing to zero when moving away from the surface. At the surface of the sphere the velocity is continuous.