INTERACTION OF AN UNSTEADY-STATE WAVE WITH A RIGID SPHERE IMMERSED IN A COMPRESSIBLE VISCOUS-FLUID

The non-stationary interaction of an immovably fixed absolutely rigid sphere immersed in a compressible viscous fluid with a plane unsteady-state longitudinal wave is considered. A Laplace integral transformation is applied to obtain an expression in the transform space for the reaction of the fluid on the sphere. This expression is inverted by analytical and numerical methods. The linearized problems for a compressible viscous fluid considered in this paper produce, in the limit, the standard results for an acoustic medium /1/. Dynamic problems for rigid bodies immersed in a compressible viscous fluid are considered in the framework of linearized Navier-Stokes equations in /2/. Linearized equations with inertial terms are the equations obtained from the non-linear Navier-Strokes equations as it applies to small-perturbation problems. We have previously used this framework to investigate the non-stationary motion of a rigid sphere under the action of an active force /3/ and an impulse /4/ imparted to the sphere at the initial time. The non-stationary interaction of rigid and deformable bodies with unsteady-state waves propagating in an acoustic medium was considered in particular, in /1, 5/.