Fluid–body interaction in the presence of uniform vorticity and density gradient

Abstract

We consider the case of a rigid or deformable body moving in a linear shear flow of an inviscid, incompressible and inhomogeneous fluid with a uniform density gradient. The body is impulsively introduced into the nonuniform ambient flow field possessing time-dependent vorticity. In order to make the analysis amenable, it is further assumed that the size of the body is small with respect to the inhomogeneity of the ambient flow. By integrating the Euler equation it is shown that analytic expressions can be obtained for the hydrodynamical reactions (forces and moments) acting on the body which determine its trajectories. In addition to the traditional purely inertial quadratic terms, three new types of interaction modes are thus revealed: Vorticity-inertia, density gradient-inertia, and vorticity-density gradient. The first two modes have been considered separately just recently but the third one is presented here for the first time. It is finally demonstrated that all three modes of interaction can be obtained from a relatively straightforward unified approach.