Convective motion and transfer of force by many-body hydrodynamic interaction

We consider hydrodynamic interactions between N rigid bodies of arbitrary shape immersed in an incompressible fluid. When the bodies are carried along by an incident flow without exerting forces or torques on the fluid then their translational and rotational velocities are linearly related to the incident flow velocity by convection kernels. In the absence of an incident flow, but with applied forces and torques, the force density acting on the fluid is linearly related to the forces and torques by transfer kernels. We show that the convection and transfer kernels are simply related by a symmetry relation. For freely moving bodies the force density exerted on the fluid is related to the incident flow by a convective friction kernel. We show that this kernel is symmetric.