On sloshing in containers with porous baffles

Sloshing eigenvalues are studied for containers with porous baffles extending throughout the constant (possibly infinite) depth. The fluid transmission across the baffles is described by Darcy's law, and so the spectral problem is nonself-adjoint. In particular, much attention is paid to vertical cylinders with circular walls and radial baffles. Explicit solutions are obtained, whose crucial feature is that the corresponding pressure difference vanishes across the baffle. These real solutions coincide with those that describe sloshing in the presence of rigid baffles, thus demonstrating that at certain frequencies the damping efficiency of porous baffles is the same as that of the rigid ones having the same configuration.