On wave-free bottom oscillations at uniform water depth

The radiation of water waves from finite oscillating bottom domains in an unbounded sea with constant depth is investigated analytically. The free-surface conditions are linearized, with radiation conditions at infinity. The far field from an oscillating bottom source is derived. General formulas are given for the radiated energy flux. Exact energy flux spectra are derived for some simple geometries. Wave-free oscillations exist for many axisymmetric structures, and for certain superpositions of locally axisymmetric structures.