Sommerfeld radiation condition

The Sommerfeld radiation condition is the far-field boundary condition that forces wave energy to propagate outward from a disturbance rather than inward, removing the spurious incoming-wave solutions that the governing equation would otherwise allow. For a velocity potential it requires the radiated field to behave as an outgoing wave at large radius, with no reflected energy returning from infinity. In ship hydrodynamics it makes the radiation-diffraction and steady wave-resistance problems well posed, fixing the otherwise ambiguous Kelvin wake. Numerically it is imposed through upstream finite differencing, as in Dawson’s Rankine method, damping beaches, or matched Green functions, so a truncated mesh does not reflect waves back.