Abstract
The radiation condition for the second‐order diffraction problem was studied. A transient elementary flow was considered, representing the interaction of a progressive plane wave train having a submerged pulsating source. A transient second‐order solution is obtained using the Fourier transform in space and the Laplace transform in time. The radiation condition is obtained by carrying out the asymptotic analysis for large time and far field. To the leading order, the waves at far field consist of a free and forced component. The free component, satisfying the homogeneous form of the free‐surface condition, is shown to represent outgoing waves, decay like 1R, and satisfy the Sommerfeld radiation condition. The forced component satisfies the far‐field form of the nonhomogeneous free‐surface condition. This forced wave component, modulated by the incident wave e-iv0x, represents outgoing or incoming waves, depending on the relative magnitudes of the incident wave and source frequencies of oscillation. The azimuthal variation of the far‐field wave disturbance was also examined.
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