Kochin Function

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The Kochin function [math]\displaystyle{ \mathbf{H}(\tau) }[/math] is given by

[math]\displaystyle{ \mathbf{H}(\tau)=\iint_{\Gamma_s}\left( -\frac{\delta\phi}{\delta n} + \phi\frac{\delta}{\delta n}\right) e^{kz}e^{ik(x\cos\tau +y\sin\tau)}\mathrm{d}S, }[/math]

where [math]\displaystyle{ \delta/\delta n }[/math] is the inward normal derivative, [math]\displaystyle{ \phi }[/math] is the velocity potential and [math]\displaystyle{ \Gamma_s }[/math] is the wetted body surface.

Many physical parameters, such as the Scattered Wave in Three-Dimensions, the Radiated Energy in Three-Dimensions, and the Wave Forces in Three-Dimensions can be calculated from the Kochin Function.