The sectional diffraction wave force is given in Equation ( 26 ), note that this equation includes the water density, r, and the wave amplitude, z. The depth attenuation exponent in the e-kx term has the opposite sign since Seakeeper sign convention has z +ve down:
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Expanding the sine and cosine terms, this may be rewritten as follows:
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( 27 ) |
where:
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ω0 |
is the wave frequency. |
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ωe |
is the frequency of the oscillation of the section (encounter frequency). |
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x,y,z |
are the longitudinal position of the section, and transverse and vertical points on the section contour respectively. |
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are the outward normal unit vector of the section. |
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Cs,dl |
are the section contour and element of arc along the section. |
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μ |
is the wave heading angle. |
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is the amplitude of the two dimensional velocity potential of the section in heave. |
Further, the time varying velocity potential is given by:
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The segment length for the integration is calculated assuming a straight line between integration points. The unit normal vector components are calculated from the slope of the mapped section.
The velocity potential on the surface of the section at p=(y, z), is calculated by combining all the individual terms in the velocity potential as per Equation( 28 ), note that it is the amplitude of the velocity potential that is required.
