Page 102 - Introduction to Naval Architecture
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THE ENVIRONMENT 89
Figure 5.3 Pressure in wave
length of the wave. The variation is due to the fact that the wave
particles move in circular orbits. It is a dynamic effect, not one due to
density variations. It can be shown that the pressure at a point z below
the wave surface is the same as the hydrostatic pressure at a depth z',
where z' is the distance between the mean, still water, axis of the surface
trochoid and that for the subsurface trochoid through the point
considered.
To obtain the forces acting on the ship in the wave the usual hydrostatic
pressure based on depth must be corrected in accordance with this
relationship. This correction is generally known as the Smith effect. Its
effect is to increase pressure below the trough and reduce it below the
crest for a given absolute depth.
The sinusoidal wave
Trochoidal waveforms are difficult to manipulate mathematically and
irregular waves are analysed for their sinusoidal components. Taking
the ^-axis in the still water surface, the same as the mid-height of the
wave, and z-axis vertically down, the wave surface height at x and time
t can be written as:
