Analysis of the wave-induced motion of underwater vehicles near the ocean surface is a difficult task. First, the action of the fluid must be decomposed into ideal (inviscid) and real (viscous) effects. Next, each effect must be modeled as to its interaction with the submerged body. The effect of the body on the waves must be considered. In shallow water, the ocean bottom has many effects: energy-dissipation tends to reduce wave height; land-proximity restricts the wave direction; and the bottom boundary changes the shape of the waves, attenuating the vertical (but not the horizontal) component of motion. This paper presents mathematical models for predicting realistic wave-generated forces and moments on submersible vehicles. Included are models which generate typical wave spectra for deep and shallow waters, models for wave kinematics as affected by flat or sloping bottoms, and models for forces and moments on submersibles due to these surface waves.

Forces and moments are computed using two alternative methods. One is a fast method based on analytical integration of dynamic pressure forces over the surface of an elongated ellipsoidal body. It gives first-order forces and moments limited to horizontal and restrained bodies. The second method, based on the Froude-Krylov approach, uses numerical integration of dynamic pressures to give forces and moments on any shape hull in any attitude. Unlike the first method, it can be extended to include broaching of the sea surface by the body. Hydrodynamic forces due to an unrestrained body’s motion are accounted for with “added mass” terms.

These mathematical models have been implemented in the C language in a real-time computer simulation. They are actively used to study the dynamic performance and control of submersibles at periscope depths.

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