MATHEMATICAL MODELING OF LARGE OBJECTS IN SHALLOW WATER WAVES AND UNIFORM CURRENT

Hsiang Wang

Abstract


A mathematical model is presented which portrays the physical system of a large axially symmetric structure in a flow field of finite water depth, large amplitude wave and strong current. The flow field, which enters as the input, is derived from a velocity potential similar to that of the cnoidal wave of Keulegan and Patterson. The inclusion of a uniform velocity in the derivation of velocity potential results in a cross interference term in addition to the well known Doppler shift effect. The numerical results are compared with experiments on a bridge pier (Ref. 6) which is partially cylindrical with base diameter equivalent to 100 feet in prototype; close to the surface, where the wave action is greatest it is conical. These results are also compared with theoretical calculations based on linear wave theory and fifth-order wave theory. It is concluded that the results based on the modified cnoidal wave theory come closest to the experimental value.

Keywords


mathematical model; shallow water; uniform current

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