Open AccessMATHEMATICAL MODELING OF LARGE OBJECTS IN SHALLOW WATER WAVES AND UNIFORM CURRENT
Author(s) -
Hsiang Wang
Publication year - 1972
Publication title -
proceedings of conference on coastal engineering/proceedings of ... conference on coastal engineering
Language(s) - English
Resource type - Journals
eISSN - 2156-1028
pISSN - 0589-087X
DOI - 10.9753/icce.v13.96
Subject(s) - conical surface , velocity potential , mechanics , cnoidal wave , axial symmetry , potential flow , wind wave , physics , wave shoaling , current (fluid) , amplitude , waves and shallow water , surface wave , field (mathematics) , classical mechanics , action (physics) , flow (mathematics) , wave propagation , optics , geometry , mathematics , longitudinal wave , mechanical wave , boundary value problem , quantum mechanics , pure mathematics , thermodynamics
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.