Open AccessA PARABOLIC REFRACTION-DIFFRACTION EQUATION IN THE RAT-FRONT COORDINATE SYSTEM
Author(s) -
Masahiko Isobe
Publication year - 1986
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.v20.24
Subject(s) - curvilinear coordinates , parabolic cylindrical coordinates , parabolic partial differential equation , diffraction , coordinate system , refraction , wave equation , mathematical analysis , cylindrical coordinate system , parabolic cylinder function , range (aeronautics) , physics , mathematics , optics , partial differential equation , geometry , materials science , composite material
The parabolic equation method has been extensively used for combined refraction and diffraction problems of water waves. However, a parabolic equation is valid only when the direction of wave propagation nearly coincides with that of a coordinate; therefore, the validity ranges of the parabolic equations developed so far are restricted. In order to achieve a wide range of validity, a parabolic equation is derived in this paper by employing a curvilinear coordinate system which has a pattern similar to that of wave rays and fronts. A computer program which is applicable to an arbitrary arrangement of coastal structures is then developed. Results of numerical calculations are compared with available analytical solutions and laboratory data. It is proved that the present parabolic equation has a high accuracy for a wide range of incident wave direction and structure arrangement.