TY - JOUR
T1 - Focusing of surface waves by variable bathymetry
AU - Griffiths, L. S.
AU - Porter, Richard
PY - 2012/1
Y1 - 2012/1
N2 - Scattering of a monochromatic train of surface gravity waves incident on a finite region of arbitrary three-dimensional smoothly varying bathymetry is considered in this paper. The full three-dimensional linear water wave theory is approximated by the depth-averaged modified mild-slope equations and a Greens function approach is used to derive domain a integral equation for the function relating to the unknown surface over the varying bed. A simple but robust and effective numerical scheme is described to approximate solutions to the integral equation. The method is applied to bathymetries which exhibit focusing in the high-frequency ray-theory limit and used to illustrate that focusing occurs at finite wavelengths where both refractive and diffractive effects are included. Specifically, examples of elliptical and bi-convex lens bathymetries are considered.
AB - Scattering of a monochromatic train of surface gravity waves incident on a finite region of arbitrary three-dimensional smoothly varying bathymetry is considered in this paper. The full three-dimensional linear water wave theory is approximated by the depth-averaged modified mild-slope equations and a Greens function approach is used to derive domain a integral equation for the function relating to the unknown surface over the varying bed. A simple but robust and effective numerical scheme is described to approximate solutions to the integral equation. The method is applied to bathymetries which exhibit focusing in the high-frequency ray-theory limit and used to illustrate that focusing occurs at finite wavelengths where both refractive and diffractive effects are included. Specifically, examples of elliptical and bi-convex lens bathymetries are considered.
KW - Arbitrary bathymetry
KW - Focusing
KW - Mild slope equations
KW - Underwater lens
KW - Water waves
UR - http://www.scopus.com/inward/record.url?scp=84855607414&partnerID=8YFLogxK
U2 - 10.1016/j.apor.2011.08.004
DO - 10.1016/j.apor.2011.08.004
M3 - Article (Academic Journal)
AN - SCOPUS:84855607414
SN - 0141-1187
VL - 34
SP - 150
EP - 163
JO - Applied Ocean Research
JF - Applied Ocean Research
ER -