Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-20T08:38:12.002Z Has data issue: false hasContentIssue false
  • English
  • Français

Second-order refraction and diffraction of surface water waves

Published online by Cambridge University Press:  29 March 2006

MENG-YI CHEN  and
CHIANG C. MEI
MENG-YI CHEN
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
CHIANG C. MEI
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The mild-slope equation is an effective approximation for treating the combined effects of refraction and diffraction of infinitesimal water waves, for it reduces the spatial dimension of the linear boundary-value problem from three to two. We extend this approximation to nonlinear waves up to the second order in wave steepness, in order to simplify the inherently three-dimensional task. Assuming that the geometrical complexity is restricted to a finite, though large, horizontal domain, the hybrid-element method designed earlier for linearized problems is modified for the two-dimensional elliptic boundary-value problems at the second order. In the special case of a semi-circular peninsula (or a vertical cylinder on a cliff) in a sea of constant depth, the solution is analytical. Effects of the angle of incidence are examined for the free-surface height along the cylinder. For a cylinder standing on a shoal of radially varying depth, numerical results are discussed.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 552 , 10 April 2006 , pp. 137 - 166
Copyright
© 2006 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)