Summary: Constructing a wave reflector to protect beaches?
Modelling assignment for
Instructional Workshop Industrial Mathematics,
2-6 December 2002, IITBombay India
Andonowati (P4M, ITBandung, Indonesia; firstname.lastname@example.org)
& E. (Brenny) van Groesen (UTwente, The Netherlands; email@example.com)
One possible way to protect beaches from incoming waves would be to try to partially reflect the waves by
constructing suitable bottom variations in the sea in front of the beach. To investigate the viability of this basic
idea is the aim of this modelling assignment. The full investigation is still outside reach, even for the best
The basic assumption that we will make is that the gravity-driven surface waves are considered to be of low
amplitude, which allows us to restrict to linear waves. Furthermore, assuming shallow water, dispersive effects
are neglected which means that we assume that each sinusoidal wave travels with a velocity that depends only
on the depth of the water. Denoting the bottom topography measured from some still-water level by h, the
propagation velocity is then given by ghc = , where g is the gravitational constant.
You could contemplate a while on this velocity-depth relation: motivate it from dimensional analysis. You
could also use it to motivate the assumption below that for `natural' beaches it is a good approximation to
assume that waves coming in from the deep sea will approach the beach perpendicular.
We consider a one-dimensional model, and consider incoming waves in the direction perpendicular to the beach.