Meylan at 23:59, 16 September 2009

2009-09-16T23:59:22Z

New page

[[Image:finite_dock.jpg|thumb|right|300px|Wave scattering by a finite dock]]

We consider here the [[Frequency Domain Problem]] for a finite dock which occupies
the region <math>-L<x<L</math> (we assume <math>e^{i\omega t}</math> time dependence).
The water is assumed to have
constant finite depth <math>h</math> and the <math>z</math>-direction points vertically
upward with the water surface at <math>z=0</math> and the sea floor at <math>z=-h</math>. The
boundary value problem can therefore be expressed as
<center>
<math>
\Delta\phi=0, \,\, -h<z<0,
</math>
</center>
<center>
<math>
\phi_{z}=0, \,\, z=-h,
</math>
</center>
<center><math>
\partial_z\phi=\alpha\phi, \,\, z=0,\,x <-L, {\rm or} \, x>L
</math></center>
<center>
<math>
\partial_z\phi=0, \,\, z=0,\,-L<x<L,
</math>
</center>
We
must also apply the [[Sommerfeld Radiation Condition]]
as <math>|x|\rightarrow\infty</math>. This essentially implies
that the only wave at infinity is propagating away and at negative infinity there is a unit incident wave
and a wave propagating away.

Template:Finite dock equations - Revision history

Meylan at 23:59, 16 September 2009