Template:Incident plane wave: Difference between revisions
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is a plane wave travelling in the <math>x</math> direction | is a plane wave travelling in the <math>x</math> direction | ||
<center><math> | <center><math> | ||
\phi^{\mathrm{I}}( | \phi^{\mathrm{I}}(x,z)=A \left\{ \frac{\cos k_0(z+h)}{\cos k_0 h} \right\} e^{-k_0 x} | ||
</math></center> | </math></center> | ||
where <math>A</math> is the wave amplitude and <math>k_0</math> is | where <math>A </math> is the wave amplitude and <math>k_0 </math> is | ||
the positive imaginary solution of the [[Dispersion Relation for a Free Surface]] | the positive imaginary solution of the [[Dispersion Relation for a Free Surface]] | ||
(note we are assuming that the time dependence is of the form <math>\exp(\mathrm{i}\omega t)</math>). | (note we are assuming that the time dependence is of the form <math>\exp(\mathrm{i}\omega t) </math>). | ||
Revision as of 09:02, 1 September 2009
The equation is subject to some radiation conditions at infinity. We usually assume that there is an incident wave [math]\displaystyle{ \phi^{\mathrm{I}}\, }[/math] is a plane wave travelling in the [math]\displaystyle{ x }[/math] direction
where [math]\displaystyle{ A }[/math] is the wave amplitude and [math]\displaystyle{ k_0 }[/math] is the positive imaginary solution of the Dispersion Relation for a Free Surface (note we are assuming that the time dependence is of the form [math]\displaystyle{ \exp(\mathrm{i}\omega t) }[/math]).
