Difference between revisions of "Template:Incident plane wave"
From WikiWaves
Jump to navigationJump to search| Line 3: | Line 3: | ||
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}}({r},z)=Ae^{k_0 x}\frac{\cos k_0(z+h)}{\cos k_0 h} | + | \phi^{\mathrm{I}}({r},z)=Ae^{-k_0 x}\frac{\cos k_0(z+h)}{\cos k_0 h} |
</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>). | ||
Revision as of 02:27, 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]).
