Difference between revisions of "Template:Incident plane wave"
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The equation is subject to some radiation conditions at infinity. We usually assume that | The equation is subject to some radiation conditions at infinity. We usually assume that | ||
| − | there is an incident wave <math>\phi^{\mathrm{ | + | there is an incident wave <math>\phi^{\mathrm{I}}\,</math> |
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{ | + | \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]]. | ||
Revision as of 10:36, 8 April 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.
