Difference between revisions of "Template:Incident plane wave 2d definition"
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Jump to navigationJump to search (Created page with '<math>\phi^{\mathrm{I}}\,</math> is a plane wave travelling in the <math>x</math> direction, <center><math> \phi^{\mathrm{I}}(x,z)=A \left\{ \frac{\cos k_0(z+h)}{\cos k_0 h} \r…') |
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\phi^{\mathrm{I}}(x,z)=A \left\{ \frac{\cos k_0(z+h)}{\cos k_0 h} \right\} e^{-k_0 x} | \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 (in potential) 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 03:22, 26 November 2009
[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 (in potential) 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]).
