Template:Incident plane wave 2d definition: Difference between revisions
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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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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}}(x,z)=A \ | \phi^{\mathrm{I}}(x,z)=A \phi_0(z) e^{\mathrm{i} k x} \, | ||
</math></center> | </math></center> | ||
where <math>A </math> is the wave amplitude | where <math>A </math> is the wave amplitude (in potential) <math>\mathrm{i} k </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>) | ||
and | |||
<center><math> | |||
\phi_0(z) =\frac{\cosh k(z+h)}{\cosh k h} | |||
</math></center> | |||
Latest revision as of 10:53, 6 November 2010
[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) [math]\displaystyle{ \mathrm{i} k }[/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]) and
