Difference between revisions of "Template:Radiation condition for diffracted potential"
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<center><math> | <center><math> | ||
\frac{\partial}{\partial x} \left(\phi^{\mathrm{D}}-\phi^{\rm | \frac{\partial}{\partial x} \left(\phi^{\mathrm{D}}-\phi^{\rm | ||
− | I} \right) \pm | + | I} \right) \pm k_0\left( \phi^{\mathrm{D}}-\phi^{\rm I}\right) |
= 0 | = 0 | ||
,\,\,\mathrm{as} | ,\,\,\mathrm{as} | ||
− | \,\,x\rightarrow | + | \,\,x\rightarrow\infty. |
</math></center> | </math></center> | ||
− | + | {{incident plane wave 2d definition}} | |
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Latest revision as of 03:22, 26 November 2009
[math]\displaystyle{ \phi^{\mathrm{D}} }[/math] satisfies the Sommerfeld Radiation Condition
[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