Meylan at 03:22, 26 November 2009

2009-11-26T03:22:40Z

← Older revision		Revision as of 03:22, 26 November 2009
Line 2:		Line 2:
	<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 ik\left( \phi^{\mathrm{D}}-\phi^{\rm I}\right)		I} \right) \pm k_0\left( \phi^{\mathrm{D}}-\phi^{\rm I}\right)
	= 0		= 0
	,\,\,\mathrm{as}		,\,\,\mathrm{as}
	\,\,x\rightarrow~~\pm~~\infty,		\,\,x\rightarrow\infty.
	</math></center>		</math></center>
	~~where~~		{{incident plane wave 2d definition}}
	~~<math>k ,\,</math> is the wavenumber,~~
	~~which is the positive real solution of the [[Dispersion Relation for a Free Surface]]~~
	~~<center><math>~~
	~~k\tanh(kh)=\omega^~~{~~2} \,~~
	~~</math></center>~~
	~~and <math>\phi^~~{~~\rm I}</math> is the~~ incident wave ~~given by~~
	~~<center><math>~~
	~~\phi^{\rm I} = \frac{\cosh(k(z+h))}{\cosh(kh)~~} ~~e^{-i kx~~} \,
	~~</math></center>~~
	~~(which has unit amplitude in potential) and~~
	~~is travelling towards positive~~
	~~infinity.~~

Meylan at 00:10, 17 September 2009

2009-09-17T00:10:07Z

New page

<math>\phi^{\mathrm{D}}</math> satisfies the [[Sommerfeld Radiation Condition]]
<center><math>
\frac{\partial}{\partial x} \left(\phi^{\mathrm{D}}-\phi^{\rm
I} \right) \pm ik\left( \phi^{\mathrm{D}}-\phi^{\rm I}\right)
= 0
,\,\,\mathrm{as}
\,\,x\rightarrow\pm\infty,
</math></center>
where
<math>k ,\,</math> is the wavenumber,
which is the positive real solution of the [[Dispersion Relation for a Free Surface]]
<center><math>
k\tanh(kh)=\omega^{2} \,
</math></center>
and <math>\phi^{\rm I}</math> is the incident wave given by
<center><math>
\phi^{\rm I} = \frac{\cosh(k(z+h))}{\cosh(kh)} e^{-i kx} \,
</math></center>
(which has unit amplitude in potential) and
is travelling towards positive
infinity.

Template:Radiation condition for diffracted potential - Revision history

Meylan at 03:22, 26 November 2009

Meylan at 00:10, 17 September 2009