Template:Incident plane wave - Revision history

Meylan at 03:15, 26 November 2009

2009-11-26T03:15:06Z

← Older revision		Revision as of 03:15, 26 November 2009
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	The equation is subject to some radiation conditions at infinity. We ~~usually~~ the following.		The equation is subject to some radiation conditions at infinity. We assume the following.
	{{incident plane wave 2d definition}}		{{incident plane wave 2d definition}}

Meylan at 03:13, 26 November 2009

2009-11-26T03:13:43Z

← Older revision		Revision as of 03:13, 26 November 2009
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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 the following.
	~~there is an incident wave <math>\phi^~~{~~\mathrm~~{~~I}}\,</math>~~		{{incident plane wave 2d definition}}
	~~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~~} ~~\right\~~} ~~e^{-k_0 x}~~
	~~</math></center>~~
	~~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]]~~
	~~(note we are assuming that the time dependence is of the form <math>\exp(\mathrm{i}\omega t) </math>).~~

Mike smith at 09:02, 1 September 2009

2009-09-01T09:02:59Z

← Older revision		Revision as of 09:02, 1 September 2009
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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}}(~~{r}~~,z)=~~Ae^~~{~~-k_0 x}~~\frac{\cos k_0(z+h)}{\cos k_0 h}		\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 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>).

Meylan at 02:27, 1 September 2009

2009-09-01T02:27:39Z

← Older revision		Revision as of 02:27, 1 September 2009
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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}}({r},z)=Ae^{k_0 x}\frac{\cos k_0(z+h)}{\cos k_0 h}		\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]]
			(note we are assuming that the time dependence is of the form <math>\exp(\mathrm{i}\omega t)</math>).

Meylan at 10:36, 8 April 2009

2009-04-08T10:36:47Z

← Older revision		Revision as of 10:36, 8 April 2009
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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{~~{In}~~}}\,</math>		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{~~{In}~~}}({r},z)=Ae^{k_0 x}\frac{\cos k_0(z+h)}{\cos k_0 h}		\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]].

Meylan at 07:21, 24 August 2008

2008-08-24T07:21:49Z

← Older revision		Revision as of 07:21, 24 August 2008
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	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]].
	~~We also have to apply the [[Sommerfeld Radiation Condition]] as <math>\left\|\mathbf{r}\right\|\rightarrow~~
	~~\infty</math>.~~

Meylan at 06:28, 24 August 2008

2008-08-24T06:28:30Z

New page

The equation is subject to some radiation conditions at infinity. We usually assume that
there is an incident wave <math>\phi^{\mathrm{{In}}}\,</math>
is a plane wave travelling in the <math>x</math> direction
<center><math>
\phi^{\mathrm{{In}}}({r},z)=Ae^{k_0 x}\frac{\cos k_0(z+h)}{\cos k_0 h}
</math></center>
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]].
We also have to apply the [[Sommerfeld Radiation Condition]] as <math>\left|\mathbf{r}\right|\rightarrow
\infty</math>.