Template:Incident plane wave 2d definition - Revision history

Adi Kurniawan at 10:53, 6 November 2010

2010-11-06T10:53:50Z

← Older revision		Revision as of 10:53, 6 November 2010
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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_0(z) e^{\mathrm{i} k x}		\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 (in potential) <math>\mathrm{i} k </math> is		where <math>A </math> is the wave amplitude (in potential) <math>\mathrm{i} k </math> is

Meylan at 22:25, 29 April 2010

2010-04-29T22:25:21Z

← Older revision		Revision as of 22:25, 29 April 2010
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	and		and
	<center><math>		<center><math>
	\phi_0(z) =\frac{\~~cos k_0~~(z+h)}{\~~cos k_0~~ h}		\phi_0(z) =\frac{\cosh k(z+h)}{\cosh k h}
	</math></center>		</math></center>

Meylan at 22:24, 29 April 2010

2010-04-29T22:24:29Z

← Older revision		Revision as of 22:24, 29 April 2010
Line 2:		Line 2:
	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_0(z) e^{~~-k_0~~ x}		\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 (in potential) <math>~~k_0~~ </math> is		where <math>A </math> is the wave amplitude (in potential) <math>\mathrm{i} k </math> is
	the ~~negative~~ 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		and

Meylan at 10:43, 28 April 2010

2010-04-28T10:43:28Z

← Older revision		Revision as of 10:43, 28 April 2010
Line 5:		Line 5:
	</math></center>		</math></center>
	where <math>A </math> is the wave amplitude (in potential) <math>k_0 </math> is		where <math>A </math> is the wave amplitude (in potential) <math>k_0 </math> is
	the ~~positive~~ imaginary solution of the [[Dispersion Relation for a Free Surface]]		the negative 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		and
	<center><math>		<center><math>
	\phi_0(z) =\frac{\cos k_0(z+h)}{\cos k_0 h}		\phi_0(z) =\frac{\cos k_0(z+h)}{\cos k_0 h}
	</math></center>		</math></center>

Meylan at 03:31, 26 November 2009

2009-11-26T03:31:00Z

← Older revision		Revision as of 03:31, 26 November 2009
Line 2:		Line 2:
	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 \~~left\{ \frac{\cos k_0~~(z+h)~~}{\cos k_0 h} \right\}~~ e^{-k_0 x}		\phi^{\mathrm{I}}(x,z)=A \phi_0(z) e^{-k_0 x}
	</math></center>		</math></center>
	where <math>A </math> is the wave amplitude (in potential) ~~and~~ <math>k_0 </math> is		where <math>A </math> is the wave amplitude (in potential) <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>)
			and
			<center><math>
			\phi_0(z) =\frac{\cos k_0(z+h)}{\cos k_0 h}
			</math></center>

Meylan at 03:22, 26 November 2009

2009-11-26T03:22:59Z

← Older revision		Revision as of 03:22, 26 November 2009
Line 4:		Line 4:
	\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>).

Meylan: Created page with ' $\phi^{\mathrm{I}}\,$ is a plane wave travelling in the $x$ direction, $\phi^{\mathrm{I}}(x,z)=A \left\{ \frac{\cos k_0(z+h)}{\cos k_0 h} \r…'$

2009-11-26T03:14:05Z

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…'

New page

<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} \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>).