Difference between revisions of "Template:Incident plane wave 2d definition"

From WikiWaves
Jump to navigationJump to search
 
(2 intermediate revisions by one other user not shown)
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
 
<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>

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,

[math]\displaystyle{ \phi^{\mathrm{I}}(x,z)=A \phi_0(z) e^{\mathrm{i} k x} \, }[/math]

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

[math]\displaystyle{ \phi_0(z) =\frac{\cosh k(z+h)}{\cosh k h} }[/math]
Retrieved from "https://wikiwaves.org/wiki/index.php?title=Template:Incident_plane_wave_2d_definition&oldid=12985"