Difference between revisions of "Standard Notation"

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* Water depth <math>h</math> with the bottom at <math>z=-h</math>
 
* Water depth <math>h</math> with the bottom at <math>z=-h</math>
 
* Time <math>t</math>
 
* Time <math>t</math>
* Velocity potential <math>\phi</math>
+
* <math>\mathbf{x}</math> Fixed Eulerian Vector
 +
* <math>\mathbf{v}</math> Flow Velocity Vector at <math>\mathbf{x}</math>
 +
* Velocity potential <math>\phi\,</math> (in frequecy domain) or <math>\Phi\,</math> in time domain
 
* Angular frequency <math>\omega</math>
 
* Angular frequency <math>\omega</math>
 
* Time dependence in frequency domain <math>e^{i\omega t}</math>  
 
* Time dependence in frequency domain <math>e^{i\omega t}</math>  

Revision as of 05:55, 18 February 2009

A list of standard notation

  • [math]\displaystyle{ x }[/math] and [math]\displaystyle{ y }[/math] in the horizontal plane with [math]\displaystyle{ z }[/math] pointing vertically upward and the free surface at [math]\displaystyle{ z=0 }[/math]
  • Water depth [math]\displaystyle{ h }[/math] with the bottom at [math]\displaystyle{ z=-h }[/math]
  • Time [math]\displaystyle{ t }[/math]
  • [math]\displaystyle{ \mathbf{x} }[/math] Fixed Eulerian Vector
  • [math]\displaystyle{ \mathbf{v} }[/math] Flow Velocity Vector at [math]\displaystyle{ \mathbf{x} }[/math]
  • Velocity potential [math]\displaystyle{ \phi\, }[/math] (in frequecy domain) or [math]\displaystyle{ \Phi\, }[/math] in time domain
  • Angular frequency [math]\displaystyle{ \omega }[/math]
  • Time dependence in frequency domain [math]\displaystyle{ e^{i\omega t} }[/math]
  • Fluid region [math]\displaystyle{ \Omega }[/math]
  • Boundary of fluid region [math]\displaystyle{ \partial \Omega }[/math]
  • Displacement of the surface [math]\displaystyle{ \zeta }[/math]