Difference between revisions of "Standard Notation"

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* Boundary of fluid region <math>\partial \Omega</math>
 
* Boundary of fluid region <math>\partial \Omega</math>
 
* Displacement of the surface <math>\zeta</math>
 
* Displacement of the surface <math>\zeta</math>
 +
* <center><math> T = \frac{2\pi}{\omega} = \mbox{Wave Period} </math></center>
 +
* <center><math> \lambda = \frac{2\pi}{k} </math>  Wave Length
 +
* <math> C= \frac{\omega}{k}  </math> Wave Phase Velocity
 +
* <math>A</math> is the wave amplitude
 +
* wave frequency is <math>\omega</math>
 +
* wave number <math> k </math>
  
  
 
[[Category:Administration]]
 
[[Category:Administration]]

Revision as of 06:08, 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]
  • [math]\displaystyle{ T = \frac{2\pi}{\omega} = \mbox{Wave Period} }[/math]
  • [math]\displaystyle{ \lambda = \frac{2\pi}{k} }[/math] Wave Length
  • [math]\displaystyle{ C= \frac{\omega}{k} }[/math] Wave Phase Velocity
  • [math]\displaystyle{ A }[/math] is the wave amplitude
  • wave frequency is [math]\displaystyle{ \omega }[/math]
  • wave number [math]\displaystyle{ k }[/math]