Difference between revisions of "Standard Notation"
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* <math>A</math> is the wave amplitude | * <math>A</math> is the wave amplitude | ||
| − | * <math> c= | + | * <math> c (=\omega / k) </math> is the wave phase velocity |
* <math>g</math> is the acceleration due to gravity | * <math>g</math> is the acceleration due to gravity | ||
| − | * | + | * <math>h</math> water depth (with the bottom at <math>z=-h</math>) |
| − | * | + | * <math> k </math> is the wave number |
| − | * <math>P</math> pressure | + | * <math>P</math> is the pressure (<math>P_1</math>, <math>P_2</math> etc are the first, second order pressures) |
| − | * | + | * <math>t</math> is the time |
| − | * <math> T = | + | * <math> T (= 2\pi / \omega)</math> is the wave period |
| − | * <math>\mathbf{v}</math> | + | * <math>\mathbf{v}</math> is the flow velocity vector at <math>\mathbf{x}</math> |
| − | * <math>\mathbf{x}</math> | + | * <math>\mathbf{x}</math> is the fixed Eulerian vector |
* <math>x</math> and <math>y</math> in the horizontal plane with <math>z</math> pointing vertically upward and the free surface at <math>z=0</math> | * <math>x</math> and <math>y</math> in the horizontal plane with <math>z</math> pointing vertically upward and the free surface at <math>z=0</math> | ||
| Line 20: | Line 20: | ||
* <math>\rho</math> is the fluid density | * <math>\rho</math> is the fluid density | ||
| − | * <math> \lambda = | + | * <math> \lambda (= 2\pi/k) </math> is the wave length |
| − | * | + | * <math>\phi\,</math> is the velocity potential in the frequency domain |
| + | * <math>\Phi\,</math> is the velocity potential in the time domain | ||
* wave/angular frequency <math>\omega</math> | * wave/angular frequency <math>\omega</math> | ||
* <math>e^{i\omega t}</math> time dependence in frequency domain | * <math>e^{i\omega t}</math> time dependence in frequency domain | ||
| − | * <math>\Omega\,</math> fluid region | + | * <math>\Omega\,</math> is the fluid region |
| − | * <math>\partial \Omega</math> | + | * <math>\partial \Omega</math> is the boundary of fluid region |
| − | * <math>\zeta</math> displacement of the surface | + | * <math>\zeta</math> is the displacement of the surface |
| − | * <math>\varepsilon</math> energy | + | * <math>\varepsilon</math> is the energy |
| + | |||
[[Category:Administration]] | [[Category:Administration]] | ||
Revision as of 20:32, 28 February 2009
A list of standard notation with definitions. If you find notation which does not appear here or non-standard notation please feel free to highlight this, or better still try and fix it. The material on these webpages was taken from a variety of sources and we know the notation is currently not always consistent between pages
Latin Letters
- [math]\displaystyle{ A }[/math] is the wave amplitude
- [math]\displaystyle{ c (=\omega / k) }[/math] is the wave phase velocity
- [math]\displaystyle{ g }[/math] is the acceleration due to gravity
- [math]\displaystyle{ h }[/math] water depth (with the bottom at [math]\displaystyle{ z=-h }[/math])
- [math]\displaystyle{ k }[/math] is the wave number
- [math]\displaystyle{ P }[/math] is the pressure ([math]\displaystyle{ P_1 }[/math], [math]\displaystyle{ P_2 }[/math] etc are the first, second order pressures)
- [math]\displaystyle{ t }[/math] is the time
- [math]\displaystyle{ T (= 2\pi / \omega) }[/math] is the wave period
- [math]\displaystyle{ \mathbf{v} }[/math] is the flow velocity vector at [math]\displaystyle{ \mathbf{x} }[/math]
- [math]\displaystyle{ \mathbf{x} }[/math] is the fixed Eulerian vector
- [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]
Greek letters
- [math]\displaystyle{ \rho }[/math] is the fluid density
- [math]\displaystyle{ \lambda (= 2\pi/k) }[/math] is the wave length
- [math]\displaystyle{ \phi\, }[/math] is the velocity potential in the frequency domain
- [math]\displaystyle{ \Phi\, }[/math] is the velocity potential in the time domain
- wave/angular frequency [math]\displaystyle{ \omega }[/math]
- [math]\displaystyle{ e^{i\omega t} }[/math] time dependence in frequency domain
- [math]\displaystyle{ \Omega\, }[/math] is the fluid region
- [math]\displaystyle{ \partial \Omega }[/math] is the boundary of fluid region
- [math]\displaystyle{ \zeta }[/math] is the displacement of the surface
- [math]\displaystyle{ \varepsilon }[/math] is the energy
