Standard Notation

2009-04-13T12:34:49Z

Mazonakis: /* Other notation, style etc. */

This is 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>A</math> is the wave amplitude
* <math> c \,(=\omega / k) </math> or sometime <math>c_p</math> is the wave phase velocity
* <math> c_g = \frac{\mathrm{d} \omega}{\mathrm{d} k} </math> is the wave group velocity
* <math>d</math> is a water depth parameter
* <math>D</math> is the modulus of rigidity for a plate
* <math>e^{i\omega t}</math> is the time dependence in frequency domain
* <math>E</math> is the Young's modulus
* <math>g</math> is the acceleration due to gravity
* <math>h</math> is the water depth (with the bottom at <math>z=-h</math>)
* <math>\mathrm{Im}</math> is the imaginary part of a complex argument
* <math> k </math> is the wave number
* <math>\mathcal{L}</math> is the linear operator at the body surface
* <math>\mathbf{n}</math> is the outward normal
* <math>\frac{\partial\phi}{\partial n}</math> is <math>\nabla\phi\cdot\mathbf{n}</math>
* <math>P</math> is the pressure (<math>P_1</math>, <math>P_2</math> etc are the first, second order pressures)
* <math>\mathcal{P}(t)</math> the energy flux is the rate of change of energy density <math> \mathcal{E}(t) </math>
* <math>\mathbf{r}</math> vector in the horizontal directions only <math>(x,y)</math>
* <math>\mathrm{Re}</math> is the real part of a complex argument
* <math>t</math> is the time
* <math> T \,(= 2\pi / \omega)</math> is the wave period
* <math>U_n</math> is the normal derivative of the moving surface of a volume
* <math>\mathbf{v}</math> is the flow velocity vector at <math>\mathbf{x}</math>
* <math>\mathbf{x}</math> is the fixed Eulerian vector <math>(x,y,z)</math>
* <math>x</math> and <math>y</math> are in the horizontal plane with <math>z</math> pointing vertically upward and the free surface at <math>z=0</math>
* <math>X_n(x)</math> is an eigenfunction arising from separation of variables in the <math>x</math> direction.
* <math>Z(z)</math> is an eigenfunction arising from separation of variables in the <math>x</math> direction.

== Greek letters ==

* <math>\alpha</math> is free surface constant <math>\alpha = \omega^2/g</math>
* <math>\mathcal{E}</math> is the energy
* <math>\zeta</math> is the displacement of the surface
* <math> \lambda \,(= 2\pi/k) </math> is the wave length
* <math>\rho</math> is the fluid density (sometimes also string density).
* <math>\rho_i</math> is the plate density
* <math>\phi\,</math> is the velocity potential in the frequency domain
* <math>\phi^{\mathrm{I}}\,</math> is the incident potential
* <math>\phi^{\mathrm{S}}\,</math> is the scattered potential
* <math>\phi^{\mathrm{D}}\,</math> is the diffracted potential
* <math>\phi^{\mathrm{R}}\,</math> is the radiated potential
* <math>\Phi\,</math> is the velocity potential in the time domain
* <math>\omega</math> is the wave/angular frequency
* <math>\Omega\,</math> is the fluid region
* <math>\partial \Omega</math> is the boundary of fluid region, <math>\partial\Omega_F</math> is the free surface, <math>\partial\Omega_B</math> is the body surface.

== Other notation, style etc. ==

* We prefer <math>\partial_x\phi</math> etc. for all derivatives or <math>\frac{\partial\phi}{\partial x}</math>. Try to avoid <math>\phi_x\,</math> or <math>\phi^{\prime}</math>
* We prefer <math>\mathrm{d}x\,\!</math> etc. for differentials. Avoid <math>dx\,\!</math>
* <math>\mathrm{Re}\,\!</math> and <math>\mathrm{Im}\,\!</math> for the real and imaginary parts.
* We use two equals signs for the first heading (rather than a single) following [http://www.wikipedia.org wikipedia] style, then three etc.
* Note: You can easily monitor changes at this wiki using this [http://www.w3monitor.com free website monitoring] tool.

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Standard Notation