# Standard Notation

From WikiWaves

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

- is the wave amplitude
- or sometime is the wave phase velocity
- is the wave group velocity
- is a water depth parameter
- is the modulus of rigidity for a plate
- is the time dependence in frequency domain
- is the Young's modulus
- is the energy density
- is the acceleration due to gravity
- is the water depth (with the bottom at )
- is the unit vector in the direction
- is the imaginary part of a complex argument
- is the unit vector in the direction
- is the unit vector in the direction
- is the wave number
- are the roots of the dispersion eqution
- is the linear operator at the body surface
- is the momentum
- is the outward normal
- is
- is the pressure (, etc are the first, second order pressures)
- the energy flux is the rate of change of energy density
- vector in the horizontal directions only
- is the radius of a cylinder
- is the real part of a complex argument
- is the free surface
- is the time
- is the wave period
- is the forward speed
- is the normal derivative of the moving surface of a volume
- is the flow in the normal direction for potential
- is the flow velocity vector at
- is the fixed Eulerian vector
- and are in the horizontal plane with pointing vertically upward and the free surface is at
- is the coordinate in a moving frame.
- is an eigenfunction arising from separation of variables in the direction.
- is an eigenfunction arising from separation of variables in the direction.

## Greek letters

- is free surface constant
- is the energy
- is the displacement of the surface
- any other displacement, most usually a body in the fluid
- any other displacement, most usually a body in the fluid
- is the wave length
- is the fluid density (sometimes also string density).
- is the plate density
- is the velocity potential in the frequency domain
- is the incident potential
- is the diffracted potential
- is the scattered potential ()
- is the radiated potential (for the mode
- is the velocity potential in the time domain
- is the velocity potential in the time domain for a moving coordinate system
- is the wave/angular frequency
- is the fluid region
- is the boundary of fluid region, is the free surface, is the body surface.

## Other notation, style etc.

- We prefer etc. for all derivatives or . Try to avoid or
- We prefer etc. for differentials. Avoid
- and for the real and imaginary parts.
- We use two equals signs for the first heading (rather than a single) following wikipedia style, then three etc.