Standard Notation

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= \frac{\omega}{k} }[/math] Wave Phase Velocity
• [math]\displaystyle{ g }[/math] is the acceleration due to gravity
• Water depth [math]\displaystyle{ h }[/math] with the bottom at [math]\displaystyle{ z=-h }[/math]
• wave number [math]\displaystyle{ k }[/math]
• [math]\displaystyle{ P }[/math] pressure
• Time [math]\displaystyle{ t }[/math]
• [math]\displaystyle{ T = \frac{2\pi}{\omega} }[/math] Wave Period
• [math]\displaystyle{ \mathbf{v} }[/math] Flow Velocity Vector at [math]\displaystyle{ \mathbf{x} }[/math]
• [math]\displaystyle{ \mathbf{x} }[/math] 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 = \frac{2\pi}{k} }[/math] Wave Length
• Velocity potential [math]\displaystyle{ \phi\, }[/math] (in frequency domain) or [math]\displaystyle{ \Phi\, }[/math] in 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] fluid region
• [math]\displaystyle{ \partial \Omega }[/math] Boundary of fluid region
• [math]\displaystyle{ \zeta }[/math] displacement of the surface
• [math]\displaystyle{ \varepsilon }[/math] energy