Standard Notation

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} }[/math] Wave Period
• [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]