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- The feild equation | - The feild equation | ||
| − | <math>\nabla \phi = 0 \quad throughout the fluid domain</math> | + | <math>\nabla \phi = 0 \quad \mathrm{throughout the fluid domain}</math> |
- The free surface boundary condition | - The free surface boundary condition | ||
Revision as of 03:03, 18 January 2010
Multipole Expansions
Moltipole expansions are a technique used in linear water wave theory where the potential is represented as a sum of singularities (multipoles) placed within any structures that are present. Multipoles can be constructed with their singularity submerged or on the free surface and these are treated seperately.
Multipoles satisfy:
- The feild equation
[math]\displaystyle{ \nabla \phi = 0 \quad \mathrm{throughout the fluid domain} }[/math]
- The free surface boundary condition
[math]\displaystyle{ \partial _z \phi = K\phi \quad on \quad z=0 }[/math]
where the z-axis is oriented vertically upwards and the zero is on the free surface
- The bed boundary condition
[math]\displaystyle{ \partial_n \phi = 0 \quad on \quad z=-h(x,y) }[/math]
