View source for Category:Linear Water-Wave Theory

{{complete pages}}

== Introduction ==

Linear water waves are small amplitude waves for which we can linearise the equations of motion ([[Linear and Second-Order Wave Theory]]). 
It is also standard to consider the problem when waves of a single frequency are incident so that only a single frequency
needs to be considered, leading to the [[Frequency Domain Problem]].
The linear theory is applicable until the wave steepness becomes sufficiently large that non-linear effects become important.

== Equations in the Frequency Domain  ==

{{standard linear problem notation}}
[[Variable Bottom Topography]]
can also easily be included but we do not consider this here.

{{standard linear wave scattering equations}}

The simplest case is for a fixed body 
where the operator is <math>L=0</math> but more complicated conditions are possible.

{{incident plane wave}}

{{sommerfeld radiation condition two dimensions}}

{{sommerfeld radiation condition three dimensions}}