Difference between revisions of "Category:Time-Dependent Linear Water Waves"
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Revision as of 11:50, 12 August 2009
Generally the focus of research is on the Frequency Domain Problem. The time-domain problem can be solved by Generalised Eigenfunction Expansion or by an Expansion over the Resonances or using Memory Effect Function.
We consider a two-dimensional fluid domain of constant depth, which
contains a finite number of fixed bodies of arbitrary geometry. We
denote the fluid domain by [math]\displaystyle{ \Omega }[/math], the boundary of the fluid domain
which touches the fixed bodies by [math]\displaystyle{ \partial\Omega }[/math], and the free
surface by [math]\displaystyle{ F. }[/math] The [math]\displaystyle{ x }[/math] and [math]\displaystyle{ z }[/math] coordinates are such that [math]\displaystyle{ x }[/math] is
pointing in the horizontal direction and [math]\displaystyle{ z }[/math] is pointing in the
vertical upwards direction (we denote [math]\displaystyle{ \mathbf{x}=\left( x,z\right) ). }[/math] The
free surface is at [math]\displaystyle{ z=0 }[/math] and the sea floor is at [math]\displaystyle{ z=-h }[/math]. The
fluid motion is described by a velocity potential [math]\displaystyle{ \Phi }[/math] and free surface by
[math]\displaystyle{ \zeta }[/math].
The equations of motion in the time domain are Laplace's equation through out the fluid
At the bottom surface we have no flow
At the free surface we have the kinematic condition
and the dynamic condition (the linearized Bernoulli equation)
The body boundary condition for a fixed body is
The initial conditions are
Pages in category "Time-Dependent Linear Water Waves"
The following 3 pages are in this category, out of 3 total.