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Figure 5.4 Current velocity profile.

5.2.2 Regular waves

General
Based on the assumption of an inviscid, irrational and incompressible fluid, the wave problem
may be formulated in terms of a velocity potential Φsuch that the velocity vector is given as:
. The velocity potential should fulfil the Laplace equation (see
e.g. Clauss et al., 1991)

(5.1)

and the following boundary conditions:
1. Kinematic boundary conditions: No flow through the sea bottom:

(5.2a)

n
where ∂∂ denotes the derivative normal to the sea bottom. In deep water, an alternative
/
formulation of this condition is:

(5.2b)

If a body is present, a ‘no flow through the body’ criterion must also be satisfied:

(5.2c)

Here v and n denote the velocity and normal vector of the body present, respectively. Further,
a fluid particle on the free surface is assumed to remain on the free surface. This is expressed
in the kinematic free surface condition: