A12. Period with changing current velocityAs in A11 we consider an infInite domain with a uniform wave field. An initial spectrum is given (narrow both in σ and in θ). In test A12 the depth is constant (=5 m), and the current velocity is varied as function of time. It is seen from theory that wave number and direction of the wave field have to remain constant. A table is written giving depth, current velocity, wavelength, direction and period (both relative and absolute) as function of time. The analytical solution for this case is:
$T\; =\; 2\; \pi \; /\; \{[g\; k\; tanh(k\; d)]1/2+\; U.k\}$
(where T is absolute period).
Since Swan uses a spectrum formulated in terms of $\sigma $; there is transport of energy in $\sigma $direction; there is also transport in $\theta $. There may be a change in the shape of the spectrum due to numerical inaccuracies. Plot file A12.plt shows (absolute) period, wavelength and direction as function of current velocity (the component in ydirection since the direction of the wave field is 90^{o}. 1 case is considered:

Swan Tests 