3.6 Comparison of Results of Numerical Wave Propagation Schemes
61
The mean wave height h( tp, {}, t) is determined as:
h 2 (tp, {}, t) = 2n j j S(w, {3, tp, {}, t) dw df3.
(3.30)
The normalized total energy of the propagating wave field is as follows:
l:::(t) = E(t)/ E(t = 0) ,
(3.31)
where:
E(t) = J J J J S(w, {3, tp, {}, t)R 2 cos 'P dw df3 dtp d{}.
(3.32)
The latitude coordinate value referred to the propagation of the wave area
centre (the time shift of the centre of mass coordinate) is determined:
('P( t)) = E~ t) J J J J 'P( t)S(w, {3, tp, {}, t) R 2 cos 'P dw df3 dtp d{} . (3.33)
The wave energy diffusion is evaluated in space with time. The parameter 8(t), characterizing this value, is determined as the square root of the
surface area. It contains waves with a height greater than 1/3 of their maximum value at the current moment t:
8(t) = JT(t)/T(O),
(3.34)
where
T(t) = JJ F(tp,{},t)R 2 costpdtpd{}
(3.35)
and F( tp, {}, t) is the Heaviside function:
(3.36)
The root mean square (RMS) error of the calculation of the wave height
over the water area can be evaluated as:
(3.37)
i,j
where N is the total number of grid points and ERR is the normalized local
wave height error:
ERR(t) = hmodel ( tp, {}, t) - hanal ( tp, {}, t)
h(t)
'
(3.38)
where h~n~(t) is the maximum value of the wave height calculated analytically over the entire area at time t.