47 
9100 -4SB -4000 -MB -9000 -SOO -2B0 -19» -1000 -900 0 9» 
Fig. 7.2.0: Bathymetry of the BSH's North-East Atlantic model 10 km. 
7.2.1 Propagation 
The propagation velocity of tsunami, i.e. of energy, is very high in deep water (about 
200 m s" 1 in 4,000 m of water as compared to 20 m s" 1 in 40 m of water). With the numerical 
method chosen for the model, also the numerical energy dissipation is higher than is to be 
expected form physical laws. An increase of single signals due to shoaling occurs at a few 
locations in Fig. 7.2.1-3 and is also seen in Fig. 7.2.6, but local increases more often result 
from superposition of the three single signals. The essential modifications during propagation 
in the deep ocean and across the continental shelf all reflect the influence of changing *[gh 
with depth (cf. section 5.3). This, e.g., causes the individual signals to be compressed and 
shortened at the shelf edge. The way turbulent momentum exchange is modelled (Dick et al. 
2001) allows the three initial signals to be clearly distinguished even on the shelf, where 
wavelength has become very small. Dispersion is not included in the analytical formulation of 
the model. With the chosen boundary condition - all single signals have the same period - 
this should not matter theoretically. Approximation by finite differences, however, destroys 
this property and the signal is modified due to numerical dispersion. Despite all restrictions, 
the simulation shows that propagation of a tsunami towards the North Sea is complex and 
highly variable in space. 
The leading input signal in all simulations propagated during a 12-hour period. Figs. 7.2.1-3 
all include a state where all three single signals have entered the model area. Then their 
evolution until reaching the northern boundary of the North Sea or the Channel entrance is 
shown. In Fig. 7.2.3, three identical signals entering the area at the boundary at equal time 
intervals have changed their distances after 1.5 hours. By the time they reach the transition 
to shallower water, i.e. when they cross the depicted 1,000 m depth contour, the back waves 
have caught up with the front waves. This effect is especially pronounced at Rockall. When 
the waves reach the deep water of the Norwegian Sea, their distance has increased again. 
A signal from the northern model boundary reaches the North Sea after nearly 2.5 hours 
(Fig. 7.2.1). The signal prescribed at the southern boundary reaches northern Scotland after 
5 hours (Fig. 7.2.2) and, as a weak signal, the northern North Sea after 7 hours. Owing to its 
shallower depth, the Channel entrance is reached hardly earlier, and signal propagation 
within the Channel is very slow (cf. section 7.3). The signal from the west reaches Scotland 
after 3.5 hours (Fig. 7.2.3). Deflected to shallower water, it enters the North sea nearly from 
the north (Fig. 7.2.3).