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5 Tsunami behaviour upon reaching shallow water 
Possible causes of tsunami that may affect the North Sea region have been compiled In 
section 3. Literature data on the probability of occurrence is either contradictory or not 
available (see section 10.1). Additional research in this field will be needed. Despite the 
paucity of data, the assumption will be discussed in this section that a tsunami entering the 
North Sea would not have impacts on the German coasts comparable to those of the 
catastrophic tsunami of December 2004 which destructed the coastline of the Indian Ocean. 
Possible analytical tsunami descriptions will be discussed first. Then, using different 
modelling concepts and simulations, the modification and propagation of a theoretical 
tsunami wave travelling from the deep ocean to the coast is discussed with a focus on 
special features regarding the North Sea. 
5.1 Wave theoretical interpretation 
The propagation of very long waves - tidal waves and external surges - into the North Sea is 
the subject of daily water level forecasts. Such waves have characteristic lengths L of the 
order of 1,000 km, and wave heights H of 2 metres when entering the North Sea, and up to 
4 m at the German coast. The dominant co-oscillating tide in the North Sea is the semidiurnal 
tide. Sea and swell in the open North Sea have periods T on the order of 10 s (Couper 1983) 
and integral wave lengths of up to 250 m. Tsunami are „in between“. Depending on their 
origin, their periods are on the order of 100 s (meteoritic impact), 10 minutes (earthquake), 
and 30 minutes (slope failure). Ward (2002) defined a „tsunami window“ by periods from 
100-1,000 s. A single tsunami has a narrower spectrum. Therefore, it is often characterised 
by a single period. Typical wavelengths of a wave with a period of 30 minutes range between 
400 km in the deep sea and 20 km in shallow water (see Table 5.1.1). Disregarding 
meteoritic impact, the period of tsunami is longer than that of wind waves by about the factor 
200, and shorter by the factor 20 than that of the semidiurnal tide. Models used for daily 
routine water level forecast thus seem to be closer to the description of tsunami than wave 
theories. On the other hand, tsunami are hardly influenced by the Earth’s rotation. The 
inertial period at the pole is about 12 hours and increases toward the equator. Therefore, 
classical irrotational wave theories have been used to understand tsunami (e.g. Voit 1987). 
They have been developed for a range extending from short wind waves to swell, and initially 
only consider single waves, i.e. progressing waves with a defined wave length, wave height, 
and wave period. 
5.1.1 Wave theories 
Starting from the three-dimensional mass and momentum balance equations (e.g. Pichler 
1984): 
—+ V-(/?v) = 0 und —+ V■ (/Tvv) + 2.Q,xpv = -Vp -pV{0 + 0 G )+ F ( 1) 
dt dt 
{pdensity, v =(v A ,v v ) velocity, p pressure, 2Û angular velocity of the earth, 
<f> gravitational potential, <f> G tidal potential, F frictional force), 
many wave theories are based on simplified advection equations for incompressible, inviscid 
fluids: 
_ dv _ _ 
V ■ v = 0 and p 0 — + p 0 vVv = -Vp - /? 0 V^ with boundary conditions 
dt 
(2) 
dî] 
Ht 
+ v h VT], p = 0 at the water surface ( r/ elevation of the water surface),