21 
Fig. 5.1.3 is limited to values of h/L> 0.01. Tsunami having a period of 10 minutes (and 
wavelength T--Jgh) reach this value in water of 500 m depth (Table 5.1.1). For /r/L = 0.01, 
the boundary to solitary waves on the H/h-axis is at H/h = 1600(L//z)” 25 , which equals 
0.016. At a depth of 500 m, this value corresponds to a wave height of 8 m. Flowever, with 
U ~ 50 in Fig. 5.1.3, the boundary toward linear hydrostatic theory on the H/h-axis is 
H/h = 100h 2 /L 2 equalling 0.0105, and hence the application of linear hydrostatic theory 
would be allowed for wave heights below 5 m in 500 m depth. 
Estimates for the parameters which enter Fig. 5.1.3 are based on the assumption of a flat 
bottom. Variable depth additionally limits the validity of solutions. For instance, generalised 
Boussinesq equations (Peregine 1972) apply only to bottom slopes of Ah/L h <h/L due to 
the way the bottom boundary condition is approximated. The continental slope typically has a 
value of 0.025 (Dietrich et al. 1975). Thus, the solution to a Boussinesq equation generalised 
for variable depth is no model for a tsunami in that area. The special types of equation, 
Korteweg-de Vries and KP, cannot be generalised at all for variable bottom topography 
(Peregine 1972). Mofjeld et al. (2000) use hydrostatic linear equations to study the influence 
of bottom topography on simple waves. 
Water depth fm/ 
L (10 minutes) 
h/L (10 minutes) 
L (30 minutes) 
h/L (30 minutes) 
5000 
132.9 
0.0376 
398.7 
0.0137 
2000 
84.0 
0.0238 
252.1 
0.0079 
1000 
59.4 
0.0168 
178.3 
0.0046 
500 
42.0 
0.0119 
126.1 
0.0040 
200 
26.6 
0.0075 
79.7 
0.0025 
100 
18.8 
0.0053 
56.4 
0.0018 
50 
13.3 
0.0038 
39.9 
0.0013 
20 
10.3 
0.0024 
25.2 
0.0008 
10 
5.9 
0.0017 
17.8 
0.0006 
Table 5.1.1: Parameter h/L with L 
= Ty[gh in km for two typical tsunami periods. 
Water depth fm/ 
U (10 m, 10 min.) U (1m, 10min.) 
U (10 m, 30 min.) U (1 m, 30 min.) 
5000 
0.7 
0.1 
6.4 
0.6 
2000 
4.4 
0.4 
39.7 
4.0 
1000 
17.7 
1.8 
158.9 
15.9 
500 
70.6 
7.1 
635.7 
63.6 
200 
441.5 
44.1 
3973.1 
397.3 
100 
1765.8 
176.3 
15892.2 
1589.2 
Table 5.1.2: Ursel I parameter 
0.5H L 2 
h H 2 
with L = T*Jgh for two typical H and T values. 
In large parts of the shelf, with an estimated L = T^[gh, values of h/L«0.01 are obtained 
(Table 5.1.1), which are outside the parameter range in Fig. 5.1.3. Considering the Ursell