59

7.4.3  Travel  Times

With  a  group  velocity  of  c i0  =  ^gh 0  and  a  constant  depth  of  70  m  (average  depth  of  the
North  Sea),  travel  times  of  10.6  hours,  5.3  hours,  and  1.1  hours  are  computed  for  distances
of  1,000  km,  500  km,  and  100  km,  respectively.
The  travel  time  from  the  northern  boundary  of  the  North  Sea  to  Borkum,  about  8  hours  for  the
primary  signal,  fits  well  with  this  simple  estimation.  In  this  simulation,  Cuxhaven  is  reached
after  about  9  hours  by  the  wave  train  starting  at  the  latitude  of  the  Shetland  Islands  (Fig.
7.4.9).  From  Aberdeen,  the  signal  travels  about  6  hours  (Fig.  7.4.8).  The  good  fit  between  the
simple  estimation  at  the  beginning  of  this  section  and  the  model  simulation  is  attributable  to
the  hydrostatic  assumption  made  in  the  model.  It  is  not  possible,  however,  to  predict  the
entry  time  of  the  secondary  signal  by  such  simple  estimation.  It  reaches  its  maximum  at
Cuxhaven  about  7  hours  after  the  lower  primary  maximum  (Fig.  7.4.9).

Aberdeen

H  5  m
H  6  m
H  7  m
H  8  m

—

03:00  04:00  05:00  06:00

Fig.  7.4.8:  Water  levels  at  Aberdeen  (input  signal:  3  positive  single  signals,  T  1800  s,  H  5  m,
from  the  north,  North  Sea  2  km)

Fig.  7.4.9:  Water  levels  at  Cuxhaven  (input  signal:  3  positive  single  signals,  T  1800  s,  H  5  m,
from  the  north,  North  Sea  2  km)