PHYSICAL PROCESSES IN A TIDAL INLET

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					  Chinese-German Joint Symposium on Hydraulic and Ocean Engineering, August 24-30, 2008, Darmstadt



               PHYSICAL PROCESSES IN A TIDAL INLET
                                               Gerbrant Ph. van Vledder*,**
                     *Alkyon Hydraulic Consultancy & Research Marknesse, The Netherlands
                             **Delft University of Technology, Delft, The Netherlands


Abstract:

The primary coastal structures in the Netherlands must be monitored every five years (2001, 2006,
2011, etc.) for the required level of protection. This check is based on Hydraulic Boundary Conditions
(HBC) that are derived every five years and approved by the Minister of Transport, Public Works and
Water Management in the Netherlands. The HBC consist of near-shore water levels and wave
conditions. The spectral wind wave model SWAN (Booij et al. 1999) plays a key role in the estimation
of these HBC. Presently, the applicability of the SWAN model for the complicated Wadden Sea area is
being assessed.


   The primary coastal structures in the Netherlands               rather well (i.e. in statistical terms), but that there is
must be monitored every five years (2001, 2006,                    some uncertainty about the amount of penetration of
2011, etc.) for the required level of protection. This             relatively long waves (say, with periods larger than
check is based on Hydraulic Boundary Conditions                    10 s) into the Wadden Sea up to the levees of the
(HBC) that are derived every five years and                        main land. Measurements suggest that more low-
approved by the Minister of Transport, Public Works                frequency waves enter the Wadden Sea than
and Water Management in the Netherlands. The                       predicted by the wave model. To investigate the
HBC consist of near-shore water levels and wave                    possible cause of this mismatch, a detailed analysis
conditions. The spectral wind wave model SWAN                      of the physical processes in a tidal inlet during storm
(Booij et al. 1999) plays a key role in the estimation             conditions was performed. This analysis was
of these HBC. Presently, the applicability of the                  performed for the tidal inlet of Ameland (indicated in
SWAN model for the complicated Wadden Sea area                     Figure 1) for the storm of 9 Feb. 2004. The
is being assessed. The Wadden Sea is a shallow                     bathymetry of the tidal inlet of Ameland is shown in
sea situated in the north of The Netherlands and                   Figure 2.
partly sheltered from the North Sea by a number of
barrier islands. The Wadden Sea is connected to the
North Sea via a number of tidal inlets. The water
depth in the Wadden Sea varies from about 25 m in
the tidal channels up to +1 m above mean sea level
on the tidal flats. Figure 1 shows the bathymetry of
the Wadden Sea. The circle indicates the location of
the tidal inlet of Ameland, which is the area of
interest for this paper.




                                                                         Figure 2. Bathymetry of the tidal inlet of Ameland.

                                                                      The present investigation is performed with the
                                                                   SWAN wave model (Booij et al., 1999). This model is
                                                                   based on the action balance equation for wind
                                                                   generated waves. It predicts the evolution of action
                                                                   density N=N(σ,θ;x,y,t) as a function of intrinsic
Figure 1. Bathymetry of the Wadden Sea and location of the tidal
                                                                   frequency σ, direction θ, time t and geographical
                inlet of Ameland (black circle).                   spaces x and y. Action density is related to the more
                                                                   commonly used concept of energy density E
   To assess the performance of the SWAN model in                  according to N(σ,θ)=E(σ,θ)/σ:
this area, hindcast studies of historicial storms were
performed and the results were compared with buoy
measurements in the tidal inlet of Ameland (Alkyon,
2008). These studies showed that SWAN is doing


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  Chinese-German Joint Symposium on Hydraulic and Ocean Engineering, August 24-30, 2008, Darmstadt



  The action balance equation reads:

  ∂N (σ ,θ ; x, y, t ) ∂                           ∂                             ∂
         ∂t
                      = {cgx N (σ ,θ ; x, y, t )} + {cgy N (σ ,θ ; x, y, t )} +
                       ∂x                          ∂y                           ∂σ
                                                                                   {cgy N (σ ,θ ; x, y, t )} + ∂∂ {cgy N (σ ,θ ; x, y, t )} (1)
                                                                                                                θ




                                                                             The first three terms are the so-called deep-water
                                                                          source terms, where Swind is generation of waves
                                                                          by wind, Swcap is dissipation due to whitecapping
   The left-hand side terms represent the temporal                        and Snl4 is exchange of energy by non-linear four-
change of action density and the change due to                            wave interactions (also called quadruplets). The
propagation in geographical and spectral space. The                       latter three terms are the so-called shallow water
right-hand- side of Eq. (1) is the source term S                          source terms, where surf breaking Sbreak is
defined as the rate of change of energy density                           dissipation by depth-limited wave breaking, Sfric is
S=∂E/∂t. The source S is considered to be sum of the                      dissipation by bottom friction and Snl3 is the
following (identified) physical processes:                                exchange of energy by non-linear three-wave
                                                                          interactions (also called triads).

Stot = S wind + S wcap + S snl 4 + Sbreak + S fric + S nl 3 (2)




 Figure 3. Geographical variation of the significant wave height Hm0 and spectral period Tm-1,0, mean wave direction and directional
                                   spreading for the storm moment 9 February 2004, 1:30 hours.




   Figure 3 shows an example of the simulated                             February 2004, 1:30 hours. The mean wave
geographical variation of the significant wave height                     direction θ is shown as Physical processes in a tidal
Hm0, the spectral periods Tm-1,0 and Tm01 and the                         inlet 4 arrows scaled with the significant wave height.
directional spreading for the storm instant of 9                          The offshore boundary conditions were Hm0=4.8 m,


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  Chinese-German Joint Symposium on Hydraulic and Ocean Engineering, August 24-30, 2008, Darmstadt


Tp=14.2s, a wind speed of 16.3 m/s and a wind and                   increase on the shallow banks next to tidal channels.
wave direction of 328º. For reference the 5m, 10m                   To determine the physical processes that are
and 20m depth contours are also plotted in this                     responsible for this behaviour, the normalized source
figure. This figure shows a strong decrease of the                  term magnitudes were visualised. These are defined
severe wave conditions in the North Sea and the                     as follows:
strong decay of the waves as they propagate
through the tidal inlet. Evidently, the shallow areas of
the tidal inlet act as an effective filter for North Sea                        1
waves. South of the tidal inlet the wave conditions                     M=
                                                                                m0   ∫∫ S(σ θ ) dσ dθ
                                                                                             ,                 (3)
are locally determined and the influence of North
Sea seems to have vanished. The effects of
refraction are clearly visible in the variation of the
directional spreading, with decreasing values on the                   with m9    = ∫∫ E(σ ,θ ) dσ dθ     is    the    total   wave
shallow beaches of the Wadden islands and an                        variance.




     Figure 4. Normalized source term magnitudes for storm instant of 9 February 2004, 1:30 hours in the tidal inlet of Ameland.




   Figure 4 shows the geographical distribution of the              the deep water source terms for wind input,
normalized source term magnitudes in the tidal inlet                whitecapping and quadruplets are more or less of
of Ameland. The results show that in the North Sea                  the same magnitude. Inside the Wadden Sea, the


                                                                                                                                   527
  Chinese-German Joint Symposium on Hydraulic and Ocean Engineering, August 24-30, 2008, Darmstadt


normalized source term for wind input and                                  Another measure to detect the relative presence of
whitecapping are much higher than in the North Sea,                     long wave components is the ratio R of the spectral
pointing to active local wave growth. The strongest                     periods R=Tm01/Tm-1,0. In areas where there is an
(normalized) source term magnitudes are found in                        increase in relatively more Physical processes in a
the shallow parts of the tidal inlet, where surf                        tidal inlet 6 energetic long wave components than
breaking and triads (at least according to the LTA                      shorter ones, this ratio will decrease. Together with
method implemented in the SWAN model) dominate                          the low-frequency wave height H10, this ratio can be
over all other source terms. In the Wadden Sea, the                     considered as an indicator of the presence of low-
normalized source term magnitudes of the deep                           frequency wave energy. Figure 5 shows the
water source terms are again more or less of equal                      geographical variation of the low-frequency wave
magnitude and generally larger than the shallow                         height H10 and the ratio R of spectral periods in the
water normalized source term magnitudes. The                            central part of the tidal inlet of Ameland for the storm
shallow water source terms are well correlated with                     instant of 9 February 2004, 1:30 hours. For reference
the bathymetry. The pattern of all tidal channels and                   the 5 m, 10 m and 20 m depth contours are also
shallow banks is clearly visible. The strength of the                   plotted in this figure. The results indicate that the
normalized source term bottom friction is relatively                    low-frequency waves do not propagate into the
high (compared to surf breaking and triads) for many                    Wadden Sea. Instead, it appears that they are
shallow areas, suggesting that it affects the evolution                 refracted out of the tidal channels towards the
of the waves over long distances. The penetration of                    shallow banks, where they dissipate. It can also be
low frequency waves is investigated by means of two                     seen that in the western part of the tidal inlet the low-
(non-standard) wave parameters. The first                               frequency waves propagate over the shallow banks,
parameter is the low-frequency wave height H10. It                      but they disappear in the tidal channels south of
is defined similar to the standard definition of the                    these areas. This is also visible from the slightly
significant wave height Hm0, but now restricted to                      higher values of this ratio in the main tidal channels.
frequencies lower than or equal to 0.10 Hz (note that                   These results suggest that propagation effects play
energy density is written here as a function of                         an important role in the penetration of low frequency
frequency f and direction θ ).                                          waves in the Wadden Sea. Low-frequency wave
                                                                        components are refracted out of the channel causing
                                                                        an accumulation of wave energy on the sides of
                 0.1 2π                                                 these channels. This accumulation might cause
   H10 = 4       ∫ ∫ E(
                  0 0
                           f ,θ )
                                    dfdθ   (4)                          diffraction to redistribute the low frequency wave
                                                                        components back into the channels.




Figure 5. Geographical variation of the low-frequency wave height H10 and the ratio R of spectral periods Tm01 and Tm-1,0 in the tidal inlet
                                                            of Ameland.




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  Chinese-German Joint Symposium on Hydraulic and Ocean Engineering, August 24-30, 2008, Darmstadt


  The main findings       of   this   study   can   be           •    The observed mismatch in the missing low-
summarized as follows.                                                frequency wave energy may be attributed to
   •   The tidal inlet of Ameland acts as an                          the omission of diffraction effects in the wave
       effective filter for North Sea storm waves;                    modelling.
   •   The wave conditions in the Wadden Sea,
       south of this tidal inlet, are locally               ACKNOWLEDGEMENT
       determined;
                                                            The work presented in this paper is part of the
   •   The “deep water” source terms are dominant         SBW (Strength and Loads on Water Defences) study
       in the North Sea and in the Wadden Sea;            commissioned by DG Water, department of the
                                                          Ministry of Public Works in The Netherlands.
   •   Surf breaking and triads (according to the
       LTA method) are dominant on the outer (on
       the North Sea side) edges of the ebb-tidal               REFERENCES
       delta;                                             [1]    Alkyon, 2008: Analysis of SWAN hindcasts Wadden Sea,
                                                                 Oosterschelde and Slotermeer.
   •   Bottom friction is relatively weak, but acts
                                                          [2]    SBW Waddenzee, Report A2085r1. G.Ph. van Vledder.
       over long distances;
                                                          [3]    Booij, N., R.C. Ris and L.H. Holthuijsen, 1999: A third generation
   •   Low frequency waves hardly penetrate into                 wave model for coastal regions, part I, Model description and
                                                                 validation. J. Geophys. Res. 104, C4, 7649-7666.
       the Wadden Sea;
   •   Low-frequency waves are refracted out of
       the tidal channels onto the shallow tidal flats,
       where they dissipate.




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