Faculty of Geosciences Physical Geography
Layout: C&M - Faculty of Geosciences - ©2014 (8674)
Individual wave celerity in the surf zone
Motivation
• Remote-sensing techniques increasingly popular to monitor morphodynamic changes in coastal areas
• Estimation of bathymetry from video images often based on wave celerity Video images ➞ Celerity (C)
➞ Water depth (h)
C = f (h,T,...)
• Good parameterization of celerity is essential, but relatively large discrepancies remain in the inner surf zone.
➞ Infl uence of infragravity waves on short-wave celerity in the surf zone?
Methods
• Wave-by-wave analysis based on 2 high-resolution laboratory datasets (GLOBEX and Van Noorloos data)
→ 11 bichromatic wave conditions, 2 beach slopes (1/80 and 1/35)
• For each condition, waves identifi ed and followed based on a simple crest-tracking method (see Fig. 1)
• Computation of individual wave characteristics
10 20 30 40 50 60 70
20 30 40 50 60 70 80 90
time (s)
cross-shore distance x (m)
η (m) 0.2
0.15
0.1
0.05
0
-0.05
0 0.5 1 1.5 2 2.5 3
−0.02 0 0.02
−0.1 0 0.1
0 2 4 6
20 30 40 50 60 70 80 90
C i (m/s)η i (m)u i (m/s)T i (s)
x (m) (a)
(b)
(c)
(d)
1.3(gh) (gh)1/2 1/2
Results
Individual wave celerity
• Strong variability of celerity in the surf zone (x>57 m, Fig. 2a)
• Fastest waves propagate on the infragravity wave crests (e.g. cyan line, Fig. 2):
positive elevation (Fig. 2b) and onshore-directed current (Fig. 2c)
Crest convergence and bore-merging
• Variability in celerity leads to the convergence of the crests, and, potentially, to their merging (see trajectories in Fig. 1, and divergence of the individual periods in Fig. 2d)
• Convergence rate depends on infragravity wave characteristics (Fig. 3)
Cross-shore change in period:
Figure 2: Cross-shore evolution of the wave celerity (a), local water level (b), local velocity (c) and period (d) for each individual wave (case B3).
One line = one wave. Vertical lines: see Fig. 1.
Figure 1: Time-space diagram of free-surface elevation (case B3, Globex data). The colored lines are the crest trajectories;
The 3 vertical lines represent, from left to right, the outer breakpoint, the inner breakpoint, and the start of the swash zone.
( ) √
∑ ( ( ) ( ) ̅( ) )
For Figure 2a (arrows with text)
( ̅)
(for the arrow the most on the left)
( ̅)
(for the arrow the most on the right)
For Figure 2b: title on vertical axis
( )
Marion Tissier (m.f.s.tissier@uu.nl) and Gerben Ruessink
Acknowledgements
We would like to thank Ap van Dongeren and J. van Noorloos for kindly providing their laboratory data. The GLOBEX experiment was supported by the European Community’s 7th Framework Programme (Hydralab IV).
Conclusions
• Large intra-wave variability of celerity observed in the inner surf zone (up to 90% of the mean celerity!)
• This variability can be explained, in a large part, by the variations of water level and velocity induced by the infragravity waves;
➞ Consequences for depth-inversion? (quantifi cation errors due to the large intra-wave variability in celerity and period)
Figure 3: CV as a function of the ratio of infragravity to sea-swell wave height for the 11 conditions.
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
0.1 0.2 0.3 0.4 0.5 0.6
CV (x surf)
Hinfra/Hsea−swell
In the inner surf zone
Van Noorloos Globex
In the inner surf zone:
