Beach and dune erosion during storm surges — Reply

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BEACH AND DUNE EROSION DURING STORM SURGES -- REPLY

P. V E L L I N G A

Delft Hydraulic Laboratory, Laboratory de Voorst, Emmeloord (The Netherlands)

Mr. Subrata Bose discusses the possibility of using the scale relations for beach profile modeling derived by the author for the mathematical simulation of wave diffraction effects. In the opinion of the author this is questionable, as will be c o m m e n t e d below. The author has derived scale relations for the small-scale reproduction of dune erosion. The results of the tests have shown that beach profiles generated in a small scale model are generally steeper than field profiles, if converted to p r o t o t y p e with a horizontal scale factor n 1 t h a t is equal to the depth scale factor n d. This is explained by the use of p r o t o t y p e size sand in the model. In the model the fall velocity is too large compared to the orbital velocity. Consequently the eroded sand settles too fast, creating profiles t h a t are too steep. By introduction of a distortion relation, n l / n d = (nd/n2w) °'2a, the model profiles can be converted to realistic field profiles. Apart from the theoretical backgrounds, the use of a distortion relation can be looked upon as a way to compensate for the improper scaling of the b o t t o m material. Regarding the reproduction of the waves in the dune erosion model tests it should be stressed that for all tests Froude scaling has been applied, so that nH = nL = n d . This means that the waves were n o t distorted. Generally, it can be said t h a t for a proper reproduction of wave conditions the Froude scale relations need to be fulfilled. When diffraction and reflection effects must be simulated the following relations are stringent requirements: nt = x / ~ and n d = n 1 So a distortion of the waves for such conditions is n o t possible. If only the refraction effects are affecting the wave field then the following relations should be satisfied: nt = ~

and n l / n d = c~

Consequently, for such conditions a model distortion is possible. The phase function for p r o t o t y p e can now be found by multiplication of the model phase with a. Using mathematical models a fictive gravitational constant gr can be introduced. However, the scale relations remain valid:

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2

for diffraction: n t g

= 1 a n d nl = n d

ndgr

So a distortion is n o t possible. 2 For refraction

n t g = 1 a n d nl/n d = ndgr

The conclusion is that the scale relation for beach profiles and any other distortion relation should n o t be applied for the physical or mathematical modelling of wave diffraction. The use of a fictive gravitational constant does n o t eliminate the requirement nd = nl for diffraction simulation.

REFERENCES Vellinga, P., 1982. Beach and d u n e erosion during storm surges. Coastal Eng., 6: 361--

387.