A MODIFIED HYPERBOLIC TANGENT EQUATION TO DETERMINE EQUILIBRIUM SHAPE OF HEADLAND BAY BEACHES
AbstractWhen designing any artificial beach, it's desirable to avoid (or minimise) future maintenance commitments by arranging the initial beach planshape so that it remains in equilibrium given the incident wave climate. Headlands bays, or embayments, where a sandy beach is held between two erosion resistant headlands, tend to evolve to a stable beach planshape with little movement of the beach contours over time. Several empirical bay shape equations have been derived to fit curves to the shoreline of headland bay beaches. One of the most widely adopted empirical equations is the parabolic bay shape equation, as it is the only equation that directly links the shoreline positions to the predominant wave direction and the point of diffraction. However, the main limitation with the application of the parabolic bay shape equation is locating the downcoast control point. As a result of research presented in this paper a new equation, based on the hyperbolic tangent shape equation was developed, which eliminates the requirement of placing the down coast control point and relies on defining a minimum beach width instead. This modified equation was incorporated into a new ArcGIS tool.
Benedet L, Klein AHF, and Hsu JRC . Practical insights and applicability of empirical bay shape equations. Proceedings 29th International Conference of Coastal Engineering. 2181-2193.
Eccleshall T, . Design of crenulate bays. Master thesis report. University College London. 104pp.
González M and Medina R . On the application of static equilibrium bay formulations to natural and man-made beaches. Coastal Engineering, 43, 209-225.
Halligan GH . Sand movement on the New South Wales coast. Proceedings Limnology Society, New South Wales, 31: 619-640.
Hsu JRC, Silvester R and Xia YM . New characteristics of equilibrium shaped bays. Proceedings of 8th Australian conf. on coastal and Ocean Eng., 3986-3999.
Hsu JRC and Evans C , Parabolic bay shapes and applications. Proceedings of Institution of Civil Engineers. Part 2, vol 87. Thomas Telford, London, 557-570.
Hsu JRC, Benedet L, Klein AHF, Raabe ALA, Tsai CP and Hsu TW . Appreciation of static bay beach concept for coastal management and protection. Journal of Coastal Research, 24, 198-215.
Hsu JRC, Yu MJ and Benedet L . Static bay beach concept for scientists and engineers: a review. Coastal Engineering, 57, 76-91.
Krumbein WC . Shore processes and beach characteristics. Technical Memorandum No.3. Beach Erosion Board, U.S. Army Corps of Engineers. 47pp.
Lausman R, Klein AHF and Stive M . Uncertainty in the application of the parabolic bay shape equation: part 1. Coastal Engineering, 57, 142-151.
Lausman R, Klein AHF and Stive M [2010a]. Uncertainty in the application of the parabolic bay shape equation: part 2. Coastal Engineering, 57, 142-151.
Lavalle PD and Lakhan VC (1997) A spatial-temporal analysis of the development of a log-spiral shaped embayment. Earth Surface Processes and Landforms, 22, 657-667.
Martino E, Moreno L, and Kraus NC . Engineering guidance for the use of bayed-beach formulations. Proceedings of Coastal Sediments 2003: American Society of Civil Engineers, vol 3, 860-875.
Mashima Y . Stable configuration of coastline. Coastal Engineering in Japan, 4:47-59.
Moreno L and Kraus NC . Equilibrium shape of headland-bay beaches for engineering design. Proceedings of Coastal Sediments 1999:American Society of Civil Engineers, vol 1, 860-875.
Oliveira FSB and Barreiro OM . Application of empircal models to bay-shaped beaches in Portugual. Coastal Engineering 57, 124-131.
Short AD and Masselink G . Embayed and structurally controlled beaches, in: Short, A.D. (Editor], Handbook of Beach and Shoreface morphodynamics. New York: John Willey; & Sons, 230-249.
Silvester R . Stabilization of sedimentary coastlines. Nature, 188:467-469.
Silvester R . Development of crenulate shaped bays to equilibrium. J. Waterways and Harbours division, 96, 275-287.
Silvester R and Ho SK . Use of crenulated shaped bays to stabilize coasts. Proceedings 13th ICCE, 2, 1347-1365.
Silvester R . Natural headland control of beaches. Continental Shelf Research, 4, 581-596.
Silvester R and Hsu JRC . Coastal stabilisation: Innovative concepts. Prentice-Hall, 578p.
Silvester R and Hsu JRC . Coastal Stabilization. Singapore: World Scientific Publishing, 578p.
Yasso WE . Plan geometry of headland bay beaches. Journal of geology, 73, 702-714.
Yu MMJ and Hsu JRC . Parabolic bay shape equation revisited for practical applications. Proceedings 30th International Conference of Coastal Engineering. Vol. 4. ASCE 3478-
Battjes, J.A., and J.P.F.M. Janssen. 1978. Energy loss and set-up due to breaking of random waves, Proceedings of 14th International Conference on Coastal Engineering, ASCE, 466-480.
De Vriend, H.J., J. Zyserman, J. Nicholson, J.A. Roelvink, P. Pechon, and H.N. Southgate. 1993. Medium-term 2DH coastal area modeling, Coastal Engineering, 21, 193-224.
Wiegel, R.L. 1965. Oceanographical Engineering, Prentice-Hall, Englewood Cliffs, New Jersey, 531 pp.