EMPIRICAL RELATIONSHIP BETWEEN INLET CROSS-SECTIONAL AREA AND TIDAL PRISM: A RE-EVALUATION

Marcel Stive, Liang Ji, Ronald L Brouwer, Co van de Kreeke, Roahanka Ranasinghe

Abstract


The well-known empirical relationship between the equilibrium cross-sectional area of tidal inlet entrances (A) and the tidal prism (P), first developed by O’Brien (1931), has been extensively reviewed. Our theoretical investigations indicate that a unique A-P relationship should only be expected for clusters of inlets that are phenomenological similar (i.e. fairly similar hydrodynamic and morphological conditions), and that the exponent q in the A-P relation should be larger than 1. However, relevant published data available to date do not clearly support this theoretical finding. A re-analysis of the available data sets by Stive et al. (2009) indicated that they may not be sufficiently reliable to verify our theoretical finding with regard to q>1 due to the violation of the condition of phenomenological similarity, and possibly also due to violating the initial definitions given by O’Brien (1931) in estimating the tidal prism. The resolution of this issue is important because slightly different values of q result in significantly variable values for the equilibrium cross-sectional area of the tidal entrance. This may have significant implications in determining the true stable equilibrium entrance cross-sectional area. Here we present a re-analysis of the available data with a focus on determining the phenomenological dependencies of the A-P relationship. The available A-P data from the US Pacific, Atlantic and Gulf coasts (Jarrett, 1976 and Powell, 2003) have been re-scrutinized and categorized following the above mentioned phenomenological similarity criteria, viz. similar tidal range, similar sediment size, similar littoral transport and similar hydraulic radius. All together, some 20 different categories were considered and A-P relationships were obtained for each category. Generally, high correlations were found between the stable inlet predicted by each A-P relationship and the corresponding data. However, only in a limited number of categories were they significantly better than the correlations for the complete datasets. Finally, we point out that only in a number of categories the q value associated with the A-P relationship exceeded unity as suggested by the theoretical derivations. In the majority of categories the q value associated with the A-P relationship does not exceed unity. This is truly disappointing, and we have no physical explanation for this and consider this issue unresolved.

Keywords


inlets; tidal prism; empirical relationship; equilibrium cross-sectional area

References


Dieckmann, R., Osterhun, M., Partenscky, H.W., 1988. A comparison between German and North American tidal inlets. Proceedings of the 21 st International Conference on Coastal Engineering, ASCE, 2681-2691

Stive M.J.F., Kreeke J. van de, Nghiem T.L., Tran Thanh T., Ranasinghe, R.W.M.R.J.B., 2009. Empirical relationships between inlet cross-section and tidal prism: a review. In M Mizuguchi & S Sato (Eds.), Proceedings of Coastal Dynamics 2009. Impacts of human activities on dynamic coastal processes (pp. 1-10). Tokyo, Japan: World Scientific Publishing Co. Pte. Ltd. http://dx.doi.org/10.1142/9789814282475_0098

Escoffier, F.F., 1940. The stability of tidal inlets. Shore and Beach 8 (4), 111 – 114

Gerritsen, F., and Louters, T, 1990. Morphological stability of inlets and channels in the Western Wadden sea. Rijkswaterstaat, Report GWAO-90.019.

Hume, T.M. and Herdendorf, C. E., 1990. Morphologic and Hydrologic Characteristics of Tidal Inlets on a Headland Dominated, Low Littoral Drift Coast, Northeastern New Zea1and, Proceedings

Skagen Symposium (2-5 Sep. 1990), Journal of Coastal Research Special Issue 9: 527-563.

Hume, T.M., Herdendorf, C. E., 1993. On the use of empirical stability relationships for characterising estuaries. Journal of Coastal Research 9 (2), 413– 422.

Jarrett, J.T., 1976. Tidal prism - inlet area relationships. GITI report no. 3. Coastal Engineering Research Center, US Army Corps of Engineers, Fort Belvoir, VA, USA

Kraus, N.C., 1998. Inlet cross-section area calculated by process-based model. Proceedings International Conference on Coastal Engineering. ASCE, Reston, VA, pp 3265—3278

LeConte, L.J., 1905. Discussion on the paper, —Notes on the improvement of river and harbor outlets in the United States‖ by D. A. Watt, paper no. 1009. Trans. ASCE 55 (December): 306—308

O'Brien, M.P., 1931. Estuary and Tidal Prisms Related to Entrance Areas. Civil Eng. 1 (8): 738-739.

O'Brien, M.P., 1969. Equilibrium flow areas of inlets on sandy coasts. J Waterway Port Coast Ocean Eng 95 (l): 43—52

Powell, M.A., R.J. Thieke and A.J. Mehta, 2006. Morphodynamic relationships for ebb and flood delta volumes at Florida's entrances. Ocean Dynamics 56: 295-307.http://dx.doi.org/10.1007/s10236-006-0064-3

Powell M.A., 2003. Ebb shoal and flood shoal volumes on the coasts of Florida: St Marys entrance to Pensacola Pass. Masters theses University of Florida.

Riedel, H.P., and Gourlay, M.R., 1980. Inlets/Estuaries Discharging into Sheltered Waters. Proceedings International Conference on Coastal Engineering, ASCE Press, NY, 2550-2562.

Shigemura, T., 1980. Tidal prism – throat area relationships of the bays of Japan. Shore and Beach, 48 1. : 30-35

Suprijo, T. and Mano A., 2004. Dimensionless parameters to describe topographical equilibrium of coastal inlets. Proc .29 th ICCE, ASCE: 2531-2543

Van de Kreeke, J., 1985. Stability of tidal inlets; Pass Cavallo, Texas. Estuarine Coastal Shelf Science, 21:33-43 http://dx.doi.org/10.1016/0272-7714(85)90004-6

Van de Kreeke, J., 1990. Stability of a two-inlet bay system. Coastal Engineering, 14: 481-497http://dx.doi.org/10.1016/0378-3839(90)90031-Q

Van de Kreeke, J., 1992. Stability of tidal inlets; Escoffier's analysis. Shore and Beach, 60 (1): 9-12

Van de Kreeke, J., 1998. Adaptation of the Frisian inlet to a reduction in basin area with special reference to the cross-sectional area of the inlet channel. In Dronkers, J. and Scheffers, M.B.A.M. (Eds). Proc. PECS conference: 355-362

Van de Kreeke, J., 2004. Equilibrium and cross-sectional stability of tidal inlets: application to the Frisian Inlet before and after basin reduction. Coastal Engineering, 51: 337-350http://dx.doi.org/10.1016/j.coastaleng.2004.05.002

Yanez, M. A., 1989. Stability of a double –inlet bay system; Marco Island, FL, USA. Master's thesis, RSMAS, University of Miami, pp 67


Full Text: PDF

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.