Land-Water Interface Modeling Using a Two-Dimensional Shallow Water Model

Authors

1 Associate Professor, Dep. of Civil Eng., Tarbiat Modares University, Tehran, Iran

2 Ph.D. Student, Dep. of Civil Eng., Tarbiat Modares University, Tehran, Iran

Abstract

In this paper the H2D shallow water model is developed which employs terms like atmospheric pressure, wind stresses, tidal forces, and boundry friction status. Adding the algorithm of wetting and drying in boundry cells, along with the changing wind and pressure fields, a new model called Surge2D is developed. The numerical 2D model developed in this study estimates the shallow water currents. The land-water interface is treated as a moving boundary in which the flooding and draining rate depend on the both simulated current and the height of water in adjacent ‘wet’ cells. This ensures realistic and smoothly varying results. In this approach for the status of a boundary cell to change from dry to wet or wet to dry, the water level should become greater or less than a specified stage, respectivly. Furthermore the fluid must cross the length of the boundary cell according to the flow velocity in the adjacent cell. The results of this model were compared to both analytical solutions and MIKE21 results. The result of the 2D model indicated an excellent agreement with the analytical solutions (differences less than 0.1%). This model is used to study the effects of Shahid Kalantary causeway on the current pattern and characteristcs in UrmiaLake, in north-western Iran.

Keywords


ولیزاده، علیرضا (1381)، "تهیه مدل عددی پیشبینی پدیدة مد طوفان"، پایاننامه‌کارشناسی‌ارشد، دانشگاه تربیت مدرس،1381.
Bode, L. and Hardy, T.A. (1997), “Progress and Recent Developments in Storm Surge Modeling”, J. Hydraulic Engineering, 123(4), pp. 315-331.
Dube, S.K., Sinha, A.D., Murty, T.S. and Bahulayan, N. (1997), “Storm Surge in the Bay of Bengal and Arabian Sea: the Problem and its Prediction”, KMAUSAM, 48(2), pp. 283-304.
Flather R.A., Proctor, R. and Wolf, J. (1991), “Oceanographic Forcast Models”, Computer Modelling in the Environmental Sciences, Proceedings of a conference organised by the NERC in association with the Environmental Mathematics Group of the IMA. BGS, Keyworth: Clarendon Press, pp.15-30.
Guo, Q.C. and Chungjin, Y. (2002), “Modeling Non-uniform Suspended Sediment Transport in Alluvial Rivers”, J. Hydraulic Engineering, 128(9), pp. 839–847.
Hai P. and Guohong, F. (1993), “An Alternating Direction Implicit (ADI) Numerical Method for Two-Dimensional Hydrodynamic Equations”, Acta Oceanology Sinica, 14(1), pp. 1-13. 
Hu, S., and Kot, S.C. (1997), “Numerical Model of Tides in Pearl River Estuary with Moving Boundary”, J. Hydraulic Engineering, 123(1). pp. 21-29.
Hubbert, G. D. and McInnes, K. L. (1999), “A Storm Surge Inundation Model for Coastal Planning and Impact Studies”, J. Coastal Research, 15(1), pp. 168-185.
Jelesnianski, C. P., Chen, J., and  Shaffer, W.A. (1992), “SLOSH: Sea, Lake, and Overland Surges from Hurricanes”, Technical Report NWS, 48, NOAA.
Li, Y.S. and Zhang, M.Y. (1996), “A Semi-Implicit 3-D Hydrodynamic Model Incorporating the Influence of Flow –Dependent Eddy  Vuscosity, Bottom Topography and Wave-Current Interaction”, Applied Ocean Research, 18, pp. 173-185.
Maa, J.P.Y. (1990), “An Efficient Horizontal Two-Dimensional Hydrodynamic Model”, j. Coastal Engineering, 14, pp. 1-18.
Matthews, K., Noye, J. and Bills, P. (1996), “A New Method for Numerical Representation of the Land-Water Boundary in lake Circulation Models”, Applied Mathematical Modelling, 20(August), pp. 562-57l.
Murty, T.S., Flather, R.A. and Henry, R.F. (1986), “The Storm Surge Problem in the Bay of Bengal”, Progressive Oceanography, 16, pp. 195-233.
Patrick, J.L., Wu, T.R. and Liu, P.L.F. (2002), “Modeling wave runup with depth-integrated equations”, J. Coastal Engineering, 46, pp. 89-107.
Reid, R. O., and Bodine, B.R. (1968), “Numerical Model for Storm Surges in GalvestonBay”, J. Waterw. Coastal Eng. Div. Proc. Am. Soc., 94, pp. 33–57.
Smith, G.D, (1978), “Numerical Solution of Partial Differential Equations: Finite Difference Method”, Oxford University Press., UK, 350 p.
Sorenson, R.M., (1997), “Basic Coastal Engineering”, 2nd edition, Hall and Chapman, Ny. 
Tang, Y.m., Holloway, P. and Grimshaw, R. (1997), “A Numerical Model of Storm Surge Generated by Tropical Cyclone Jane”, J. of Physical Oceanography, 27, pp. 963-976.
Weiyan, T., (1992), Shallow Water Hydrodynamics, Water & Power press,Beijing, China.
Zangh, M.Y. and Li, Y.S. (1996), “The Dynamic Coupling of a Third- Generation Wave Model and a 3D Hydrodynamic Model Through Boundary Layers”, Continential Shelf Research, 17(10), pp. 1141-1170.