Abstract
We present a nonlinear shallow water numerical wave model based on the purpose of radar monitoring in shallow sea. The model is based on the ocean dynamics boundary conditions of finite water depth. Firstly, we used the perturbation method to educe the “nonlinear long wave” discrete solution of the modulation between a long wave and a short wave at different depth, the “nonlinear long wave” will modulate another short wave and it produces a new “nonlinear long wave”. And then, using the same method we derived the nonlinear wave expression of linear mild slope, and educed the nonlinear shallow sea wave model. Finally, we achieved relatively good simulation results. This model avoids the limitation of the analytical solution which is used to solve the nonlinear sea wave model of modulation just between a single long-wave and a single short-wave. In theory, it can characterize the sea wave model that a long wave modulates infinite short waves. Establishing an accurate model of the shallow sea is essential to improve the accuracy of monitoring.
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References
Osborne, A.R., Segre, E., Boffetta, G., Cavaleri, L.: Soliton basis states in shallow water ocean surface waves. Physical Review Letters 67, 592–595 (1991), doi:10.1103/PhysRev-Lett.67.592
Grataloup, G.L., Mei, C.C.: Localization of harmonics generated in nonlinear shallow water waves. Physical Review E 68, 026314-1–026314-9 (2003), doi:10.1103/PhysRevE.68.026314
Onorato, M., Ambrosi, D., Osborne, A.R., Serio, M.: Interaction of two quasi-monochromatic waves in shallow water. Physics of Fluids 15, 3871–3874 (2003), doi:10.1063/1.1622394
Le Roux, D.Y., Staniforth, A., Lin, C.A.: A semi-implicit semi-Lagrangian finite-element shallow-water ocean model. Monthly Weather Review 128, 1384–1401 (2000); doi: 10.1175/1520-0493(2000)128<1384:ASISLF>2.0.CO;2
Danilov, S., Kivman, G., Schröter, J.: A finite element ocean model: principles and evaluation. Ocean Modelling 6, 125–150 (2004), doi:10.1016/S1463-5003(02)00063-X
White, L., Deleersnijder, E., Legat, V.: A three-dimensional unstructured mesh finite element shallow-water model, with application to the flows around an island and in a wind-driven, elongated basin. Ocean Modelling 22, 26–47 (2008), doi:10.1016/j.ocemod.2008.01.001
Iskandarani, M., Haidvogel, D.B., Boyd, J.B.: A staggered spectral element model with application to the oceanic shallow water equations. International Journal for Numerical Methods in Fluids 20, 393–414 (1995), doi:10.1002/fld.1650200504
Casulli, V., Walters, R.A.: An unstructured grid, three-dimensional model based on the shallow water equations. International Journal for Numerical Methods in Fluids 32, 331–348 (2000), doi:10.1002/(SICI)1097-0363(20000215)32:3<331::AID-FLD941>3.0.CO;2-C
Chen, C., Liu, H., Beardsley, R.C.: An unstructured grid, finite-volume, three-dimensional, primitive equations ocean model: Applications to coastal ocean and estuaries. Journal of Atmospheric and Oceanic Technology 20, 159–186 (2003), doi:10.1175/1520-0426(2003)020
Ham, D.A., Pietrzak, J., Stelling, G.S.: A scalable unstructured grid 3-dimensional finite volume model for the shallow water equations. Ocean Modelling 10, 153–169 (2005), doi:10.1016/j.ocemod.2004.08.004
Winther, N.G., Evensen, G.: A hybrid coordinate ocean model for shelf sea simulation. Ocean Modelling 13, 221–237 (2006), doi:10.1016/j.ocemod.2006.01.004
Comblen, R., Legrand, S., Deleersnijder, E., Legat, V.: A finite element method for solving the shallow water equations on the sphere. Ocean Modelling 28, 12–23 (2009), doi:10.1016/j.ocemod.2008.05.004
Hanert, E., Le Roux, D.Y., Legat, V., Deleersnijder, E.: An efficient Eulerian finite element method for the shallow water equations. Ocean Modelling 10, 115–136 (2005), doi:10.1016/j.ocemod.2004.06.006
Behrens, J.: Atmospheric and ocean modeling with an adaptive finite element solver for the shallow-water equations. Applied Numerical Mathematics 26, 217–226 (1998), doi:10.1016/S0168-9274(97)00090-1
Levin, J.C., Haidvogel, D.B., Chua, B., Bennett, A.F., Iskandarani, M.: Euler–Lagrange equations for the spectral element shallow water system. Ocean Modelling 12, 348–377 (2006), doi:10.1016/j.ocemod.2005.06.002
Longuet-Higgins, M.S., Stewart, R.W.: Changes in the form of short gravity waves on long waves and tidal currents. Journal of Fluid Mechanics Digital Archive 8, 565–583 (1960), doi:10.1017/S0022112060000803.
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Guanghui, Z., Hailan, K., Tao, X., Chuanping, T., Wei, C. (2012). Numerical Simulation of Nonlinear Sea Wave Model in Shallow Water. In: Lee, G. (eds) Advances in Computational Environment Science. Advances in Intelligent and Soft Computing, vol 142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27957-7_31
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DOI: https://doi.org/10.1007/978-3-642-27957-7_31
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