A non-hydrostatic algorithm for free-surface ocean modelling |
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| Authors: | Francis Auclair Claude Estournel Jochem W Floor Marine Herrmann Cyril Nguyen Patrick Marsaleix |
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| Institution: | 1. Université Pierre et Marie Curie, UMR 7093, Laboratoire d’Océanographie de Villefranche, F-06230 Villefranche-sur-Mer, France;2. Centre National de la Recherche Scientifique (CNRS), UMR 7093, Laboratoire d’Océanographie de Villefranche, Villefranche-sur-Mer, France;3. Geosciences Environment Toulouse (GET), Midi-Pyrenees Observatory (OMP), 14 Avenue Edouard Belin, 31400 Toulouse, France;4. Centre National de la Recherche Scientifique (CNRS), Laboratoire d’Aérologie, 14 Avenue Edouard Belin, 31400 Toulouse, France;5. International Atomic Energy Agency, Environment Laboratories, 4 Quai Antoine 1er, MC 98000, Monaco;1. Department of Biology, University of Florence, via Romana 17, Firenze, Italy;2. Department of Biology, University of Florence, via Romana 17, Firenze, Italy;3. Department of Biology, University of Florence, via Romana 17, Firenze, Italy;4. University of Tunis El Manar, Faculty of Sciences, Departement of Biology, Research Unit Bio-Ecology and Evolutionary Systematics, 2092 Manar II, Tunisia;5. Institute for Marine Biology Biotechnology and Aquaculture, Hellenic Centre for Marine Research, Heraklion, Crete, Greece;6. Department of Biology, University of Florence, via Romana 17, Firenze, Italy;1. College of Harbor, Coastal and Offshore Engineering, Hohai University, Nanjing 210098, P. R. China;2. HYDROCHINA Huadong Engineering Corporation, Hangzhou 310014, P. R. China;3. State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, State Oceanic Administration, Hangzhou 310012, P. R. China;1. Hokkaido National Fisheries Research Institute, Japan Fisheries Research and Education Agency, 116 Katsurakoi, Kushiro, Hokkaido 085-0802, Japan;2. National Research Institute of Fisheries Science, Japan Fisheries Research and Education Agency, 2-12-4 Fukuura, Kanazawa, Yokohama, Kanagawa 236-8648, Japan;3. Graduate School of Fisheries Science, Hokkaido University, 3-1-1 Minato, Hakodate, Hokkaido 041-8611, Japan;4. National Research Institute of Fisheries and Environment of Inland Sea, Japan Fisheries Research and Education Agency, Maruishi 2-17-5, Hatsukaichi, Hiroshima 739-0452, Japan;5. Hokkaido National Fisheries Research Institute, Japan Fisheries Research and Education Agency, 2-1 Tsukushikoi, Akkeshi, Hokkaido 088-1108, Japan;1. State Key Laboratory of Geodesy and Earth''s Dynamics, Institute of Geodesy and Geophysics, Chinese Academy of Sciences, 340 Xudong Road, Wuhan 430077, PR China;2. CNES/GRGS, 18 Avenue E. Belin, Toulouse 31401, France |
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| Abstract: | An original implementation of a non-hydrostatic, free-surface algorithm based on a pressure correction method is proposed for ocean modelling. The free surface is implemented through an explicit scheme combined with a mode-spitting method but the depth-averaged velocity and the position of the free surface are updated at each non-hydrostatic iteration. The vertical momentum equation is also integrated up to the surface enabling a natural and accurate treatment of the surface layer. The consistent specification of the numerical schemes provides balanced transfers of potential and kinetic energy. This algorithm is well-suited for implementation as a non-hydrostatic kernel on originally hydrostatic free-surface ocean models such as Symphonie (http://poc.obs-mip.fr/pages/research_topics/modelling/symphonie/symphonie.htm) for which it has originally been developed.Energy balances associated with the propagation of short surface waves and solitary waves are presented for two dedicated well-documented configurations over closed domains. The buoyancy flux, the work rate of the pressure force together with the power of the advective terms are evaluated and discussed for the generation and the propagation of these two types of waves. The dissipation rate is in particular shown to be several orders of magnitude smaller than the work rates of the hydrostatic and non-hydrostatic pressure forces confirming the necessity for the exchanges of energy to be numerically balanced. The algorithm is subsequently applied to the complex generation of non-linear solitary internal waves by surface tides over Georges Bank, in the Gulf of Maine. The generation and the propagation of the observed non-linear and non-hydrostatic features in this region are correctly reproduced. |
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