Abstract
The oceans and marginal seas play an important role in the global climate system. Their surface and deep currents redistribute heat, salt, and chemical compounds all over the world. Ocean and shelf sea thermohaline circulations have a complicated vertical and horizontal structure which is determined by atmospheric forcing, sea ice, distribution of continents, and bottom relief.
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References
Arakawa A., 1966. Computational design for long term numerical integration of the equations of field motion: Two-dimensional incompressible flow, Part I. J. Comp. Phys. Res. 1: 119–163.
Bryan K., 1969. A numerical method for the study of the circulation of the world ocean. J. Comp. Phys. 4: 347–376.
Bubnov V. F. and F. V. Kazhikhov, 1971. Existence of a unique solution of the fundamental boundary value problem in the linear theory of oceanic circulation. Sov. Phys. Dokl. 16: 429–431.
Burchard H., 2002. GETM – A General Estuarine Transport Model. Scientific Documentation. Technical Report EUR 20253 EM, European Commission, 157pp.
Delecluse P. and V. B. Zalesny, 1996. Problems of numerical modelling of equatorial dynamics. Oceanology 36(1): 26–42.
Friedrich H. J., 1970. Preliminary results from a numerical multilayer model for the circulation in the North Atlantic. D. Hydr. Zeit. 23(4): 145–164.
Grotkop G., 1982. Finite element analysis of long-period water waves. Comp. Math. Appl. Med. Eng. 2: 89–112.
Hansen W., 1956. Strömungen in Randmeeren nebst Anwendungen. Tellus 3: 283–300.
Hansen W., 1959. Wind und Massenverteilung als Ursache der Meeresströmungen. The Rossby Memorial Volume, Oxford University Press, 102–106.
Ivanov Yu. A., K. V. Lebedev, and A. S. Sarkisyan, 1997. Generalized hydrodynamic adjustment method (GHDAM). Izv Ross. Akad Nauk, Fit. Atmos. Okeana 33(6): 812–818 (in Russian).
Kazantsev Ch., S. N. Moshonkin, and V. B. Zalesny, 1998. Mathematical modelling of the global ocean dynamics: solvability, numerical algorithm, calculations. In: Proc. of 4-th Conf. ‘Variability and Predictability of Atmospheric and Oceanic Circulations’. Moscow, Russia, 81–95.
Kordzadze A. A., 1982. Mathematical Questions for Solving the Problem of Ocean Dynamics. Novosibirsk, Sib. Branch, USSR Academy of Science (in Russian), 148 pp.
Kreiss H.-O., 1959. Über die Lösung des Cauchy Problems für lineare partielle Differentialgleichungen mit Hilfe von Differenzen gleichungen. Acta Math. 101: 179–199.
Kuzin V. I., 1985. The Finite Element Method in Modelling of Oceanic Processes. Novosibirsk, Sib. Branch, USSR Academy of Science (in Russian), 189 pp.
Lebedev V. I., 1997. Explicit difference schemes with variable time steps for solving stiff systems of equations. In: Numerical Analysis and its Applications. Lecture Notes in Computer Science 1196. Springer, 274–283.
Lilly D. K., 1965. On the computational stability of numerical solutions of time-dependent nonlinear geophysical fluid dynamics problems. Monthly Weather Rev. 93: 11–26.
Lions J. L., R. Temam, and S. Wang, 1992. On the equations of the large scale ocean. Nonlinearitv 5: 1007–1053.
Manabe S. and K. Bryan, 1969. Climate and the ocean circulation. Monthly Weather Rev. 97(11): 739–774.
Marchuk G. I., 1969. On the numerical solution of the Poincaré problem for oceanic circulations Dokl. Akad. Nauk SSSR 185(5): 1041–1044 (in Russian).
Marchuk G. I., 1980. Methods of Computational Mathematics. Nauka, Moscow, 536 pp.
Marchuk G. I., 1988. Splitting-Up Methods. Nauka, Moscow, 263 pp.
Marchuk G. I., 1995. Adjoint Equations and Analysis of Complex Systems. Kluwer Academic Publishers, Dordrecht, 466 pp.
Marchuk G. I. and G. V. Demidov, 1966. Theorem for existence of a solution for the short-range weather prediction problem. Dokl. Akad. Nauk SSSR 7(5): 1006–1008 (in Russian).
Marchuk G. I., J. Sündermann, and V. B. Zalesny, 2001a. Mathematical modelling of marine and ocean currents. Russ. J. Numer. Anal. Math. Modelling 16(4): 331–362.
Marchuk G. I., V. P. Dymnikov, and V. B. Zalesny, 1987. Mathematical Models in Geophysical Fluid Dynamics and Numerical Methods of Their Realization. Leningrad, Gidrometeoizdat (in Russian), 296 pp.
Marchuk G. I., V. P. Shutyaev, and V. B. Zalesny, 2001b. Approaches to the solution of data assimilation problems. In: Menaldi J. L. et al. (eds.), Optimal Control and Partial Differential Equations. IOS Press, Amsterdam, 489–497.
Mesinger F. and A. Arakawa, 1982. Numerical Methods Used in Atmospheric Models. GARP Publ. Ser. 17, I, WMO, 64pp.
Munk W. H., 1950. On the wind-driven ocean circulation. J. Meteorol. 7: 79–93.
Ovsyannikov L. V., 1966. Theorem on a Unique Solution for Linearized System of Ocean Dynamics Equations. Preprint of the Novosibirsk State University (in Russian), 12 pp.
Pontryagin L. S., V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishenko, 1962. The Mathematical Theory of Optimal Processes. John Wiley, New York, 360 pp.
Rolinski S., J. Segschneider, and J. Sündermann, 2001. Long-term propagation of tailings from deep-sea mining under variable conditions by means of numerical simulations. Deep Sea Res. II: 3465–3485.
Sarkisyan A. S., 1954. Calculation of steady-state wind currents in the ocean. Izv. Akad. Nauk SSSR, Ser. Geofiz. 6: 554–561 (in Russian).
Sarkisyan A. S., 1961. On the role of the density advection by wind in dynamics of baroclinic ocean. Izv. Ross. Acad. Nauk SSSR 9: 1396–1407.
Sarkisyan A. S., 1962. On dynamics of wind-driven currents in a baroclinic ocean. Oceanologia. II(3): 393–409.
Sarkisyan A. S., 1969a, Theory and computation of ocean currents, U.S. Dept. of Commerce and the NSF, Washington, DC, 90 pp.
Sarkisyan A. S., 1969b. Deficiencies of barotropic models of ocean circulation. Izv. Acad. Nauk SSSR, Ser. Fiz. Atmos. Okeana 5(8): 818–835 (AGU English translation).
Sarkisyan A. S. and Ju. L. Demin, 1983. A semidiagnostic method of sea currents calculation. Large-Scale Oceanographic Experiments in the WCRP 2(1): 210–214.
Sarkisyan A. S. and V. B. Zalesny, 2000. Splitting-up method and adjoint equation method in the ocean dynamics problem. Russ. J. Numer. Anal. Math. Modelling 15(3–4): 333–347.
Sarkisyan A. S. and V. F. Ivanov, 1971. Joint effect of baroclinity and bottom topography as an important factor in sea dynamics. Izv. Acad. Nauk SSSR, Ser. Fiz. Atmos. Okeana 2(6): 818–835 (AGU English translation).
Schtockman V. B., 1946. Equations of full flow fields induced by wind in nonhomogeneous sea. Dokl Akad. Nauk SSSR 54(5): 403–406 (in Russian).
Segschneider J. and J. Sündermann, 1997. Response of a global ocean circulation model to real time forcing and implications to Earth’s rotation. J. Phys. Ocean. 27: 2370–2380.
Segschneider J. and J. Sündermann, 1998. Simulating large scale transport of suspended matter. J. Mar. Syst. 14: 81–97.
Stockdale T. N., A. J. Busalacchi, D. E. Harrison, and R. Seager, 1998. Ocean modelling for ENSO. J. Geophys. Res. 103(C7): 14325–14355.
Stommel H., 1948. The westward intensification of wind-driven ocean currents. Trans. Amer. Geophys. Union 29: 202–206.
Sukhonosov V. I., 1983. On globally well-posed boundary value problems for models of dynamics of the atmosphere and the ocean. Sov. Phys. Dokl. 27(2): 387–391.
Sündermann J., 1994. Circulation and Contaminant Fluxes in the North Sea. Springer, 654pp.
Sverdrup H. U., 1947. Wind-driven currents in a baroclinic ocean; with application to the equatorial currents of the Eastern Pacific. Proc. Nat. Acad. Sci. Wash. 33(11): 318–326.
Thomas M., J. Sündermann, and E. Maier-Reimer, 2001. Consideration of ocean tides in an OGCM and implications for polar motion. Geophys. Res. Lett. 28(12): 2457–2460.
Yanenko N. N., 1967. Method of Fractional Steps for Solution of Multidimentional Problems of Mathematical Physics. Nauka, Novosibirsk (in Russian), 195 pp.
Zalesny V. B., 1997. Variability and equilibrium states of the world ocean circulation. Russ. J. Numer. Anal. Math. Modelling 12(6): 547–567.
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Sarkisyan, A.S., Sündermann, J.E. (2009). Mathematical Background and Methods of Ocean Modelling. In: Modelling Ocean Climate Variability. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9208-4_1
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