Bibliography

Arakawa, A., and V. R. Lamb, Computational design of the basic dynamical processes of the UCLA General Circulation Model, Meth. Comput. Phys., pp. 173-263, 1977.

Backhaus, J. O., A three-dimensional model for the simulation of shelf sea dynamics, Dt. Hydrogr. Z., 38, 165-187, 1985.

Baretta, J. W., W. Ebenhöh, and P. Ruardij, The European Regional Seas Ecosystem Model, a complex marine ecosystem model, Neth. J. Sea Res., 33, 233-246, 1995.

Baumert, H., and G. Radach, Hysteresis of turbulent kinetic energy in nonrotational tidal flows: A model study, J. Geophys. Res., 97, 3669-3677, 1992.

Beckers, J.-M., and E. Deleersnijder, Stability of a FBTCS scheme applied to the propagation of shallow-water inertia-gravity waves on various space grids, J. Computat. Phys., 108, 95-104, 1993.

Beckers, J.-M., H. Burchard, J.-M. Campin, E. Deleersnijder, and P.-P. Mathieu, Another reason why simple discretizations of rotated diffusion operators cause problems in ocean models. Comments on the paper isoneutral diffusion in a z-coordinate ocean model by Griffies et al., J. Phys. Oceanogr., 28, 1552-1559, 1998.

Beckers, J.-M., H. Burchard, E. Deleersnijder, and P.-P. Mathieu, On the numerical discretisation of rotated diffusion operators in ocean models, Monthly Weather Review, 128, 2711-2733, 2000.

Blumberg, A. F., and G. L. Mellor, A description of a coastal ocean circulation model, in Three dimensional ocean models, edited by N. S. Heaps, pp. 1-16, American Geophysical Union, Washington, D.C., 1987.

Bryan, K., A numerical model for the study of the world ocean, J. Computat. Phys., 4, 347-376, 1969.

Burchard, H., Turbulenzmodellierung mit Anwendungen auf thermische Deckschichten im Meer und Strömungen in Wattengebieten, Ph.D. thesis, Institut für Meereskunde, Universität Hamburg, published as: Report 95/E/30, GKSS Research Centre, 1995.

Burchard, H., Presentation of a new numerical model for turbulent flow in estuaries, in Hydroinformatics '98, edited by V. Babovic and L. C. Larsen, pp. 41-48, Balkema, Rotterdam, Proceedings of the third International Conference on Hydroinformatics, Copenhagen, Denmark, 24-26 August 1998, 1998.

Burchard, H., Energy-conserving discretisation of turbulent shear and buoyancy production, Ocean Modelling, 4, 347-361, 2002a.

Burchard, H., Applied turbulence modelling in marine waters, Lecture Notes in Earth Sciences, vol. 100, 215 pp. pp., Springer, Berlin, Heidelberg, New York, 2002b.

Burchard, H., Quantification of numerically induced mixing and dissipation in discretisations of shallow water equations, International Journal on Geomathematics, submitted, 2012.

Burchard, H., and H. Baumert, On the performance of a mixed-layer model based on the $ k$- $ \varepsilon $ turbulence closure, J. Geophys. Res., 100, 8523-8540, 1995.

Burchard, H., and J.-M. Beckers, Non-uniform adaptive vertical grids in one-dimensional numerical ocean models, Ocean Modelling, 6, 51-81, 2004.

Burchard, H., and K. Bolding, GETM - a general estuarine transport model. Scientific documentation, Tech. Rep. EUR 20253 EN, European Commission, 2002.

Burchard, H., and O. Petersen, Hybridisation between $ \sigma $ and $ z$ coordinates for improving the internal pressure gradient calculation in marine models with steep bottom slopes, Int. J. Numer. Meth. Fluids, 25, 1003-1023, 1997.

Burchard, H., and H. Rennau, Comparative quantification of physically and numerically induced mixing in ocean models, Ocean Modelling, 20, 293-311, 2008.

Burchard, H., K. Bolding, and M. R. Villarreal, Three-dimensional modelling of estuarine turbidity maxima in a tidal estuary, Ocean Dynamics, 54, 250-265, 2004.

Burchard, H., K. Bolding, W. Kühn, A. Meister, T. Neumann, and L. Umlauf, Description of a flexible and extendable physical-biogeochemical model system for the water column, J. Mar. Sys., 61, 180-211, 2006.

Casulli, V., and E. Cattani, Stability, accuracy and efficiency of a semi-implicit method for three-dimensional shallow water flow, Computers Math. Appl., 27, 99-112, 1994.

Chu, P. C., and C. Fan, Hydrostatic correction for reducing horizontal pressure gradient errors in sigma coordinate models, J. Geophys. Res., 108, 3206, doi: 10.1029/2002JC001,668, 2003.

Cox, M. D., A primitive equation, 3-dimensional model for the ocean, Tech. Rep. 1, Geophysical Fluid Dynamics Laboratory, University of Princeton, Princeton, N. J., 75 pp., 1984.

de Kok, J. M., A 3D finite difference model for the computation of near- and far-field transport of suspended matter near a river mouth, Cont. Shelf Res., 12, 625-642, 1992.

Deleersnijder, E., and K. G. Ruddick, A generalized vertical coordinate for 3D marine problems, Bulletin de la Société Royale des Sciences de Liège, 61, 489-502, 1992.

Duwe, K., Modellierung der Brackwasserdynamik eines Tideästuars am Beispiel der Unterelbe, Ph.D. thesis, Universität Hamburg, published in: Hydromod Publ. No. 1, Wedel, Hamburg, 1988.

Espelid, T. O., J. Berntsen, and K. Barthel, Conservation of energy for schemes applied to the propagation of shallow-water inertia-gravity waves in regions with varying depth, Int. J. Numer. Meth. Engng, 49, 1521-1545, 2000.

Fairall, C. W., E. F. Bradley, D. P. Rogers, J. B. Edson, and G. S. Young, Bulk parameterization of air-sea fluxes for Tropical Ocean-Global Atmosphere Coupled-Ocean Atmosphere Response Experiment, J. Geophys. Res., 101, 3747-3764, 1996.

Fofonoff, N. P., and R. C. Millard, Algorithms for the computation of fundamental properties of seawater, Unesco technical papers in marine sciences, 44, 1-53, 1983.

Freeman, N. G., A. M. Hale, and M. B. Danard, A modified sigma equations' approach to the numerical modeling of Great Lakes hydrodynamics, J. Geophys. Res., 77, 1050-1060, 1972.

Gerdes, R., A primitive equation ocean circulation model using a general vertical coordinate transformation. 1. Description and testing of the model, J. Geophys. Res., 98, 14,683-14,701, 1993.

Haidvogel, D. B., and A. Beckmann, Numerical Ocean Circulation Modelling, Series on Environmental Science and Management, vol. 2, 318 pp. pp., Imperial College Press, London, 1999.

Jackett, D. R., T. J. McDougall, R. Feistel, D. G. Wright, and S. M. Griffies, Updated algorithms for density, potential temperature, conservative temperature and freezing temperature of seawater, Journal of Atmospheric and Oceanic Technology, submitted, 2005.

Jerlov, N. G., Optical oceanography, Elsevier, 1968.

Kagan, B. A., Ocean-atmosphere interaction and climate modelling, Cambridge University Press, Cambridge, 1995.

Kantha, L. H., and C. A. Clayson, Small-scale processes in geophysical fluid flows, International Geophysics Series, vol. 67, Academic Press, 2000a.

Kantha, L. H., and C. A. Clayson, Numerical models of oceans and oceanic processes, International Geophysics Series, vol. 66, Academic Press, 2000b.

Kondo, J., Air-sea bulk transfer coefficients in diabatic conditions, Bound. Layer Meteor., 9, 91-112, 1975.

Krone, R. B., Flume studies of the transport of sediment in estuarial shoaling processes, Tech. rep., Hydraulic Eng. Lab. US Army Corps of Eng., 1962.

Lander, J. W. M., P. A. Blokland, and J. M. de Kok, The three-dimensional shallow water model TRIWAQ with a flexible vertical grid definition, Tech. Rep. RIKZ/OS-96.104x, SIMONA report 96-01, National Institute for Coastal and Marine Management / RIKZ, The Hague, The Netherlands, 1994.

Large, W. G., J. C. McWilliams, and S. C. Doney, Oceanic vertical mixing : a review and a model with nonlocal boundary layer parameterisation, Rev. Geophys., 32, 363-403, 1994.

Leonard, B. P., The ULTIMATE conservative difference scheme applied to unsteady one-dimensional advection, Comput. Meth. Appl. Mech. Eng., 88, 17-74, 1991.

Leonard, B. P., M. K. MacVean, and A. P. Lock, The flux integral method for multidimensional convection and diffusion, App. Math. Modelling, 19, 333-342, 1995.

Madala, R. V., and S. A. Piacsek, A semi-implicit numerical model for baroclinic oceans, J. Computat. Phys., 23, 167-178, 1977.

Martinsen, E. A., and H. Engedahl, Implementation and testing of a lateral boundary scheme as an open boundary condition in a barotropic ocean model, Coastal Engineering, 11, 603-627, 1987.

Mathieu, P.-P., E. Deleersnijder, B. Cushman-Roisin, J.-M. Beckers, and K. Bolding, The role of topography in small well-mixed bays, with application to the lagoon of Mururoa, Cont. Shelf Res., 22, 1379-1395, 2002.

Mellor, G. L., T. Ezer, and L.-Y. Oey, The pressure gradient conundrum of sigma coordinate ocean models, Journal of Atmospheric and Oceanic Technology, 11, 1126-1134, 1994.

Patankar, S. V., Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York, 1980.

Paulson, C. A., and J. J. Simpson, Irradiance measurements in the upper ocean, J. Phys. Oceanogr., 7, 952-956, 1977.

Pedlosky, J., Geophysical fluid mechanics, 2. ed., Springer, New York, 1987.

Phillips, N. A., A coordinate system having some special advantages for numerical forecasting, J. Meteorol., 14, 184-185, 1957.

Roe, P. L., Some contributions to the modeling of discontinuous flows, Lect. Notes Appl. Math., 22, 163-193, 1985.

Shchepetkin, A. F., and J. C. McWilliams, A method for computing horizontal pressure-gradient force in an oceanic model with a nonaligned vertical coordinate, J. Geophys. Res., 108, 10.1029/2001JC001,047, 2003.

Song, Y., A general pressure gradient formulation for ocean models. Part I: Scheme design and diagnostic analysis, Monthly Weather Review, 126, 3213-3230, 1998.

Song, Y., and D. B. Haidvogel, A semi-implicit ocean circulation model using a generalised topography-following coordinate, J. Computat. Phys., 115, 228-244, 1994.

Stelling, G. S., and J. A. T. M. van Kester, On the approximation of horizontal gradients in sigma co-ordinates for bathymetry with steep bottom slopes, Int. J. Numer. Meth. Fluids, 18, 915-935, 1994.

Umlauf, L., H. Burchard, and K. Bolding, General Ocean Turbulence Model. Source code documentation, Tech. Rep. 63, Baltic Sea Research Institute Warnemünde, Warnemünde, Germany, 2005.

van Leer, B., Toward the ultimate conservative difference scheme. V: A second order sequel to Godunov's method, J. Computat. Phys., 32, 101-136, 1979.

Zalezak, S. T., Fully multidimensional flux-corrected transport algorithms for fluids, J. Computat. Phys., 31, 335-362, 1979.

Zalezak, S. T., A preliminary comparison of modern shock-capturing schemes: linear advection, in Advances in computer methods for partial differential equations, edited by R. V. aand R. S. Stepleman, pp. 15-22, Publ. IMACS, 1987.

Zanke, U., Berechnung der Sinkgeschwindigkeiten von Sedimenten, Mitteilungen des Franzius-Institutes, 46, 231-245, 1977.



kklingbe 2017-10-02