Abstract
This chapter introduces the reader to nonhydrostatic finite-difference solvers of the Navier-Stokes equations. For a start, the ocean is treated as as vertical slice. Flow and gradients of variables normal to this plane are assumed to vanish, and the Coriolis force is ignored. Exercises address deep-water (short) surface gravity waves, bottom-attached density-driven currents, internal waves, instabilities of vertical shear flows, lee waves, double-diffusive instability, double-diffusive layering and free convection.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Bibliography
Arakawa, A., and V. Lamb, 1977: Computational design of the basic dynamical processes of the ucla general circulation model. In Methods in Computational Physics, vol. 17. Academic Press, San Francisco, pp. 174–267.
Bénard, H., 1900: Les tourbillons cellulairs dans une nappe liquide. Rev. Gén. Sci. Pure Appl., 11, 1309–1328.
Britter, R. A., and P. F. Linden, 1980: The motion of the front of a gravity current travelling down an incline. J. Fluid Mech., 99(3), 531–543.
Brown, 1866: Miscellaneous Botanical Works Vol. 1 (edited by J. J. Bennett), R. Hardwicke, London
Courant, R., K. Friedrichs, and H. Lewy, 1928: Über die partiellen Differenzengleichungen der mathematischen Physik. Mathematische Annalen, 100 (1), 32–74.
Cushman-Roisin, B., 1994: Introduction to Geophysical Fluid Dynamics, Prentice Hall, New York, 320pp.
Deleersnijder, E., J.-M. Campin, and E. J. M. Delhez, 2001: The concept of age in marine modelling. 1. Theory and preliminary model results. J. Mar. Syst., 28, 229–267.
Fringer, O. B., S. W. Armfield, and R. L. Street, 2005: Reducing numerical diffusion in interfacial gravity wave simulations. Int. J. Numer. Meth. Fluids, 49(3), 301–329, doi: 10.1002/fld.992.
Froude, W.: 1874: On useful displacement as limited by weight of structure and of propulsive power. Trans. Inst. Naval Architects, 15, 148–155.
Gill, A. E., 1982: Atmosphere-Ocean Dynamics, Academic Press, London, 662pp.
Kundu, P. K., 1990: Fluid Mechanics, Academic Press, Orlando, Florida, 638pp.
Marshall, J., and F. Schott, 1999: Ocean-ocean convection: observations, theory, and models. Rev. Geophys., 37(1), 1–64.
Pond, S. G., and L. Pickard, 1983: Introductory Dynamical Oceanography, 2nd edition, Pergamon Press, Oxford, 329pp.
Press W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, 1989: Numerical Recipes. The Art of Scientific Computing. Cambridge University Press, Cambridge, 702pp.
Rayleigh, L., 1916: On convection currents in a horizontal layer of fluid when the higher temperature is on the other side. Philos. Mag., 32, 529–543.
Richardson, L. F., 1920: The supply of energy from and to atmospheric eddies. Pros. Roy. Soc. London, A 97, 354–373.
Ruddick, B. 1983: A practical indicator of the stability of the water column to double-diffusive activity. Deep-Sea Res., 30, 1105–1107.
Turner, J. S., 1973: Buoyancy Effects in Fluids, Cambridge University Press, Cambridge, 367pp.
Wu, W., 2007: Computational River Dynamics, CRC Press, USA, 508pp.
Kämpf, J., 2009: Ocean Modelling for Beginners (using open-source software), Springer, 175pp.
Bernoulli, D., 1738: Hydrodynamica, J. R. Dulsecker, Strasbourg.
Euler, L., 1755: Principes generaux de l’etat d’equilibre des fluides; Principes generaux du mouvement des fluides; Continuation des recherches sur la theorie du mouvement des fluides. Histoire de l’Acacdernie de Berlin.
Thomson, W. (Lord Kelvin), 1871: Hydrokinetic solutions and observations. Phil. Mag., 42, 362–377.
Helmholtz, H. L. F. von, 1868: Über discontinuierliche Flüssigkeits-Bewegungen [On the discontinuous movements of fluids], Monatsberichte der Königlichen Preussichen Akademie der Wissenschaften zu Berlin [Monthly Reports of the Royal Prussian Academy of Philosophy in Berlin], vol. 23, pp. 215ff.
Flinders, M., 1814: A voyage to Terra Australis. 1.
Pacanowksi, R., and S. G. H. Philander, 1981: Parameterization of vertical mixing in numerical models of tropical oceans. J. Phys. Oceanogr., 11(11), 1443–1451.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Kämpf, J. (2010). Basics of Nonhydrostatic Modelling. In: Advanced Ocean Modelling. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10610-1_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-10610-1_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-10609-5
Online ISBN: 978-3-642-10610-1
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)