Abstract
This chapter provides a short introduction to the most commonly used numerical methods in computational fluid dynamics, and some specific aspects of numerical modelling of ocean currents. When working with numerical models, it is essential to have a basic understanding of the possibilities and limitations of the modelling toolbox. The first part gives a demonstration on how the model differential equations for fluid motions can be transformed into computer code instructions. Important concepts such as consistency, stability and convergence are discussed. The second part of the chapter provides an introduction to ocean modelling, with emphasis on the approximations that are commonly used in general circulation models.
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Notes
- 1.
In Eq. (3.5) the expression f (j)(x 0) indicates the j-th derivative of the function f, not to be confused with the discretization notation f (n).
- 2.
The ‘Big O’ notation describes the limiting behaviour of a function f by comparing it to the behaviour of a simpler function g. Therefore, if
$$\lim_{x \rightarrow x_0} \frac{f(x)}{g(x)} = C $$where C is some finite number, then \(f(x) = \mathcal{O}(g(x))\) as x→x 0. When discussing finite difference schemes it is implicitly understood that the approximation is valid for Δx→0, and therefore this condition is usually not stated explicitly in the formulas.
- 3.
Note that the rotation of the Earth is not a driving force in itself. When Newton’s laws of motion are applied in a rotating frame of reference, motion along a straight line appears to be deflected to the left or right. The Coriolis and centrifugal forces are introduced to account for such deflections. These forces are often called inertial forces or fictitious forces in order to emphasize that they are not connected to any physical force, but to the acceleration of the rotating system itself.
- 4.
GFDL Modular Ocean Model, http://www.gfdl.noaa.gov/ocean-model.
- 5.
M.I.T. general circulation model, http://mitgcm.org/.
- 6.
Princeton Ocean Model, http://aos.princeton.edu/WWWPUBLIC/htdocs.pom/.
- 7.
Regional Ocean Modeling System, http://www.myroms.org/.
- 8.
Miami Isopycnic Coordinate Ocean Model.
- 9.
Navy Layered Ocean Model, http://www7320.nrlssc.navy.mil/global_nlom/.
- 10.
HYbrid Coordinate Ocean Model, http://hycom.org/.
- 11.
Finite Volume Coastal Ocean Model, http://fvcom.smast.umassd.edu/FVCOM/.
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Acknowledgements
This work, originally motivated by the BONUS project BalticWay, was supported by the European Union through the Mobilitas grant MTT63 and through support to the Estonian Centre of Excellence for Non-linear Studies (CENS) from the European Regional Development Fund, and by targeted financing by the Estonian Ministry of Education and Research (grant SF0140007s11).
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Torsvik, T. (2013). Introduction to Computational Fluid Dynamics and Ocean Modelling. In: Soomere, T., Quak, E. (eds) Preventive Methods for Coastal Protection. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00440-2_3
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