Abstract
This lecture describes the basics of hyperbolic systems as needed to solve the initial boundary value problem for hydrostatic atmospheric modeling. We examine the nature of waves in the hydrostatic primitive equations and how the modal decomposition can be used to effect a complete solution in the interior of an open domain. The relevance of the open boundary problem for the numerical problem of static and adaptive mesh refinement is discussed.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Kasahara A (1974) Various vertical coordinate systems used for numerical weather prediction. Mon Wea Rev 102(3):504–522
Kasahara A, Puri K (1981) Spectral representation of three-dimensional global data by expansion in normal mode functions. Mon Wea Rev 109(1):37–51
Lions JL, Temam R, Wang S (1992a) New formulations of the primitive equations of the atmosphere and application. Nonlinearity 5(2):237–288
Lions JL, Temam R, Wang S (1992b) On the equations of the large-scale ocean. Nonlinearity 5(4):1007–1053
Oliger J, Sundström A (1978) Theoretical and practical aspects of some initial boundary value problems in fluid mechanics. SIAM J Appl Math 35(3):419–446
Staniforth A, Wood N (2003) The deep-atmosphere equations in a generalized vertical coordinate. Mon Wea Rev 131(8):1931–1938
Temam R, Tribbia J (2003) Open boundary conditions for the primitive and Boussinesq equations. J Atmos Sci 60(8):2647–2660
Thuburn J, Wood N, Staniforth A (2002) Normal modes of deep atmospheres. II: f–F-plane geometry. Q J R Meteorol Soc 128(6):1793–1806
Weiyan T (1992) Shallow water hydrodynamics. Elsevier Oceanography Series; Elsevier, Holland 55:1–434
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Tribbia, J., Temam, R. (2011). Waves, Hyperbolicity and Characteristics. In: Lauritzen, P., Jablonowski, C., Taylor, M., Nair, R. (eds) Numerical Techniques for Global Atmospheric Models. Lecture Notes in Computational Science and Engineering, vol 80. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11640-7_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-11640-7_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11639-1
Online ISBN: 978-3-642-11640-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)