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Water Waves in Isotropic and Anisotropic Media: A comparison

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The Mathematics of Marine Modelling

Part of the book series: Mathematics of Planet Earth ((MPE,volume 9))

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Abstract

Restoring forces as gravity, Coriolis force or their combination, endow geo and astrophysical fluids with an anisotropy direction. Breaking the underlying hydrostatic or cyclostrophic force balances in fluids that are stratified in density or angular momentum results in obliquely-propagating internal waves. These waves differ in nearly every conceivable aspect from external, surface gravity and capillary waves. Differences between linear internal and external waves stem to a large part from the complementary way in which their frequency depends on the wave vector. While these differences may be hiding in symmetrically-shaped basins, these become fully apparent when the boundary shape breaks the symmetry imposed by the anisotropy. These underlying force balances also constrain any wave-driven mean flows. Interestingly, the lack of a clear force balance in a homogeneous, non-rotating fluid that is stratified in linear momentum, renders waves, perturbations on these shear flows, ‘problematic’.

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Acknowledgements

Comments by Uwe Harlander and Evgeny Ermanyuk are gratefully acknowledged.

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Authors and Affiliations

  1. Institute for Marine and Atmospheric Research (IMAU), Utrecht University, Utrecht, Netherlands

    Leo R. M. Maas

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  1. Leo R. M. Maas
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Correspondence to Leo R. M. Maas .

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Editors and Affiliations

  1. Department of Applied Mathematics, Delft University of Technology, Delft, The Netherlands

    Henk Schuttelaars

  2. Department of Applied Mathematics, Delft University of Technology, Delft, The Netherlands

    Arnold Heemink

  3. Institute of Mechanics, Materials and Civil Engineering (IMMC) and Earth and Life Institute (ELI), Université Catholique de Louvain, Louvain-la-Neuve, Belgium

    Eric Deleersnijder

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Maas, L.R.M. (2022). Water Waves in Isotropic and Anisotropic Media: A comparison. In: Schuttelaars, H., Heemink, A., Deleersnijder, E. (eds) The Mathematics of Marine Modelling. Mathematics of Planet Earth, vol 9. Springer, Cham. https://doi.org/10.1007/978-3-031-09559-7_2

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