Oceanography The Official Magazine of
The Oceanography Society
Volume 31 Issue 03

View Issue TOC
Volume 31, No. 3
Pages 12 - 13

FROM THE GUEST EDITORS: Introduction to the Special Issue on Mathematical Aspects of Physical Oceanography

Adrian Constantin George Haller
First Paragraph

Our knowledge and understanding of ocean dynamics is far from complete, but is expanding thanks in great part to new developments in mathematics. Some of the most important oceanographic discoveries have been made as a result of an integrated, multidisciplinary approach. The deepest understanding and the most interesting results almost always evolve from the interplay between theory and observation. A substantial body of theory to aid in the interpretation of observations has been developed, yet the ocean offers continually new data to challenge existing ideas—modern fieldwork is much more than cataloguing oceanic features, being designed as much to test theoretical hypotheses as it is to detect new phenomena.

Citation

Constantin, A., and G. Haller. 2018. Introduction to the special issue on mathematical aspects of physical oceanography. Oceanography 31(3):12–13, https://doi.org/10.5670/oceanog.2018.303.

References

Apel, J.R. 1987. Principles of Ocean Physics. Academic Press, 634 pp.

Boyd, J.P. 2018. Dynamics of the Equatorial Ocean. Springer, https://doi.org/​10.1007/​978-​3-​662-55476-0.

Constantin, A., and R.S. Johnson. 2015. The dynamics of waves interacting with the Equatorial Undercurrent. Geophysical & Astrophysical Fluid Dynamics 109:311–358, https://doi.org/10.1080/​03091929.2015.1066785.

Constantin, A., and R.S. Johnson. 2017a. A nonlinear, three-dimensional model for ocean flows, motivated by some observations of the Pacific Equatorial Undercurrent and thermocline. Physics of Fluids 29, 056604, https://doi.org/​10.1063/1.4984001.

Constantin, A., and R.S. Johnson. 2017b. Large gyres as a shallow-water asymptotic solution of Euler’s equation in spherical coordinates. Proceedings of the Royal Society A 473(2200), https://doi.org/​10.1098/rspa.2017.0063.

Dellar, P.J. 2011. Variations on a beta-plane: Derivation of non-traditional beta-plane equations from Hamilton’s principle on a sphere. Journal of Fluid Mechanics 674:174–195, https://doi.org/10.1017/S0022112010006464.

Haller, G. 2005. An objective definition of a vortex. Journal of Fluid Mechanics 525:1–26, https://doi.org/10.1017/S0022112004002526.

Haller, H., A. Hadjigjasem, M. Farazmand, and F. Huhn. 2016. Defining coherent vortices objectively from the vorticity. Journal of Fluid Mechanics 795:136–173, https://doi.org/10.1017/jfm.2016.151.

Johnson, G.C., M.J. McPhaden, and E. Firing. 2001. Equatorial Pacific Ocean horizontal velocity, divergence, and upwelling. Journal of Physical Oceanography 31(3):839–849, https://doi.org/10.1175/1520-0485(2001)031​<0839:EPOHVD>2.0.CO;2.

Paldor, N. 2015. Shallow Water Waves on the Rotating Earth. Springer, https://doi.org/​10.1007/​978-3-319-20261-7.

Saffman, P.G. 1981. Dynamics of vorticity. Journal of Fluid Mechanics 106:49–58, https://doi.org/10.1017/S0022112081001511.

Talley, L.D., G.L. Pickard, W.J. Emery, and J.H. Swift. 2011. Descriptive Physical Oceanography: An Introduction. Academic Press, 560 pp.