Articles | Volume 25, issue 1
Nonlin. Processes Geophys., 25, 201–205, 2018
https://doi.org/10.5194/npg-25-201-2018
Nonlin. Processes Geophys., 25, 201–205, 2018
https://doi.org/10.5194/npg-25-201-2018

Brief communication 06 Mar 2018

Brief communication | 06 Mar 2018

Brief communication: A nonlinear self-similar solution to barotropic flow over varying topography

Ruy Ibanez et al.

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Subject: Nonlinear Waves, Pattern Formation, Turbulence | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere
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Cited articles

Blasius, H.: Grenzschichten in Flüssigkeiten mit kleiner Reibung, Z. Angew. Math. Phys., 56, 1–37, 1908.
Csanady, G. T.: The arrested topographic wave, J. Phys. Oceanogr., 8, 47–62, 1978.
Cushman-Roisin, B.: Introduction to Geophysical Fluid Dynamics, 320 pp., Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1994.
Ibanez, R.: Analytic Modeling and Applications of Barotropic Flows over Sloping Topographies Using Similarity Solutions, Masters Thesis, Baylor University, 2016.
Kuehl, J. J.: An analytic solution for barotropic flow along a variable slope topography, Geophys. Res. Lett., 41, 7591–7594, https://doi.org/10.1002/2014GL061188, 2014.
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Short summary
We present a nonlinear analytic solution for barotropic flow relevant to the oceanographic slope region. A similarity approach is adopted and the solution takes the form of a Lambert W-function. A more general class of linear solutions is also discussed which take the form of error functions. The equations solved are similar to the heat equation and thus the results may be of interest beyond the geophysical community.