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Nonlin. Processes Geophys., 25, 201-205, 2018
https://doi.org/10.5194/npg-25-201-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
Brief communication
06 Mar 2018
Brief communication: A nonlinear self-similar solution to barotropic flow over varying topography
Ruy Ibanez1, Joseph Kuehl2, Kalyan Shrestha3, and William Anderson3 1Mechanical Engineering Department, University of Rochester, Rochester, NY 14627, USA
2Mechanical Engineering Department, University of Delaware, Newark, DE 19716, USA
3Mechanical Engineering Department, University of Texas Dallas, Dallas, TX 75080, USA
Abstract. Beginning from the shallow water equations (SWEs), a nonlinear self-similar analytic solution is derived for barotropic flow over varying topography. We study conditions relevant to the ocean slope where the flow is dominated by Earth's rotation and topography. The solution is found to extend the topographic β-plume solution of Kuehl (2014) in two ways. (1) The solution is valid for intensifying jets. (2) The influence of nonlinear advection is included. The SWEs are scaled to the case of a topographically controlled jet, and then solved by introducing a similarity variable, η = cxnxyny. The nonlinear solution, valid for topographies h = h0 − αxy3, takes the form of the Lambert W-function for pseudo velocity. The linear solution, valid for topographies h = h0 − αxyγ, takes the form of the error function for transport. Kuehl's results considered the case −1 ≤ γ < 1 which admits expanding jets, while the new result considers the case γ < −1 which admits intensifying jets and a nonlinear case with γ = −3.
Citation: Ibanez, R., Kuehl, J., Shrestha, K., and Anderson, W.: Brief communication: A nonlinear self-similar solution to barotropic flow over varying topography, Nonlin. Processes Geophys., 25, 201-205, https://doi.org/10.5194/npg-25-201-2018, 2018.
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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.
We present a nonlinear analytic solution for barotropic flow relevant to the oceanographic slope...
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