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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

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https://doi.org/10.5194/npg-2017-66
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 4.0 License.
Brief communication
14 Nov 2017
Review status
This discussion paper is a preprint. A revision of this manuscript was accepted for the journal Nonlinear Processes in Geophysics (NPG) and is expected to appear here in due course.
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 (SWE), 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 SWE are scaled to the case of a topographically controlled jet, 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 − αxy−γ, 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 consider 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. Discuss., https://doi.org/10.5194/npg-2017-66, in review, 2017.
Ruy Ibanez et al.
Interactive discussionStatus: closed
AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment
Printer-friendly Version - Printer-friendly version      Supplement - Supplement
 
RC1: 'review of the manuscript', Anonymous Referee #1, 22 Dec 2017 Printer-friendly Version Supplement 
AC1: 'Response to reviewer 1 and 2', Joseph Kuehl, 05 Jan 2018 Printer-friendly Version Supplement 
EC1: 'further revisions', Juan Restrepo, 08 Jan 2018 Printer-friendly Version 
 
RC2: 'Review', Anonymous Referee #2, 04 Jan 2018 Printer-friendly Version 
AC2: 'Response to reviewer 1 and 2', Joseph Kuehl, 05 Jan 2018 Printer-friendly Version Supplement 
Ruy Ibanez et al.
Ruy Ibanez et al.

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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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