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Articles | Volume 25, issue 1
https://doi.org/10.5194/npg-25-201-2018
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, Joseph Kuehl, Kalyan Shrestha, and William Anderson

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.

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We present a nonlinear analytic solution for barotropic flow relevant to the oceanographic slope...
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