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

Ruy Ibanez,Kalyan Shrestha,William Anderson,Joseph Kuehl

doi:10.5194/npg-25-201-2018

Abstract

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 − 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 considers the case γ < −1 which admits intensifying jets and a nonlinear case with γ = −3.

Highlights

Slope topography represents both a barrier to large-scale geophysical fluid transport as well as an important location of mesoscale feature generation
Slope topography creates a barrier between the open and coastal oceans, often inhibiting the transport of nutrient-rich waters into the coastal zone and at the same time trapping pollutants in the coastal zone. As both numerical and observational approaches have limitations with respect to modeling the slope region, the objective of this brief communication is to provide an analytic framework for flow along slope topographies
Such a framework will serve as an idealized backbone upon which observational, numerical, experimental and further theoretical work can build and provide a point of comparison for better interpretation of the respective dynamics

Summary

Introduction

Slope topography represents both a barrier to large-scale geophysical fluid transport as well as an important location of mesoscale feature generation. Slope topography creates a barrier between the open and coastal oceans, often inhibiting the transport of nutrient-rich waters into the coastal zone and at the same time trapping pollutants in the coastal zone. As both numerical and observational approaches have limitations with respect to modeling the slope region, the objective of this brief communication is to provide an analytic framework for flow along slope topographies. The results presented have implications for cross-topography exchange and provide significant insight into the coupling between the slope bottom boundary layer and interior water column dynamics

Problem formulation

Expanding jet

Compressing jet

Nonlinear solution

Discussion