Perturbation Analysis for the Surface Deflection Angle of Ekman-Type Flows with Variable Eddy Viscosity

Luigi Roberti

doi:10.1007/s00021-021-00586-y

Abstract

In the setting of steady wind-driven oceanic currents in a non-equatorial two-layer ocean with constant eddy viscosity in the lower layer and a general continuous eddy viscosity profile in the upper layer, we derive a formula for the change of the surface deflection angle due to a perturbation (in the upper layer) of a given eddy viscosity profile for which the solution to the problem is known. This extends and generalizes previous results for perturbations of a constant eddy viscosity. The perturbation analysis is performed using a recent reformulation of the linear second-order governing equations for Ekman-type flows as a nonlinear first-order Riccati-type equation.

Highlights

Wind-driven currents are one of the main aspects of oceanic circulation, which is largely responsible for the heat transport between different geographical regions and has a crucial impact on the Earth’s climate [15]
It is observed in practice that such wind-induced currents do not follow the direction of the generating wind, but instead are deflected to the right of the wind direction in the Northern Hemisphere, the amplitude of the observed deflection angle being generally within the range 10◦–75◦
The Ekman layer is named after the Swedish scientist who, in 1905, was the first to write down and investigate a model that should explain the observations of the surface deflection angle that had been made at that time

Summary

Introduction

Wind-driven currents are one of the main aspects of oceanic circulation, which is largely responsible for the heat transport between different geographical regions and has a crucial impact on the Earth’s climate [15]. The Ekman layer is named after the Swedish scientist who, in 1905, was the first to write down and investigate a model that should explain the observations of the surface deflection angle that had been made at that time In his classical work [10], the eddy viscosity (a quantity introduced as a measure of the frictional effects in the boundary layer—see the section) is set as a constant, yielding a solution that, at the surface, is directed at an angle of 45◦ to the right (left) of the wind direction in

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The Governing Equations

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Discussion

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