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\begin{document}

\title{An algorithm for computing the deflection angle of surface ocean
currents relative to the wind direction}



\author[1]{Adrian Constantin}%
\author[2]{David G. Dritschel}%
\author[3]{Nathan Paldor}%
\affil[1]{University of Vienna}%
\affil[2]{Mathematical Institute, University of St Andrews, UK}%
\affil[3]{Hebrew University of Jerusalem}%


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  \date{May 18, 2024}


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\begin{abstract}
The angle between the wind stress that overlies the ocean and the
resulting current at the ocean surface is calculated for a two-layer
ocean with uniform eddy viscosity in the lower layer and for several
assumed eddy viscosity profiles in the upper layer. The calculation of
the deflection angle is greatly simplified by transforming the linear,
second order, vertical structure equation to its associated nonlinear,
first order, Riccati equation. Though the transformation to a Riccati
equation can be used as an alternate numerical scheme, its main
advantage is that it yields analytic expressions for particular eddy
viscosity profiles.%
\end{abstract}%



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