31 Aug 2022
31 Aug 2022
Status: this preprint is open for discussion.

Extension of Ekman (1905) wind-driven transport theory to the β-plane

Nathan Paldor1 and Lazar Friedland2 Nathan Paldor and Lazar Friedland
  • 1Fredy and Nadine Herrmann Institute of Earth Sciences, Hebrew University of Jerusalem, Jerusalem, Israel
  • 2Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem, Israel

Abstract. The seminal, Ekman (1905)’s, f-plane theory of wind driven transport at the ocean surface is extended to the β-plane by substituting the pseudo angular momentum for the zonal velocity in the Lagrangian equation. The addition of the β term implies that equations become nonlinear, which greatly complicates the analysis. Though rotation relates the momentum equations in the zonal and the meridional directions, the transformation to pseudo angular momentum greatly simplifies the longitudinal dynamics, which yields a clear description of the meridional dynamics in terms of a slow drift compounded by fast oscillations, which can then be applied to describe the motion in the zonal direction. Both analytical expressions and numerical calculations underscore the critical role of the equator in determining the trajectories of water columns forced by eastward directed wind stress even when the water columns are far from the equator. Our results demonstrate that the averaged motion in the zonal direction is highly dependent on the meridional oscillations and for some initial conditions can be as large as the meridional mean motion.

Nathan Paldor and Lazar Friedland

Status: open (until 02 Nov 2022)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • CC1: 'Comment on egusphere-2022-831', Adrian Constantin, 15 Sep 2022 reply
    • RC1: 'Reply on CC1', Anonymous Referee #1, 17 Sep 2022 reply

Nathan Paldor and Lazar Friedland

Nathan Paldor and Lazar Friedland


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Short summary
When the wind blows over an ocean the resulting mean current can assume many directions relative to the wind direction and does not have to perpendicular to the direction of the wind. This in contrast to a simpler, 120 year-old, theory that completely ignored Earth's sphericity and predicted that the mean ocean current should always be perpendicular to the direction of the overlying wind. In the new theory the direction of the mean current is determined by the values of several parameters.