Extension of Ekman (1905) wind-driven transport theory to the <i>β</i> plane
<p>The seminal Ekman (1905) <span class="inline-formula"><i>f</i></span>-plane theory of wind-driven transport at the ocean surface is extended to the <span class="inline-formula"><i>β</i></span> plane by substituting the pseu...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2023-01-01
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| Series: | Ocean Science |
| Online Access: | https://os.copernicus.org/articles/19/93/2023/os-19-93-2023.pdf |
| Summary: | <p>The seminal Ekman (1905) <span class="inline-formula"><i>f</i></span>-plane theory of wind-driven
transport at the ocean surface is extended to the <span class="inline-formula"><i>β</i></span> plane by
substituting the pseudo-angular momentum for the zonal velocity in
the Lagrangian equation. When the <span class="inline-formula"><i>β</i></span> term is added, the
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; this can then be applied to
describe the motion in the zonal direction. Both analytical
expressions and numerical calculations highlight the critical role
of the Equator in determining the trajectories of water columns
forced by eastward-directed (in the Northern Hemisphere) wind stress
even when the water columns are initiated far from the Equator. Our
results demonstrate that the averaged motion in the zonal direction
depends on the amplitude of the meridional oscillations and is
independent of the direction of the wind stress. The zonal drift is
determined by a balance between the initial conditions and the
magnitude of the wind stress, so it can be as large as the mean
meridional motion; i.e., the averaged flow direction is not
necessarily perpendicular to the wind direction.</p> |
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| ISSN: | 1812-0784 1812-0792 |