Wind-driven transport at the ocean surface: Beyond the f-plane

Nathan Paldor (HU of Jerusalem)

May 22. 2023, 14:00 — 14:45

Ekman's seminal and elegant theory of wind-driven transport was developed in1905 on the f-plane and was extended to the $\beta$-plane and the sphere only 120 years later in 2023. The theory describes the trajectory of a water column as a combination of a steady motion (perpendicular to the wind direction) compounded by (inerial) oscillations at the uniform Coriolis frequency. The inclusion of the latitudinal change of the Coriolis frequency turns the equations non-linear and introduces the equator as the latitude where the Coriolis frequency vanises. The inclusion of the $/beta$ causes a drift of the water column trajectory parallel to the wind direction, which is completely missing on the f-plane. As a dynamical system, the WKB method is employed based on the slow changes in the steady states due to the smallness of the nondimenional wind-stress and the fast rotation about the steady states. The dynamics is resolved by transforming the zonal velocity to the conserved pseudo angular momentum. The extension of the theory to spherical coordinates are also resolved by considering the temporal evolution of the angular momentum instead of the zonal velocity. The analytic estmates of the water column trajecories in this case are accurate though the angular momentum evolution is nonlinear even for uniform wind- stress. Further extensions to the wind-driven transport on the continental shelf, where the bottom slope provides the counterpart of the $\beta$ effect, can be similarly developed.               

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
The Dynamics of Planetary-scale Fluid Flows (Thematic Programme)
Adrian Constantin (U of Vienna)
David Dritschel (U of St Andrews)
Nathan Paldor (HU of Jerusalem)