Time-dependent, coupled, Ekman boundary layer solutions incorporating Stokes drift

• Published in: Dynamics of atmospheres and oceans 2004-05, Vol.37 (4), p.313-351
• Main Authors: Lewis, D.M., Belcher, S.E.
• Format: Article
• Language: English
• Subjects: Angular deflections; Dynamics of the ocean (upper and deep oceans); Earth, ocean, space; Ekman currents; Exact sciences and technology; External geophysics; Inertial oscillations; Physics of the oceans; Stokes drift; Transients
• ISSN: 0377-0265; 1872-6879
• DOI: 10.1016/j.dynatmoce.2003.11.001

Recent technological advances in current measuring devices has resulted in a large observational database related to wind-driven motions in the upper ocean mixed layer. This has served to highlight the fact that transient motions make up a substantial contribution of the resulting Ekman currents. At the same time, certain discrepancies have emerged between the observed angular deflections of the steady-state currents from the surface wind stress, both at the surface and at sub-surface depths, which cannot be reconciled using the classical Ekman model. This paper seeks to tackle these two issues. First a general analytical method is presented for solving the time dependent horizontal momentum Ekman equations. Analysis of the unsteady terms that arise from simple special cases shows how the evolution proceeds through three stages. At early times, the Coriolis acceleration is insignificant, and the current is unidirectional and deepens through downward diffusion of momentum. Later Coriolis acceleration deflects the current vectors in the upper layers, whilst downward diffusion of momentum continues to deepen the layer. Finally, once diffusion has penetrated down to the depth of the steady-state current, then the transients decay on the inertial or diffusive timescale, depending upon the boundary conditions of the particular problem. In the second half of the paper, a new steady-state model is developed that includes the effects of wind-generated waves, through the action of their Stokes drift on the planetary vorticity. Comparisons between observations and the theoretical predictions, demonstrate that inclusion of the Stokes drift is the key to reconciling the discrepancies in the angular deflections of the steady-state currents. This leads to the conclusion that Ekman layer currents are significantly influenced by the surface waves.