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

185

265

The interaction between the Coriolis force and the Stokes drift associated with ocean surface waves leads to a vertical transport of momentum, which can be expressed as a force on the mean momentum equation in the direction along wave crests. We investigate how this Coriolis-Stokes forcing affects the mean current profile in a wind-driven mixed layer, using simple models, results from large eddy simulations and observational data.The effects of the Coriolis-Stokes forcing on the mean current profile is examined by re-appraising analytical solutions to the Ekman model that include the Coriolis-Stokes forcing. Turbulent momentum transfer is modelled using an eddy viscosity model, first with a constant viscosity, and second with a linearly varying eddy viscosity. Although the Coriolis-Stokes forcing penetrates only a small fraction of the depth of the wind-driven layer for parameter values typical of the ocean, the analytical solutions show how the current profile is substantially changed through the whole depth of the wind-driven layer. We show how, for this oceanic regime, the Coriolis-Stokes forcing supports a fraction of the applied wind stress, changing the boundary condition on the wind-driven component of the flow, and hence changing the current profile through all depths.The analytical solution with the linearly varying eddy viscosity is shown to reproduce reasonably well the effects of the Coriolis-Stokes forcing on the current profile computed from large eddy simulations, which resolve the three-dimensional overturning motions associated with the turbulent Langmuir circulations in the wind-driven layer. Finally, the analytical solution with the Coriolis-Stokes forcing is shown to agree reasonably well with current profiles from historical observational data and certainly agrees much better than the 1 standard Ekman model. This finding provides compelling evidence that the Coriolis-Stokes forcing is an important mechanism in controlling the dynamics of the upper ocean.2

“…Thirdly, the current speed is rapidly attenuated with depth. The Ekman model cannot explain all these observed features (Lewis and Belcher 2003).…”

Section: Introductionmentioning

confidence: 99%

Section: Evidence For Effects Of Coriolis-stokes Forcing In Observatimentioning

confidence: 99%

The Role of Wave-Induced Coriolis–Stokes Forcing on the Wind-Driven Mixed Layer

Polton

Lewis

Belcher

2005

185

265

“…The study done by Lewis and Belcher (2003) demonstrates that the inclusion of the Stokes drift is the key to reconciling the discrepancies in the angular deflections of the steady-state currents. Polton et al (2005) also found that the surface current direction is affected by the presence of ocean waves.…”

Section: Introductionmentioning

confidence: 99%

The Influence of Fetch on the Response of Surface Currents to Wind Studied by HF Ocean Surface Radar

Mao

Heron

2008

The momentum transfer from wind to sea generates surface currents through both the wind shear stress and the Stokes drift induced by waves. This paper addresses issues in the interpretation of HF radar measurements of surface currents and momentum transfer from air to sea. Surface current data over a 30-day period from HF ocean surface radar are used to study the response of surface currents to wind. Two periods of relatively constant wind are identified-one for the short-fetch condition and the other for the long-fetch condition. Results suggest that the ratio of surface current speed to wind speed is larger under the long-fetch condition, while the angle between the surface current vector and wind vector is larger under the short-fetch condition. Data analysis shows that the Stokes drift dominates the surface currents under the long-fetch condition when the sea state is more mature, while the Stokes drifts and Ekman-type currents play almost equally important roles in the total currents under the short-fetch condition. The ratios of Stokes drift to wind speed under these two fetch conditions are shown to agree well with results derived from the empirical wave growth function. These results suggest that fetch, and therefore sea state, significantly influences the total response of surface current to wind in both the magnitude and direction by variations in the significance of Stokes drift. Furthermore, this work provides observational evidence that surface currents measured by HF radar include Stokes drift. It demonstrates the potential of HF radar in addressing the issue of momentum transfer from air to sea under various environmental conditions.

“…forcing (Polton et al 2005), eastward velocity displacement (Heinloo and Toompuu 2012), more complex eddy viscosity profiles (Madsen 1977;Lewis and Belcher 2004;Zikanov et al 2003;Polton et al 2005;McWilliams and Huckle 2006;McWilliams et al 2012), or frequencydependent effects (Elipot and Gille 2009). However, we demonstrate that the associated increase in complexity is not necessarily justified given the (quantified) uncertainty in these data.…”

Section: Discussionmentioning

confidence: 46%

Can Drake Passage Observations Match Ekman's Classic Theory?

Polton

Lenn

Elipot

et al. 2013

Ekman's theory of the wind-driven ocean surface boundary layer assumes a constant eddy viscosity and predicts that the current rotates with depth at the same rate as it decays in amplitude. Despite its wide acceptance, Ekman current spirals are difficult to observe. This is primarily because the spirals are small signals that are easily masked by ocean variability and cannot readily be separated from the geostrophic component. This study presents a method for estimating ageostrophic currents from shipboard acoustic Doppler current profiler data in Drake Passage and finds that observations are consistent with Ekman's theory. By taking into account the sampling distributions of wind stress and ageostrophic velocity, the authors find eddy viscosity values in the range of 0.08-0.12 m 2 s 21 that reconcile observations with the classic theory in Drake Passage. The eddy viscosity value that most frequently reconciles observations with the classic theory is 0.094 m 2 s 21, corresponding to an Ekman depth scale of 39 m.