Note on Coriolis-Stokes force and energy

Broström, Göran; Christensen, Kai Håkon; Drivdal, Magnus; Weber, Jan Erik H.

doi:10.1007/s10236-014-0723-8

Cited by 16 publications

(11 citation statements)

References 26 publications

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“…On the other hand, Broström et al . [] concludes that the CS force will not provide any direct energy input for the vertically integrated system when the effect of the moving surface is taken into account. We here perform a more complete analysis of the vertically integrated energy in the presence of periodic surface waves, and derive an exact equation for the rate of change of the total average energy density in the fluid.…”

Section: Introductionmentioning

confidence: 99%

Some aspects of the Coriolis‐Stokes forcing in the oceanic momentum and energy budgets

et al. 2015

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The Coriolis‐Stokes (CS) force is a wave‐induced forcing of the Eulerian mean motion in a rotating ocean. For idealized conditions, it is demonstrated by comparison with Lagrangian results that the appropriate surface boundary condition for the Eulerian mean wave‐induced flow is that of vanishing vertical shear. The Eulerian mean current derived by applying this condition plus the inviscid Stokes drift yield the Lagrangian wave‐induced drift velocity, apart from a small boundary‐layer correction. Appreciation of the importance of the CS force in the momentum balance has led to investigations of the role of the CS force in the energy budget. The present study shows that the CS force is not a source for the rate of change of the total average energy density in the fluid, when the vertical integration is performed to the moving material surface. However, results to fourth order in wave steepness confirm earlier findings that the CS force acts to change the vertically integrated Eulerian kinetic energy of the mean flow. A new interpretation relates this effect to the fact that the mean Eulerian Coriolis force performs work in acting along the motion of the Lagrangian wave‐induced mass (caused by the divergence effect) at the surface.

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Section: Introductionmentioning

confidence: 99%

Some aspects of the Coriolis‐Stokes forcing in the oceanic momentum and energy budgets

et al. 2015

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“…The effect was first presented by Hasselmann [] and has since been investigated for idealized cases by Weber [], Jenkins [], McWilliams and Restrepo [], and McWilliams and Sullivan [] among others. The force is variously known as the Stokes‐Coriolis force or the Hasselmann force depending on whether it is considered to be purely an effect of the average Coriolis force acting on a particle with a Lagrangian velocity as given by the mean currents and the waves or as a tilting of the planetary vorticity [ Polton et al ., ; Broström et al ., ]. The force does not directly modify the total mass transport but it will alter the distribution of momentum over the depth of the Ekman layer [ McWilliams and Restrepo , ; Polton , ].…”

Section: Introductionmentioning

confidence: 99%

Surface wave effects in the NEMO ocean model: Forced and coupled experiments

et al. 2015

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The NEMO general circulation ocean model is extended to incorporate three physical processes related to ocean surface waves, namely the surface stress (modified by growth and dissipation of the oceanic wavefield), the turbulent kinetic energy flux from breaking waves, and the Stokes-Coriolis force. Experiments are done with NEMO in ocean-only (forced) mode and coupled to the ECMWF atmospheric and wave models. Ocean-only integrations are forced with fields from the ERA-Interim reanalysis. All three effects are noticeable in the extratropics, but the sea-state-dependent turbulent kinetic energy flux yields by far the largest difference. This is partly because the control run has too vigorous deep mixing due to an empirical mixing term in NEMO. We investigate the relation between this ad hoc mixing and Langmuir turbulence and find that it is much more effective than the Langmuir parameterization used in NEMO. The biases in sea surface temperature as well as subsurface temperature are reduced, and the total ocean heat content exhibits a trend closer to that observed in a recent ocean reanalysis (ORAS4) when wave effects are included. Seasonal integrations of the coupled atmosphere-wave-ocean model consisting of NEMO, the wave model ECWAM, and the atmospheric model of ECMWF similarly show that the sea surface temperature biases are greatly reduced when the mixing is controlled by the sea state and properly weighted by the thickness of the uppermost level of the ocean model. These wave-related physical processes were recently implemented in the operational coupled ensemble forecast system of ECMWF.

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“…The difference in the momentum flux to waves and from waves will appear as a storage of momentum in the wave field; this is also known as the Stokes drift. On time scales longer than the rotational period, the Coriolis force will act on the waves and give rise to a force known as the Coriolis-Stokes force (e.g., Ursell, 1950;McWilliams et al, 1997;Polton et al, 2005;Broström et al, 2014). Directed at right angles to the direction of wave propagation (Northern Hemisphere), the Coriolis-Stokes force leads to an additional deflection of the current (i.e., Eulerian current), similar to the effect of the Coriolis force.…”

Section: Introductionmentioning

confidence: 99%

Wave-induced mixing and transport of buoyant particles: application to the Statfjord A oil spill

2014

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Abstract. This study focuses on how wave-current and wave-turbulence interactions modify the transport of buoyant particles in the ocean. Here the particles can represent oil droplets, plastic particles, or plankton such as fish eggs and larvae. Using the General Ocean Turbulence Model (GOTM), modified to take surface wave effects into account, we investigate how the increased mixing by wave breaking and Stokes shear production, as well as the stronger veering by the Coriolis-Stokes force, affects the drift of the particles. The energy and momentum fluxes, as well as the Stokes drift, depend on the directional wave spectrum obtained from a wave model. As a first test, the depth and velocity scales from the model are compared with analytical solutions based on a constant eddy viscosity (i.e., classical Ekman theory). Secondly, the model is applied to a case in which we investigate the oil drift after an oil spill off the west coast of Norway in 2007. During this accident the average net drift of oil was observed to be both slower and more deflected away from the wind direction than predicted by oildrift models. In this case, using wind and wave forcing from the ERA Interim archive it is shown that the wave effects are important for the resultant drift and have the potential to improve drift forecasting.

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Note on Coriolis-Stokes force and energy

Cited by 16 publications

References 26 publications

Some aspects of the Coriolis‐Stokes forcing in the oceanic momentum and energy budgets

Some aspects of the Coriolis‐Stokes forcing in the oceanic momentum and energy budgets

Surface wave effects in the NEMO ocean model: Forced and coupled experiments

Wave-induced mixing and transport of buoyant particles: application to the Statfjord A oil spill

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