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  • Author or Editor: Øyvind Saetra x
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Arne Melsom
and
Øyvind SÆtra

Abstract

A theoretical model for the near-surface velocity profile in the presence of breaking waves is presented. Momentum is accumulated by growing waves and is released upon wave breaking. In effect, such a transition is a process involving a time-dependent surface stress acting on the mean current. In this paper, conventional theory for the Stokes drift is expanded to fourth-order accuracy in wave steepness. It is shown that the higher-order terms lead to an enhancement of the surface Stokes drift and a slight retardation of the Stokes volume flux. Furthermore, the results from the wave theory are used to obtain a bulk parameterization of momentum exchange during the process of wave breaking. The mean currents are then obtained by application of a variation of the “level 2.5” turbulence closure theory of Mellor and Yamada. When compared with the traditional approach of a constant surface stress, the mean Eulerian current exhibits a weak enhancement in the near-surface region, compensated by a negative shift deeper in the water column. However, it is found that the results of Craig and Banner and the results of Craig are not significantly affected by the present theory. Hence, this study helps to explain why the Craig and Banner model agrees well with observations when a realistic, time-varying surface stress acts on the drift currents.

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Arne Melsom
and
Øyvind SÆtra

Abstract

A theoretical model for the near-surface velocity profile in the presence of breaking waves is presented. Momentum is accumulated by growing waves and is released upon wave breaking. In effect, such a transition is a process involving a time-dependent surface stress acting on the mean current. In this paper, conventional theory for the Stokes drift is expanded to fourth-order accuracy in wave steepness. It is shown that the higher-order terms lead to an enhancement of the surface Stokes drift and a slight retardation of the Stokes volume flux. Furthermore, the results from the wave theory are used to obtain a bulk parameterization of momentum exchange during the process of wave breaking. The mean currents are then obtained by application of a variation of the “level 2.5” turbulence closure theory of Mellor and Yamada. When compared with the traditional approach of a constant surface stress, the mean Eulerian current exhibits a weak enhancement in the near-surface region, compensated by a negative shift deeper in the water column. However, it is found that the results of Craig and Banner and the results of Craig are not significantly affected by the present theory. Hence, this study helps to explain why the Craig and Banner model agrees well with observations when a realistic, time-varying surface stress acts on the drift currents.

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Øyvind Saetra
,
Trygve Halsne
,
Ana Carrasco
,
Øyvind Breivik
,
Torstein Pedersen
, and
Kai Håkon Christensen

Abstract

The Lofoten Maelstrom has been known for centuries as one of the strongest open-ocean tidal currents in the world, estimated to reach 3 m s−1, and by some estimates as much as 5 m s−1. The strong current gives rise to choppy seas when waves enter the Moskenes Sound, making the area extremely difficult to navigate. Despite its reputation, few studies of its strength exist, and no stationary in situ measurements for longer time periods have been made due to the challenging conditions. By deploying for the first time in situ wave and current instruments, we confirm some previous estimates of the strength of the current. We also show that its strength is strongly connected with wave breaking. From a consideration of specific forcing terms in the dynamical energy balance equation for waves on a variable current, we assess the impact of the underlying current using a convenient metric formulated as a function of the horizontal current gradients. We find that the horizontal gradients are a likely explanation for the observed enhanced wave breaking during strong currents at a rising tide.

Open access
Øyvind Saetra
,
Jon Albretsen
, and
Peter A. E. M. Janssen

Abstract

The impact of wave-dependent surface stress on the ocean circulation has been studied using surface stresses calculated from a numerical wave model. The main questions to be investigated were what the effect would be on the Ekman currents in the upper ocean and what the impact would be on storm surge predictions. To answer the first question, the response of wave-dependent forcing on an Ekman type of model was studied. Here, the wave forcing was provided by a one-gridpoint version of the wave model. Second, the impact of the waves was studied with a three-dimensional ocean circulation model for the North Sea. Three different experiments were performed for a period of 1 yr. To test the effect on the storm surge signal, the results have been compared with sea level observations from 22 stations along the Norwegian and Dutch coasts. One of the main findings is that calculating stresses in the wave model, thereby introducing sea-state-dependent momentum fluxes, has a strong positive impact on the storm surge modeling compared with applying a traditional parameterization of surface stresses from the 10-m wind speed. When all cases with sea level deviation from the mean of less than 0.5 m were removed, the root-mean-square error for 1 yr averaged over all stations was reduced by approximately 6 cm. Splitting the momentum budget into an Eulerian and a wave part (Stokes drift) has only a negligible effect on the modeling of the sea surface elevation but increases the angular turning of the Eulerian surface drift to the right of the wind direction with an angle of about 4°.

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Jan Erik H. Weber
,
Göran Broström
, and
Øyvind Saetra

Abstract

It is demonstrated that the Eulerian and the Lagrangian descriptions of fluid motion yield the same form for the mean wave-induced volume fluxes in the surface layer of a viscous rotating ocean. In the Eulerian case, the volume fluxes are obtained in the familiar way by integrating the horizontal components of the Navier–Stokes equation in the vertical direction, as seen, for example, in the book by Phillips. In the direct Lagrangian approach, the perturbation equations for the second-order mean drift are integrated in the vertical direction. This yields the advantage that the form drag, which is a source term for the wave-induced transports, can be related to the virtual wave stress that acts to transfer dissipated mean wave momentum into mean currents. In particular, for waves that are periodic in space and time, comparisons between empirical and theoretical relations for the form drag yield an estimate for the wave-induced bulk turbulent eddy viscosity in the surface layer. A simplistic approach extends this analysis to account for wave breaking. By a generalization from a wave component to a wave spectrum, a set of equations for the wave-induced transport in the surface layer is derived for a fully developed sea. Solutions are discussed for an idealized spectral formulation. The problem is formulated such that a numerical wave prediction model can be used to generate the wave-forcing terms in a numerical barotropic ocean surge model. Results from the numerical simulations with a wave-influenced surge model are discussed and compared with similar results from forcing the surge model only by the traditional mean horizontal wind stress computed from the 10-m wind speed. For the simulations presented here, the wave-induced stress constitutes about 50% of the total atmospheric stress for moderate to strong winds.

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