One-dimensional modelling of upper ocean mixing by turbulence due to wave orbital motion

M Ghantous,A V Babanin

doi:10.5194/npg-21-325-2014

M Ghantous, A V Babanin

Open Access

https://doi.org/10.5194/npg-21-325-2014

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Abstract

Abstract. Mixing of the upper ocean affects the sea surface temperature by bringing deeper, colder water to the surface. Because even small changes in the surface temperature can have a large impact on weather and climate, accurately determining the rate of mixing is of central importance for forecasting. Although there are several mixing mechanisms, one that has until recently been overlooked is the effect of turbulence generated by non-breaking, wind-generated surface waves. Lately there has been a lot of interest in introducing this mechanism into ocean mixing models, and real gains have been made in terms of increased fidelity to observational data. However, our knowledge of the mechanism is still incomplete. We indicate areas where we believe the existing parameterisations need refinement and propose an alternative one. We use two of the parameterisations to demonstrate the effect on the mixed layer of wave-induced turbulence by applying them to a one-dimensional mixing model and a stable temperature profile. Our modelling experiment suggests a strong effect on sea surface temperature due to non-breaking wave-induced turbulent mixing.

Highlights

For many applications ocean waves can be adequately modelled using potential wave theory, meaning the water is presumed inviscid, incompressible and the motion adiabatic
Several approaches to parameterising non-breaking waveinduced mixing in numerical models have already been tried, and they have all been successfully used to improve model results. They fall into three broad categories: those that attempt to parameterise Langmuir circulation; those that are scaled with wind stress; and those that, like the present one, are based on the notion that a fundamental property of the wave orbital motion is capable of generating turbulence which can lead to mixing
While there are several different approaches available to modellers wishing to incorporate the effect of non-breaking wave-induced turbulence in their forecasting models, on closer inspection several of these cannot deal with situations of zero wind stress and here, in the context of wave-only mixing, had to be discarded from consideration

Summary

Introduction

For many applications ocean waves can be adequately modelled using potential wave theory, meaning the water is presumed inviscid, incompressible and the motion adiabatic. The wave orbital motion, which in potential theory is irrotational, is often presumed incapable of producing turbulence, and unable to contribute to ocean mixing. (A recent paper by Beyá et al, 2012 argued, based on experiments they carried out, that the deviations from irrotational motion are entirely negligible. We discuss this paper in Appendix B.) Yet real waves by definition do produce vorticity (for example Kinsman, 1965; Landau and Lifshitz, 1987), and it may be shown that even potential waves can, by stressing vortex lines, amplify pre-existing vorticity (Phillips, 1961; Kinsman, 1965; Benilov et al, 1993). Despite the encouraging results the existing approaches are in large part guesses, undeniably useful though they are, and a parameterisation based on the underlying physical principles is still needed

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