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

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.

Modeling the Effect of Waves on the Diurnal Temperature Stratification of a Shallow Lake

“…The well-known two-equation MellorYamada 2.5 turbulence closure model was extended by the appropriate terms according to the analyzed schemes. The main difference between the schemes is whether we introduce TKE into the water column via the production term in the TKE transport equation [19,40] or we enhance vertical mixing through the direct increase of eddy viscosity and turbulent diffusivity based on the wave spectrum [12,20]. In the latter case eddy viscosity is strengthened without regard to TKE production and destruction.…”

“…As to non-breaking waves, it has been shown experimentally and theoretically that they introduce turbulent mixing due to their orbital motion [11,17,18,19]. This action is less intensive that of breaking waves but it occurs more frequently and penetrates deeper, so it also warrants attention.…”

“…Pleskachevsky et al [14] argue that these two additional terms (B v and P wave ) have to be incorporated simultaneously, while Ghantous and Babanin [19] opined that this is wrong: there should be no need to invoke any explicit addition to turbulent viscosity with an explicit production term because the effect of wave-induced turbulence would be counted twice. According to Kantha and Clayson [10], in addition to a TKE production term, the recalibration of the empirical turbulence closure constants should be the other possibility to improve the modeling of mixing due to non-breaking waves.…”

“…For example the spatial distribution of the Stokes drift field depends on the shape of wave spectrum [24]. If the wave spectrum is narrow enough bulk parameters can indeed characterize the effect of the irregular wave motion with sufficient accuracy, as opposed to deriving turbulent mixing and shear production from the spectrum [19]. In the absence of a wave spectrum (modeled or measured), many researchers successfully applied mixing parametrizations based on bulk characteristic [14,23] but it has to be underlined that several studies reported that model results improve significantly by using a 2D spectral wave model since wave mixing can be overestimated by bulk parametrizations [25,26].…”

“…According to Kantha and Clayson [10], in addition to a TKE production term, the recalibration of the empirical turbulence closure constants should be the other possibility to improve the modeling of mixing due to non-breaking waves. It is important to note that in many numerical experiments the effect of P wave was moderate and the direct increase of eddy viscosity with B v lead to better results [19].…”