Performance of two-equation turbulence closures in three-dimensional simulations of the Red Sea overflow

Mehmet Ilicak, Tamay M Ozgokmen, Hartmut Peters, Helmut Z. Baumert, Mohamed Iskandarani

Research output: Contribution to journalArticle

42 Citations (Scopus)

Abstract

Mixing of overflows released from polar and marginal seas is a key process shaping the structure of the meridional overturning circulation. Ocean general circulation models have difficulty in resolving the overflows, and therefore they must rely on parameterizations. In this study, the performance of a set of turbulence closures in reproducing mixing of an overflow is quantified. We simulate the Red Sea overflow by employing standard k-ε, k-ω and Mellor-Yamada schemes with various stability functions, as well as a modified k-ε model that relies on the prescription of the turbulent Prandtl number rather than on stability functions. The simpler KPP mixing scheme and experiments without turbulent fluxes serve as useful references. To our knowledge, this is the first time that the performance of two-equation turbulence models has been examined so closely using data from an overflow. It is found that without turbulence closures, the hydrodynamic model has difficulty in reproducing the correct three-dimensional pathway of the Red Sea overflow, consisting of a distinct bifurcation into two diverging channels. All turbulence models capture the vertical structure of this overflow consisting of an interfacial layer, characterized by the density gradient, and a well-mixed bottom layer. Mean eddy diffusivity values from most closures are comparable those from observations. But we find that KPP leads to eddy diffusivity values that are too small while those from Mellor-Yamada with Galperin [Galperin, B., Kantha, L.H., Hassid, S., Rosati, A., 1988. A quasi-equilibrium turbulent energy model for geophysical flows. J. Atmos. Sci. 45, 55-62] stability functions are too large. Such high diffusivities lead to excessive mixing in the bottom layer of the overflow, ultimately resulting in a salinity deficit of approximately 1 psu in the product water mass. Salinity deviations between the models and observations are quantified using both data taken along the channels and two sections across the overflow. KPP and Mellor-Yamada with Galperin (1988) stability functions produce the largest deviations from the observations, while the modified k-ε exhibits the smallest deviations. The other four closures fall in between, showing results similar to one another. The performance of the Mellor-Yamada turbulence closure is improved considerably by using the stability functions by Kantha and Clayson [Kantha, L.H., Clayson, C.A., 1994. An improved mixed layer model for geophysical applications. J. Geophys. Res. 99 (December), 25235-25266], which allow for a stationary Richardson number of 0.21. In conclusion, we find that most turbulence closures lead to a satisfactory reproduction of the Red Sea overflow, within the temporal and spatial sampling uncertainties of the REDSOX data, provided that fairly high-resolution regional models are used.

Original languageEnglish (US)
Pages (from-to)122-139
Number of pages18
JournalOcean Modelling
Volume24
Issue number3-4
DOIs
StatePublished - 2008

Fingerprint

Turbulence
turbulence
simulation
diffusivity
Turbulence models
eddy
Bifurcation (mathematics)
salinity
Prandtl number
marginal sea
Richardson number
Parameterization
sea
meridional circulation
bifurcation
water mass
mixed layer
Hydrodynamics
general circulation model
parameterization

Keywords

  • k-ε
  • k-ω
  • Mixing
  • Red Sea overflow
  • Two-equation turbulence model

ASJC Scopus subject areas

  • Atmospheric Science
  • Oceanography
  • Geotechnical Engineering and Engineering Geology
  • Computer Science (miscellaneous)

Cite this

Performance of two-equation turbulence closures in three-dimensional simulations of the Red Sea overflow. / Ilicak, Mehmet; Ozgokmen, Tamay M; Peters, Hartmut; Baumert, Helmut Z.; Iskandarani, Mohamed.

In: Ocean Modelling, Vol. 24, No. 3-4, 2008, p. 122-139.

Research output: Contribution to journalArticle

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AU - Iskandarani, Mohamed

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AB - Mixing of overflows released from polar and marginal seas is a key process shaping the structure of the meridional overturning circulation. Ocean general circulation models have difficulty in resolving the overflows, and therefore they must rely on parameterizations. In this study, the performance of a set of turbulence closures in reproducing mixing of an overflow is quantified. We simulate the Red Sea overflow by employing standard k-ε, k-ω and Mellor-Yamada schemes with various stability functions, as well as a modified k-ε model that relies on the prescription of the turbulent Prandtl number rather than on stability functions. The simpler KPP mixing scheme and experiments without turbulent fluxes serve as useful references. To our knowledge, this is the first time that the performance of two-equation turbulence models has been examined so closely using data from an overflow. It is found that without turbulence closures, the hydrodynamic model has difficulty in reproducing the correct three-dimensional pathway of the Red Sea overflow, consisting of a distinct bifurcation into two diverging channels. All turbulence models capture the vertical structure of this overflow consisting of an interfacial layer, characterized by the density gradient, and a well-mixed bottom layer. Mean eddy diffusivity values from most closures are comparable those from observations. But we find that KPP leads to eddy diffusivity values that are too small while those from Mellor-Yamada with Galperin [Galperin, B., Kantha, L.H., Hassid, S., Rosati, A., 1988. A quasi-equilibrium turbulent energy model for geophysical flows. J. Atmos. Sci. 45, 55-62] stability functions are too large. Such high diffusivities lead to excessive mixing in the bottom layer of the overflow, ultimately resulting in a salinity deficit of approximately 1 psu in the product water mass. Salinity deviations between the models and observations are quantified using both data taken along the channels and two sections across the overflow. KPP and Mellor-Yamada with Galperin (1988) stability functions produce the largest deviations from the observations, while the modified k-ε exhibits the smallest deviations. The other four closures fall in between, showing results similar to one another. The performance of the Mellor-Yamada turbulence closure is improved considerably by using the stability functions by Kantha and Clayson [Kantha, L.H., Clayson, C.A., 1994. An improved mixed layer model for geophysical applications. J. Geophys. Res. 99 (December), 25235-25266], which allow for a stationary Richardson number of 0.21. In conclusion, we find that most turbulence closures lead to a satisfactory reproduction of the Red Sea overflow, within the temporal and spatial sampling uncertainties of the REDSOX data, provided that fairly high-resolution regional models are used.

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