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Indirect air–sea interactions simulated with a coupled turbulence-resolving model

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Abstract

A turbulence-resolving parallelized atmospheric large-eddy simulation model (PALM) has been applied to study turbulent interactions between the humid atmospheric boundary layer (ABL) and the salt water oceanic mixed layer (OML). The most energetic three-dimensional turbulent eddies in the ABL–OML system (convective cells) were explicitly resolved in these simulations. This study considers a case of shear-free convection in the coupled ABL–OML system. The ABL–OML coupling scheme used the turbulent fluxes at the bottom of the ABL as upper boundary conditions for the OML and the sea surface temperature at the top of the OML as lower boundary conditions for the ABL. The analysis of the numerical experiment confirms that the ABL–OML interactions involve both the traditional direct coupling mechanism and much less studied indirect coupling mechanism (Garrett Dyn Atmos Ocean 23:19–34, 1996). The direct coupling refers to a common flux-gradient representation of the air–sea exchange, which is controlled by the temperature difference across the air–water interface. The indirect coupling refers to thermal instability of the Rayleigh–Benard convection, which is controlled by the temperature difference across the entire mixed layer through formation of the large convective eddies or cells. The indirect coupling mechanism in these simulations explained up to 45 % of the ABL–OML co-variability on the turbulent scales. Despite relatively small amplitude of the sea surface temperature fluctuations, persistence of the OML cells organizes the ABL convective cells. Water downdrafts in the OML cells tend to be collocated with air updrafts in the ABL cells. The study concludes that the convective structures in the ABL and the OML are co-organized. The OML convection controls the air–sea turbulent exchange in the quasi-equilibrium convective ABL–OML system.

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Abbreviations

c pa  = 1, 005 [J kg−1 K−1]:

specific heat capacity of air

c pw  = 4, 218 [J kg−1 K−1]:

specific heat capacity of water

L e  = 2,262.6108 103 [J kg−1]:

latent heat of evaporation

g = 9.81 [m s−2]:

gravity acceleration

ρ a  = 1.0 [kg m−3]:

density of air (stipulated)

ρ w   [kg m−3]:

potential density of sea water (calculated after Jackett et al. 2006)

θ va [K]:

virtual potential temperature of air

q [kg kg−1]:

absolute humidity of air

θ w [K]:

temperature of water

s [psu]:

water salinity

\( {\overrightarrow{u}}_a={u}_{ia}=\left({u}_a,{v}_a,{w}_a\right) \) [m s−1]:

velocity of air (zonal, meridional, and vertical components)

\( {\overrightarrow{u}}_w \) [m s−1]:

velocity of water

\( {u}_{*}={\left(\frac{\left|{\tau}_{ia}\right|}{\rho_a}\right)}^{1/2}={\left(\frac{\left|{\tau}_{iw}\right|}{\rho_w}\right)}^{1/2} \) [m s−1]:

surface friction velocity

\( {\tau}_{ia}={\rho}_a{\left({\left(\overline{u{\prime}_aw{\prime}_a},\kern0.5em \right)}^2+{\left(\overline{v{\prime}_aw{\prime}_a},\kern0.5em \right)}^2\right)}^{1/2} \) [kg s−2 m−1]:

vertical turbulent momentum flux in air; it is calculated at the ABL bottom boundary using the Monin–Obukhov relationships

\( {\tau}_{iw}={\rho}_w{\left({\left(\overline{u{\prime}_ww{\prime}_w}\right)}^2+{\left(\overline{v{\prime}_ww{\prime}_w}\right)}^2\right)}^{1/2} \) [kg s−2 m−1]:

vertical turbulent momentum flux in water; it is passed to the OML from the ABL as the boundary condition

F a  = F Sa  + F La [W m−2]:

total turbulent heat flux in air it is calculated at the ABL bottom boundary using the Monin–Obukhov relationships

\( {F}_{Sa}={\rho}_a{c}_{pa}\overline{w{\prime}_a\theta {\prime}_a} \) [W m−2]:

sensible heat flux in air

\( {F}_{La}={\rho}_a{L}_e\overline{w{\prime}_aq{\prime}_a} \) [W m−2]:

latent heat flux (ABL)

\( {F}_w={\rho}_w{c}_{pw}\overline{w{\prime}_w\theta {\prime}_w}\kern0.5em ={F}_a \) [W m−2]:

total turbulent heat flux in water; it is passed to the OML from the ABL as the boundary condition

\( B=-\frac{ g\alpha}{c_{pw}{\rho}_w}{F}_a+ g\beta s{\rho}_w\overline{w{\prime}_aq{\prime}_a} \) [W kg−1]:

buoyancy flux at the ABL–OML interface

\( \alpha =-\frac{1}{\rho}\frac{\partial \rho }{\partial \theta } \) [K−1]:

thermal expansion coefficient (α = 0.03 in air)

\( \beta =\frac{1}{\rho}\frac{\partial \rho }{\partial S} \) [psu−1]:

haline contraction coefficient

L = − u 3* /kF Sa ρ a c pa L = − u 3* /kF Sa ρ a c pa :

the Monin–Obukhov length scale in the ABL

k = 0.4:

Von Karman constant

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Acknowledgements

This study was supported by the Norwegian Centre for Climate Dynamics (SKD), the Norway-Russia bilateral project CLIMARC and the European Research Council Advanced Grant PBL-PMES n227915. The author is grateful to Prof. S. Raash, Dr. B. Maronga, and Dr. M. Letzel for their help with the model development, set up, runs and discussions. The Norwegian Metacenter for Computational Science (NOTUR), accounts nn2343k and nn2993k, provided the computational infrastructure for this study.

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  1. Nansen Environmental and Remote Sensing Centre/Bjerknes Centre for Climate Research, Thormohlensgt. 47, 5006, Bergen, Norway

    Igor Esau

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Correspondence to Igor Esau.

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Responsible Editor: Richard John Greatbatch

This article is part of the Topical Collection on the 5th International Workshop on Modelling the Ocean (IWMO) in Bergen, Norway 17–20 June 2013

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Esau, I. Indirect air–sea interactions simulated with a coupled turbulence-resolving model. Ocean Dynamics 64, 689–705 (2014). https://doi.org/10.1007/s10236-014-0712-y

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