Surface shear stress dependence of gas transfer velocity parameterizations using DNS

Abstract

Air‐water gas‐exchange is studied in direct numerical simulations (DNS) of free‐surface flows driven by natural convection and weak winds. The wind is modeled as a constant surface‐shear‐stress and the gas‐transfer is modeled via a passive scalar. The simulations are characterized via a Richardson number Ri=Bν/u*4 where B, ν, and u* are the buoyancy flux, kinematic viscosity, and friction velocity respectively. The simulations comprise 0<Ri<∞ ranging from convection‐dominated to shear‐dominated cases. The results are used to: (i) evaluate parameterizations of the air‐water gas‐exchange, (ii) determine, for a given buoyancy flux, the wind speed at which gas transfer becomes primarily shear driven, and (iii) find an expression for the gas‐transfer velocity for flows driven by both convection and shear. The evaluated gas transfer‐velocity parametrizations are based on either the rate of turbulent kinetic energy dissipation, the surface flow‐divergence, the surface heat‐flux, or the wind‐speed. The parametrizations based on dissipation or divergence show an unfavorable Ri dependence for flows with combined forcing whereas the parametrization based on heat‐flux only shows a limited Ri dependence. The two parametrizations based on wind speed give reasonable estimates for the transfer‐velocity, depending however on the surface heat‐flux. The transition from convection‐ to shear‐dominated gas‐transfer‐velocity is shown to be at Ri≈0.004. Furthermore, the gas‐transfer is shown to be well represented by two different approaches: (i) additive forcing expressed as kg,sum=AShearu*|Ri/Ric+11/4Sc−n where Ric=AShear/ABuoy4, and (ii) either buoyancy or shear dominated expressed as, kg=ABuoy|Bν1/4Sc−n, Ri>Ric or kg=Ashearu*Sc−n, Ri<Ric. Here ABuoy=0.4 and AShear=0.1 are constants, and n is an exponent that depends on the water surface‐characteristics.

Turbulence in a small arctic pond

“…At winds above 2.5 m s −1 , both followed the regression equation under heating in MacIntyre et al (). At low winds, our predictions are similar to those of Fredriksson et al ( a ) and Heiskanen et al (). Fredriksson et al ( a ) predict that convection will combine with shear leading to higher values of k 600 than from shear alone when a Richardson number, defined as Ri = βν / , exceeds 0.004.…”

“…b). Our averaged k 600 were similar to predictions in the modeling by Fredriksson et al ( a ) who included shear and convection in their direct numerical simulations. These processes dominate turbulence production in small ponds with reduced influence of surface waves.…”

“…The contribution of cooling to near surface turbulence has been the subject of numerous papers, with its contribution quantified by the turbulent velocity scale from cooling, w * , obtained from the buoyancy flux (Imberger ; MacIntyre et al ; Read et al ) or from buoyancy flux directly (Tedford et al ; Fredriksson et al a , b ). Values of u * w , the water friction velocity, and w * both tended to be low and comparable in magnitude, ∼ 0.002 m s −1 , for much of the study (data not shown).…”

Using eddy covariance to measure the dependence of air–sea CO&lt;sub&gt;2&lt;/sub&gt; exchange rate on friction velocity

“…(10) slightly underestimates the wind-speed binned data for u 10 N < 5 m s −1 and would predict negative k 660 for u * ≤ 0.07 m s −1 (u 10 N ≤ 2.3 m s −1 ). However, since our estimations of the Richardson number (Ri = B 0,w ν w u −4 * ,w ) remained below the critical value of Ri ≈ 0.004, which was suggested by Fredriksson et al (2016), we do not expect significant contribution of buoyancy-driven processes to the gas exchange rates observed during SOAP. Here, B 0,w , ν w , and u * ,w are the water-side surface buoyancy flux, kinematic viscosity of sea water, and water-side friction velocity, respec- .…”

“…Extrapolation of this linear k vs. EC u * relationship outside of the wind-speed range of the SOAP data set is not recommended, because there are physical reasons why this relationship might not hold. At lower wind speeds, buoyancy-driven processes may contribute significantly to gas transfer (Soloviev, 2007;Fredriksson et al, 2016). In fact, Eq.…”