An evaluation of gas transfer velocity parameterizations during natural convection using DNS

Abstract

Direct numerical simulations (DNS) of free surface flows driven by natural convection are used to evaluate different methods of estimating air‐water gas exchange at no‐wind conditions. These methods estimate the transfer velocity as a function of either the horizontal flow divergence at the surface, the turbulent kinetic energy dissipation beneath the surface, the heat flux through the surface, or the wind speed above the surface. The gas transfer is modeled via a passive scalar. The Schmidt number dependence is studied for Schmidt numbers of 7, 150 and 600. The methods using divergence, dissipation and heat flux estimate the transfer velocity well for a range of varying surface heat flux values, and domain depths. The two evaluated empirical methods using wind (in the limit of no wind) give reasonable estimates of the transfer velocity, depending however on the surface heat flux and surfactant saturation. The transfer velocity is shown to be well represented by the expression, ks=A |Bν1/4 Sc−n, where A is a constant, B is the buoyancy flux, ν is the kinematic viscosity, Sc is the Schmidt number, and the exponent n depends on the water surface characteristics. The results suggest that A=0.39 and n≈1/2 and n≈2/3 for slip and no‐slip boundary conditions at the surface, respectively. It is further shown that slip and no‐slip boundary conditions predict the heat transfer velocity corresponding to the limits of clean and highly surfactant contaminated surfaces, respectively.

Turbulence in a small arctic pond

“…For the deeper mixing, w rms / w * and u rms / w * equaled 0.3 and 0.1 and for the shallower mixing depth, the ratios were 0.5 and 0.2, respectively. Fredriksson et al ( b ) obtained 0.6 and 0.3, respectively at depths within 20–80% of the surface, depths which encompass our measurements. Following Chou et al (), at our measurement depths and h = 0.4 m, w rms / w * = 0.7, similar to Fredriksson et al ( b ).…”

“…Fredriksson et al (2016b) obtained 0.6 and 0.3, respectively at depths within 20-80% of the surface, depths which encompass our measurements. Following Chou et al (1986), at our measurement depths and h 5 0.4 m, w rms /w * 5 0.7, similar to Fredriksson et al (2016b). Lenschow et al (1980), reported in Chou et al (1986), obtained w rms /w * 5 0.5, through much of the actively mixing layer during penetrative convection.…”

A Structure Function Model Recovers the Many Formulations for Air‐Water Gas Transfer Velocity

“…which is identical to equation (4) when c s = √ 2∕(15 1∕4 ) ≈ 0.7. This estimate is in acceptable agreement with the recent DNS studies reported by Fredriksson et al (2016), where c s = 0.57 was determined from fitting to DNS using surface state variables. It also agrees with estimates by Ledwell (1984) In what follows, the k L = [ D ww (r) ] 1∕2 interpretation is still employed.…”

“…Another multisite study reported a 0.39 < < 0.43 (Vachon et al, 2010) and noted the sensitivity of their inferred to the method and depth used when estimating . Also, the predicted here agrees with recent DNS analysis (Fredriksson et al, 2016) estimating an = 0.39 for the free slip case at the air-water interface. The original work of Lamont and Scott (1970) also reported an = 0.4.…”

“…Equation agrees with predictions from a surface renewal model (Soloviev & Schlüssel, ) that assumes the mean renewal time is proportional to ν ( α T g q o ) −1/2 (Foster, ). Moreover, equation is in agreement with DNS runs (Fredriksson et al, ) that reported an expression, given by that fits their free convective runs.…”