Surface age of surface renewal in turbulent interfacial transport

Abstract

[1] We use direct numerical simulation to study characteristics of interfacial transfer of gas and heat in free-surface turbulence. Using Lagrangian tracing, we are able to directly quantify surface age of surface renewal for the first time. The physical meaning of surface renewal and various representations of surface age, including the use of heat as a proxy, are discussed. Results show that the Higbie penetration theory and the Danckwerts random surface renewal model are inappropriate for gas transfer. [2] Surface renewal is a critical process in turbulent interfacial transport that is important to many applications including sea surface temperature and atmosphere -ocean gas transfer. Scalar transport in the upper ocean is governed by the interplay of molecular diffusion at the sea surface and turbulent mixing underneath. When a surface renewal occurs, fluid is brought from the bulk towards the surface, the scalar is highly mixed, and the gradient of scalar concentration is increased at the surface to enhance interfacial diffusion.[3] An influential model of surface renewal is the penetration theory of Higbie [1935], which stated that the surface is intermittently exposed to turbulent upwelling flows. The turbulent mixing process was considered instant, with the scalar well mixed. After this surface renewal, molecular diffusion was assumed to dominate in the scalar boundary layer till the next surface renewal is generated by the turbulence below. Take gas as an example. Its concentration c is governed by the diffusion equation:2 ). Here D is the molecular diffusivity and z is the vertical coordinate. Subject to the boundary conditions at the surface c(z = 0, t) = c 0 and in the deep region c(z = À1, t) = c bulk , and the initial condition c(z, t = 0) = c bulk , the gas flux at the surface q g obtains asIn the above, the time elapsed since the surface renewal is called the surface age t.[4] Danckwerts [1951] elaborated the penetration theory in his random surface renewal model by assuming that the chance of a surface element being renewed by fresh fluid from the bulk flow is independent of its surface age. Therefore, the probability density function (pdf) of the surface age governed by dp(t)/dt = Às p(t), where p is the pdf and s is the fractional rate of surface elements being renewed (assumed to be constant by Danckwerts), has an exponential solution: p(t) = s exp(Àst). With this pdf, average surface age can be obtained as t = 1/s, and average gas flux at the surface is q g = (c 0 1951] did not account for effects of vertical turbulent advection after t = 0. Near the surface, the advection is in the form of upwelling and can be measured by surface divergency a = @u/@x + @v/@y = À@w/@z (so that w = Àaz), which was considered by Ledwell [1984] and Banerjee [1990]. The relative effects of diffusion and advection can be seen in the upwelling stagnation flow model of Chan and Scriven [1970], in which the advectiondiffusion equation @c/@t = az(@c/@z) + D(@ 2 c/@z 2 ) is solved to obtain the surface gas flux base...

Temperature dependence of stream aeration coefficients and the effect of water turbulence: A critical review

“…Several studies have shown that the Kolmogorov distribution function (a log-normal distribution) was more appropriate (e.g. Garbe et al, 2004;Kermani and Shen, 2009). This said, the average surface age from Dankckwerts' random surface renewal model was surprisingly close to hybrid Lagrangian tracing and temperature method, the state of the art in gas transfer modelling at the interface between a liquid and the atmosphere (Kermani et al, 2011).…”

Direct numerical simulation of turbulent scalar transport across a flat surface

“…The surface age can be thought of as the time between two surface renewal events. Kermani & Shen (2009) concluded that Higbie's model is inappropriate for describing the gas transfer and Danckwert's model is only applicable at large surface age where the gas transfer is actually insignificant. Hasegawa & Kasagi (2009) performed a hybrid DNS/LES calculation of a coupled air-water turbulent flow and associated mass transfer for Sc = 1 and 100 at Re τ = 150 (Re τ is the Reynolds number based on the interfacial friction velocity).…”

“…Magnaudet & Calmet (2006) used a large-eddy simulation (LES) to perform a statistical analysis of the structure of the near-surface region of an open-channel flow at a high Reynolds number. Kermani & Shen (2009) used DNS to study characteristics of interfacial mass transfer driven by free-surface turbulence. They investigated the quantification of the surface age related to the surface renewal models pioneered by Higbie's penetration theory (Higbie 1935) and further elaborated by Danckwert's random surface renewal model (Danckwerts 1951).…”

High-resolution variability of the enrichment of fluorescence dissolved organic matter in the sea surface microlayer of an upwelling region

“…For example, at the UP3 station, peaks appeared approximately every ten minutes, resulting in 6% variability in the enrichment of FDOM. Although seemingly small, this variability nevertheless indicates that surface renewal, potentially enhanced by advection in upwelling regions (Kermani and Shen, 2009;Thomas et al, 2013), occurs within very short time intervals. At the UP2 station (Figure 3b), the temporal decrease in FDOM enrichment was caused by increasing FDOM concentrations in bulk water as the catamaran approached the front (Ribas-Ribas et al, 2017).…”