Turbulent One-dimensional Interfacial Scalar Transport: Statistical Random Square Waves Solution

Abstract

In this study the mass transport through free turbulent liquid surfaces, or gas/liquid interfaces, is considered. The main direction of mass transfer is perpendicular to the interface, so that a one-dimensional point of view is followed. The equations for the interfacial gas/liquid transport are presented using the random square waves method (RSW), a statistical tool that models the fluctuations of physical variables as ideal signals. The method defines three statistical functions (partition, reduction, and superposition), related to fluctuations of concentration and velocity, which were introduced into the mass advection-diffusion equation generating a set of differential equations adequate for boundary layer problems. Solution profiles of the partition and reduction functions, and of turbulent fluxes across the boundary layer were obtained for transient situations. The solutions use Taylor series centered at the immersed border of the concentration boundary layer. For practical applications, the series were truncated and the coefficients were calculated in order to satisfy adequate physical conditions. The proposed procedure substitutes coefficients of the higher order parcels of the truncated series, enabling them to satisfy boundary conditions in the two borders of the domain of interest, which is the region of variation of the mass concentration. The theoretical profiles for concentration and turbulent fluxes close to the interface agree with measurements and predictions found in the literature.