Methods for surface age estimation and study of evaporative cooling induced air-water gas transfer

Abstract

This thesis presents numerical studies of fundamental fluid mechanical mechanisms that play a role in the transfer of atmospheric gases across the air-water interface. At first numerical methods are discussed that allow the calculation of the mean surface age and the interfacial gas transfer velocity from snapshots of the interfacial flow field. After constructing the near-surface three-dimensional (3D) velocity field from the interfacial velocity field, first the Lagrangian particle tracking method is employed to estimate the mean surface age. Subsequently, a new continuum method was developed as an alternative to the Lagrangian approach. To estimate the mean surface age, a continuous surface age density was introduced to replace the point particles used in the Lagrangian method. To obtain a smooth initial density distribution on the uniform base mesh in the z-direction, N number of mesh cells were used. Each grid cell was refined in the x, y and z-direction by a factor of RXY = 5 and RZ = 10, respectively. On the refined mesh, an unsteady three-dimensional convection equation for the surface age density was solved using the fifth-order-accurate WENO-Z scheme for the convection terms combined with a third-order Runge-Kutta method for the time-integration. For the surface age density, ρτ , a symmetry boundary condition was used at the surface, while below the region where the initial surface age density was introduced, ρτ was set to zero, to model that the surface age density left the near surface region. The results obtained with the continuum method were in good agreement with the results from the Lagrangian particle tracking method. Subsequently, the effects of Marangoni forces, induced by temperature differences at the air-water interface, on the instantaneous development of a buoyant convective instability for several Sc-numbers was studied by Direct Numerical Simulation (DNS). Simultaneously with the flow, five scalar convection diffusion equations were solved. The first scalar, the temperature, is non passive as it affects the flow through buoyancy forces. The other scalars are passive and represent the transport of atmospheric gases. The Prandtl number for the temperature was P r = 7 and the Schmidt numbers for the mass transport were Sc = 16, 50, 100, 200. The latter simulations allow a non biased comparison of the effect of Schmidt number on the gas transfer velocity KL. For the flow solver, the convective terms were solved using the fourth order ki- netic energy conserving discretization, while the diffusive term was solved using the fourth order central scheme. After substituting the descritized momentum equations into the continuity equation a Poison equation for the pressure was obtained. This Poison equation for the pressure was solved using the conjugate gradient method with simple diagonal decomposition. Time integration was performed using the second or- der Adams-Bashforth method. It was shown that Marangoni forces that promote the Rayleigh instability result in significant increases in the amount of atmospheric gases transferred across the air-water interface and should not be neglected.