A numerical investigation of energy conversions in geophysical boundary layers

Sammanfattning: The detailed energy conversions in turbulent geophysical boundary layers are examined and quantified. The governing transport equations are solved by utilizing turbulence modelling. Different turbulence closures have been adopted for the boundary layers examined. LowReynolds number modelling is required, since energy conversions are large in the near-wall region. The three examined boundary layers are: open channel flow, wind-induced countercurrent flow, and ice-covered channel flow. In addition, a generalized eddy-viscosity hypothesis is proposed. In the standard eddy-viscosity concept. zero shear stress coincides with zero shear. This is not realistic for many flows. such as wind-induced countercurrent Row. This limitation is relaxed in the new hypothesis, by recognizing the influence of gradients in the turbulent length scale and the shear. In open channel flow, energy is released to the kinetic energy of the mean flow by the lowering of the centre of mass. Between 20-70 % (depending on the Reynolds number) of the energy is dissipated by viscous forces working directly on the mean shear. The remaining portion is a source of turbulent kinetic energy, which is balanced by the dissipation. Eventually all of the energy will leave the domain as a boundary beat flux. In the modelling of open channel flow, a one-equation turbulence model and Reynolds analogy is used. In wind-induced countercurrent flow. energy is supplied to the mean flow by the wind acting on the free surface. Most of the mean kinetic energy is dissipated or transformed to turbulent kinetic energy in the surface drift current. Only about 5-10 % is supplied to the return flow underneath. As with open channel flow, 20-70 % of the mean kinetic energy is dissipated without entering the turbulent kinetic energy budget. The dissipated heat is considered to leave the domain through the free surface. A Reynolds stress model was adopted for the windinduced boundary layer, in conjunction with the "generalized gradient diffusion hypothesis" for beat flux. A detailed description is presented, of the spatial distribution and the depth-averaged features of energy conversions in the two boundary layers mentioned above. In the study of ice-covered channel flow, the analysis is focused on beat transfer characteristics. In water of a temperature close to 00C, the conversion from kinetic energy to heat may be of influence to the heat transfer in an ice-covered channel. In water of higher temperatures buoyancy effects may develop. In addition the melting ice-cover constitutes a moving boundary problem. These three effects are considered in the study, in which the predicted beat transfer characteristics are presented as Nusselt number relations. To make adequate predictions of the boundary layer flow beneath an ice-cover, a Reynolds stress and heat flux transport model is employed. Equations for the transport of temperature variance and its dissipation rate are also solved.