Convectively unstable turbulent open channel flow with stable surface stratification

Abstract

We use direct numerical simulations to examine fully developed turbulent open channel flow where the near wall region is unstably stratified and the outer boundary layer is stably stratified. The simulations are a model for flow in shallow turbid river channels with incident solar radiation. The aim is to determine under what conditions and by what mechanism the stably stratified layer is overturned. The flow is attained by applying a radiative heat flux at the free surface of the open channel. The absorption and transmission of the radiation follows the Beer--Lambert law with a constant absorption coefficient. We examine conditions where approximately 20% of the incident radiative heat flux penetrates through to the wall, releasing heat at the wall as a heat flux. The problem is specified by our buoyancy parameter which is analogous to the bulk Obukhov length scale. In the stable outer boundary layer we observe that the flux Richardson number reaches the limiting value, as was observed in the atmospheric boundary layer under sheared convective conditions.