Stratification and temporal evolution of mixing regimes in diurnally heated river flows

Direct numerical simulations of stratified open channel flows subject to a varying surface heat flux is performed. The influence of the diurnal heating time on the spatial and temporal variation of mixing in the flow and the characteristics of the mean flow state is also examined. The bulk buoyancy parameter 𝝀 𝑩 is defined through the ratio of the channel height 𝜹 and a bulk Obukhov length scale 𝓛 𝑩 . The non-dimensional diurnal time scale ˆ𝒕 is defined as the ratio of the heating time to an eddy turnover time. The Prandtl number 𝑷𝒓 and Reynolds number 𝑹𝒆 𝝉 is limited to 1 and 400, respectively, with ˆ𝒕 ranging between 1 to 24. A regime map for each behaviour of the laminar layer depth (LLD) and stratified layer depth (SLD) is presented. The LLD is defined as the depth when the buoyancy Reynolds number 𝑹𝒆 𝑩 ≤ 7 and the SLD is the depth when the turbulent Froude number 𝑭𝒓 ≤ 1 . Three classifications exist for each layer depth. The first; a neutral flow where the LLD or SLD does not exist, denoted by NL and NS, respectively. The second is a stratified flow where the LLD or SLD are diurnally varying, denoted as DL and DS. The last describes a persistent layer of the LLD or SLD, denoted as PL and PS. The transition between the NL to DL is ˆ𝒕 ∝ 𝑹𝒆 𝓛 4.5 , DL to PL is ˆ𝒕 ∝ 𝑹𝒆 𝓛 −0.5 , NS to DS is ˆ𝒕 ∝ 𝝀 0 and DS to PS is ˆ𝒕 ∝ 𝝀 1 . These classifications form the basis of the regime map for this flow.