Influence of Diurnal Heating on a Stratified Open Channel Flow

This study employs direct numerical simulation (DNS) to investigate stably stratified open channel flows that are subjected to a time-varying surface radiative forcing whose function is approximated by a diel solar heating cycle. This paper follows from the earlier work of a statistically steady state open channel flow with a constant heat source. The simulations have a Prandtl number $Pr$ of 1 and a friction Reynolds number $Re_{\tau}$ of 400. It’s bulk buoyancy parameter $\lambda$ of 1, defined by the ratio of the channel depth $\delta$ and a bulk Obukhov length scale $\mathscr{L}$, corresponds to strongly stratified conditions and the diurnal timescales, normalised by the wall friction velocity $u_{\tau}$ over $\delta$, cover the range between $t^{*} = 6 - 12$. Results demonstrate strong mixing and re-stratification during the ‘night and day’ heating cycle. Numerical results have been found to be in agreement with existing parameterisation and scaling relations for the irreversible flux Richardson number $Ri_{f}^{*}$ and turbulent Froude number $Fr$ and eddy diffusivity $k_{h}$ and local buoyancy Reynolds number $Re_{b}$ at certain positions along the water column.