Destratification of thermally stratified turbulent open-channel flow by surface cooling

Abstract

Destratification of thermally stratified open-channel flow by surface cooling is investigated using direct numerical simulation. The initial states are the equilibrium states resulting from radiative heating. Using these states as initial conditions, a series of direct numerical simulations was run with radiative heating removed and a constant, uniform cooling flux applied at the upper surface. The flow evolves until the initial stable stratification is broken down and replaced by unstable stratification driven by surface cooling. The destratification process is described with reference to the evolution of the internal structure of the turbulent flow field. Based on these observations, we conclude that the dominant time scales in the flow from the perspective of destratification are the time scales associated with shear tτ , convection t∗ and stable density stratification tN . Scaling arguments are then used to derive a scaling relationship for destratification rate as a function of a friction Richardson number Riτ=(tτ/tN)^2 and a convection Richardson number Ri∗=(t∗/tN)^2 . The relationship takes the form DN=C1Riτ^−1+C2Ri∗^−1 , where DN is the destratification rate non-dimensionalised with respect to tN and C1 and C2 are model coefficients. The relationship is compared with simulation results and is shown to accurately predict the destratification rate in the simulations across a range of parameters. This relationship is then integrated to give a formula for the time taken for the flow to destratify.