Evolution of thermally stratified turbulent open channel flow after removal of the heat source

Abstract

Evolution of thermally stratified open channel flow after removal of a volumetric heat source is investigated using direct numerical simulation. The heat source models radiative heating from above and varies with height due to progressive absorption. After removal of the heat source the initial stable stratification breaks down and the channel approaches a fully mixed isothermal state. The initial state consists of three distinct regions: a near-wall region where stratification plays only a minor role, a central region where stratification has a significant effect on flow dynamics and a near-surface region where buoyancy effects dominate. We find that a state of local energetic equilibrium observed in the central region of the channel in the initial state persists until the late stages of the destratification process. In this region local turbulence parameters such as eddy diffusivity $k_{h}$ and flux Richardson number $R_{f}$ are found to be functions only of the Prandtl number $Pr$ and a mixed parameter ${\mathcal{Q}}$, which is equal to the ratio of the local buoyancy Reynolds number $Re_{b}$ and the friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}$. Close to the top and bottom boundaries turbulence is also affected by $Re_{\unicode[STIX]{x1D70F}}$ and vertical position $z$. In the initial heated equilibrium state the laminar surface layer is stabilised by the heat source, which acts as a potential energy sink. Removal of the heat source allows Kelvin–Helmholtz-like shear instabilities to form that lead to a rapid transition to turbulence and significantly enhance the mixing process. The destratifying flow is found to be governed by bulk parameters $Re_{\unicode[STIX]{x1D70F}}$, $Pr$ and the friction Richardson number $Ri_{\unicode[STIX]{x1D70F}}$. The overall destratification rate ${\mathcal{D}}$ is found to be a function of $Ri_{\unicode[STIX]{x1D70F}}$ and $Pr$.

Roles of Shear and Convection in Driving Mixing in the Ocean

“…Thus Ri f = Ri f ( L O , L S , L ρ ), and the DNS results of Kirkpatrick et al. (2019) are entirely consistent with Equation . As argued by Ivey et al.…”

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

“…We have presented a study of destratification of thermally stratified turbulent open-channel flow after the imposition of surface cooling. This study builds on our previous studies of the equilibrium state due to radiative heating (Williamson et al 2015) and the response of this system to removal of the heat source (Kirkpatrick et al 2019).…”

“…In a previous study, (Kirkpatrick et al 2019, henceforth KWAZ) we investigated the transient evolution of this flow when the solar heat source is removed and the flow allowed to evolve in time with no heat flux through the upper or lower boundaries. This model represents the situation in which solar forcing stops, due for example to an increase in cloud cover, while atmospheric conditions are such that surface heat fluxes are small.…”

The Influence of Sharp Meanders on Thermally Stratified Open Channel Flow

“…The Reynolds number Re τ = u τ H/ν = 180 and the non-dimensional buoyancy coefficient λ = 0.5. All variables are non-dimensionalised in terms of channel depth H, average friction velocity on the bottom surface and sidewalls u τ and a temperature scale based on the radiative heat flux (see [12] for details. )…”

“…The simulation was performed using the PUFFIN code [10]. The code has been validated for turbulent stratified flows against experimental data [11] and against other published correlations and scaling relationships [12]. The grid cell sizes in viscous wall units are n + 0 = 2.9 in the channel centreline, and n + 0 = 0.4 near the walls.…”