Analysis of Effects of Meander Curvature in Thermally Stratified Turbulent Open-channel Flow

Thermal stratication can lead to the damping of turbulence, which reduces the mixing of solutes in a uid body, and in turn, aects river health. A series of Direct Numerical Simulation (DNS) solutions sweeping through a range of four dierent channel radius of curvature is obtained to investigate the eect of curvature on stratication in meandering thermally stratied turbulent open channel ow. This range of radius of curvature will cover a range of the curvature parameter 0.2 < < 1.5, which is typical of rivers in the sharp to mild curvature range. Here = Cf-1 (H/Rmin) is a dominant control parameter with respect to velocity redistribution in curved open-channel ow, where Cf is the Chezy friction coecient, Rmin the minimum radius of curvature, which occurs at the meander apex, H the meander height. An internal heat source models radiative heating from above following an exponential Beers law prole, which varies with height due to progressive absorption. Based on the DNS results, the present paper addresses two issues. Firstly, the inuence of changing curvature on the complex tri-cellular pattern of the secondary ow is investigated, including the distribution of turbulent stresses. Secondly, the eect of changing curvature on the degree of stratication is analysed. Stratication can be characterised by the friction Richardson number Ri = (gH)/u2, and the bulk Richardson number Rib = (gH)/ubulk2. Here is the dierence between the mean temperature at the top and bottom of the channel, u the mean friction velocity on the solid surfaces bounding the channel, ubulk the domain averaged streamwise velocity, the volumetric coecient of expansion and g gravity. Stratication can also be viewed in terms of the transfer of energy from mean ow kinetic energy to potential energy via buoyancy uxes. We study the eect of curvature on stratication by investigating its eect on the friction and bulk Richardson numbers, the global available, background, total potential energy, and the domain averaged kinetic energy. It is found that with the increase of curvature, Ri and Rib decrease, while available potential energy increases due to increased overturning of the ow, indicating that increasing curvature leads to a decrease in the level of stratication.