Enhanced diffusion from a continuous point source in shallow free-surface flow with grid turbulence

Abstract

Shallow flows are ubiquitous in nature and are prone to instabilities that result in the formation of large-scale, two-dimensional coherent structures that are expected to significantly enhance eddy diffusivities compared to the stable turbulent base flow. We present the results of an experimental study in free-surface flow to determine the mixing coefficient for a passive tracer plume in two-dimensional grid turbulence. The grid consists of a row of cylinders 2.5 times the water depth and spaced to achieve a porosity of 50%. Depth-averaged dye concentrations are measured using a light absorption planar concentration analysis method; turbulence statistics are calculated from measurements of horizontal flow velocity using a two-component laser Doppler velocimeter. A base case without grid turbulence (having only bottom-generated turbulence) and three cases with grid turbulence are presented. For experiments with grid turbulence, injections were made at 40 water depths downstream of the grid, at the cylinder shoulders, and in the middle of the gap between cylinders. For the base case without grid turbulence, spreading rates agreed well with turbulent diffusion coefficients evaluated by others for wide channel flows. Eddy diffusivities for injections with grid turbulence were an order of magnitude greater than the base case; injections at the grid had larger diffusivities than for the injection downstream of the grid. For all experiments, the eddy diffusivity is shown to agree with Taylor’s theorem and to correlate with the size and turbulent intensity of the largest-scale coherent structures.

2D and 3D Turbulent Fluctuations in Open Channel Flow with Re τ = 590 Studied by Large Eddy Simulation

“…17. Both compare well with corresponding experimental distributions reported by Rummel et al [21]. The structures made visible by the concentration distributions in Fig.…”

“…Dye-spreading experiments in wide open channels with smooth bed have yielded dimensionless mixing coefficients of * y = y /u τ h ≈ 0.1 − 0.2 [4] where an approximate average of * y = 0.15 was obtained and recommended for modelling. More recent experiments in wide flumes with smooth beds yielded a value of * y = 0.17 [21,26]. Fischer et al [4] explain the large scatter by the significant influence which small transverse motions may have and that, if such a motion is somehow excited in a wide channel, there is no physical obstacle to its continuation.…”

On the Values for the Turbulent Schmidt Number in Environmental Flows

“…Hence, the data of the spatial variance of the tracer transverse profile were plotted against the travel time of the plume t, as suggested by [77]. In this plot, the transverse mixing coefficient D t-y was taken as the fitting parameter, and the line was forced to go through zero.…”

Depth-Integrated Numerical Modeling of Turbulent Transport by Long Waves and Currents

“…Therefore the 3D turbulence effects in the equation (9) should be included in the case of destabilization by internal transverse shear. Comparison to Taylor's Theorem Rummel et al (2005) presented the results of an experimental study to determine the magnitude of mixing coefficient for a passive tracer plume in shallow open channel flow. Also they presented two analytical solutions for the near field and far field mixing based on the Taylor's theorem (1921).…”

“…In the numerical simulation, the C B =70 resulted in the i y =0.06 and randomly distributed scalar distribution. In the experiment done by Rummel et al (2005), the channel length was 13.5m and the width was 5.5m. The water depth was h=0.025m and the velocity was U=0.16 m/s, resulting in the Re=4000.…”