A Numerical Study of Shallow Mixing Development over Flat Surface and Dunes

Abstract

Results of a high resolution Detached Eddy Simulation (DES) are used to characterize the evolution of a shallow mixing layer developing between two parallel streams in a long open channel with a smooth flat bed and dunes. The study discusses the vertical non-uniformity in the mixing layer structure and provides a quantitative characterization of the growth of the large-scale quasi two-dimensional (2D) coherent structures with the distance from the splitter plate. Results show that in streamwise sections situated between 75D (D is the channel depth) and 150D from the splitter plate the width of the mixing layer close to the free surface is 20-30% more than the width in the near-bed region in the case in which the channel bed is flat. This is mostly because of the tilting of the mixing layer interface on the low-speed side toward the low speed stream as the free surface is approached. Power spectra of the horizontal velocity components show the presence of a -3 subrange at streamwise locations situated more than 10D from the splitter plate consistent with the presence of large-scale quasi 2D horizontal eddies and the transfer of energy (inverse energy cascade) from the smaller scales toward these eddies. Consistent with visualizations of the mass transport of a passive scalar within the mixing layer close to the free surface the estimated streamwise length of the quasi 2D mixing layer eddies is about 2.5 to 3.0 times larger than the local width of the mixing layer. The presence of large-scale roughness elements in the form of an array of two-dimensional dunes with a maximum height of 0.25D (D is the channel depth) induces a much more rapid and larger shift of the centerline of the mixing layer due to the increased influence of the bottom roughness.