Large-scale coherent structures in turbulent shallow flows

Abstract

Shallow flows are three-dimensional flows with two dimensions being signifcantly larger than the third dimension. Coherent structures, also called eddies, are areas in the flow, where velocity fluctuations are correlated, with a certain rotation. Although, generally, coherent structures of the order of the waterdepth contain most of the turbulent kinetic energy, compared to coherent structures of other length-scales, coherent structures of all length-scales have a certain amount of energy. This research was particularly focussed on the amount of energy of coherent structures with length-scales larger than the water-depth, the so-called supra-depth length-scales. It turned out, that these coherent structures are of large importance with regard to the, for quasi-two-dimensional flow characteristic, upcascading to larger length-scales, which is clearly visible by a peak-shift to the low-frequency side of the energy-density spectra. Considering that large-scale coherent structures are less dissipative compared to smaller-scale coherent structures, it can be inferred that imposing perturbations has a clear effect with respect to the conservation of turbulent kinetic energy in (by definition hypothetical) two-dimensional flows. This knowledge can be used and applied in two-dimensional depth-averaged simulations (e.g. RANS, TRANS, etc.,), where the large-scale part of general spectral distributions can be mimicked by a kinematic simulation. This thus formulated and used model (2D-TRANS+ks) has been applied to a channel flow with a grid of obstacles at the inow boundary. Considering the quantities energy and enstrophy, and the energy-density spectra, the model performed reasonably well. Nevertheless, this model should be applied with care and a critical eye, as three-dimensional effects are difficult to represent in a two-dimensional model.