Coherent structures in flow over two- dimensional dunes

Key Points streaks penetrate away from dunes over a distance of about 3 times their dunes large scale streaks are due to formation of arrays of large scale hairpins new mechanism for formation of large-scale hairpins over dunes The instantaneous turbulent flow fields over a smooth bed and a bed containing large-scale roughness elements are characterized by the presence of elongated low and high streamwise momentum regions or streaks. If the bed contains large-scale roughness elements (e.g., dunes), the size of the streaks increases and is of the order of the size of these elements and the flow depth. The present large eddy simulation (LES) study focuses on the case of developing flow within wide channels containing at the bottom a long array of spanwise-oriented sinusoidal 2-D dunes (2a/h=0.1, /h=1, is the wavelength, 2a is the dune height, and h is the mean flow depth) and an array of 2-D asymmetric dunes (2a/h=0.25, /h=3.75) of closer shape to the ones observed in natural streams. For the case of an incoming steady flow, the instantaneous flow fields, in the region where the flow transitions toward a fully developed turbulent flow regime, contain arrays of highly organized hairpin vortices, whose dimensions are larger than the dune height. The LES shows that for relatively shallow channels (e.g., channels with 2a/h=0.25), the large-scale hairpins and the streaks penetrate regularly up to the free surface, thus affecting mass transport and mixing over the whole water column. This paper explained the mechanism for the formation of these arrays of hairpin vortices and discussed the changes between a case with asymmetric dunes that are characterized by a large value of /2a (= 15) and a long upslope face and a case with symmetric dunes for which /2a=10, the upslope face is relatively short, and the rate of change of the bed curvature around the dune's crest is relatively small. The study discusses the main mechanisms through which large-scale hairpin form and how these mechanisms change between two dune geometries (sinusoidal versus asymmetric dunes). This study also shows that hairpin eddies play the primary role in the formation of the streaks over the region containing dunes and provides an estimation of the average dimensions of these streaks. The presence of resolved turbulence in the incoming flow reduces the streamwise distance needed for the streaks to develop over the region containing dunes, but does not qualitatively affect the transition process toward the fully developed flow regime nor the spacing of the streaks in the fully developed flow region.