Large‐eddy simulations of unidirectional water flow over dunes

Abstract

[1] The unidirectional, subcritical flow over fixed dunes is studied numerically using large-eddy simulation, while the immersed boundary method is implemented to incorporate the bed geometry. Results are presented for a typical dune shape and two Reynolds numbers, Re = 17,500 and Re = 93,500, on the basis of bulk velocity and water depth. The numerical predictions of velocity statistics at the low Reynolds number are in very good agreement with available experimental data. A primary recirculation region develops downstream of the dune crest at both Reynolds numbers, while a secondary region develops at the toe of the dune crest only for the low Reynolds number. Downstream of the reattachment point, on the dune stoss, the turbulence intensity in the developing boundary layer is weaker than in comparable equilibrium boundary layers. Coherent vortical structures are identified using the fluctuating pressure field and the second invariant of the velocity gradient tensor. Vorticity is primarily generated at the dune crest in the form of spanwise ''roller'' structures. Roller structures dominate the flow dynamics near the crest, and are responsible for perturbing the boundary layer downstream of the reattachment point, which leads to the formation of ''horseshoe'' structures. Horseshoe structures dominate the near-wall dynamics after the reattachment point, do not rise to the free surface, and are distorted by the shear layer of the next crest. The occasional interaction between roller and horseshoe structures generates tube-like ''kolk'' structures, which rise to the free surface and persist for a long time before attenuating.

Large-eddy simulation of three-dimensional dunes in a steady, unidirectional flow. Part 1. Turbulence statistics

“…In that paper, we examined average velocities and Reynolds stresses along six vertical lines in the channel with those in previous simulation and experiment, and excellent agreement was obtained. Contours of turbulence statistics on the xy-planes also showed remarkable agreement with previous work (Stoesser et al 2008;Grigoriadis et al 2009). Furthermore, a grid refinement study was performed for Cases 2 and 5, in which 384 × 128 × 384 grid points were used; firstand second-order statistics were within 5% of each other.…”

“…Contours of streamwise velocity in Figure 3 show that the fluid separates over the crest, forming a recirculation bubble on the lee side of the dune. At the saddle and node, the flow then reattaches on the stoss side, similar to what is observed in the 2D case (Kostaschuk & Church 1993;Nelson et al 1993;Nezu & Nakagawa 1993;McLean et al 1994;Bennett & Best 1995;Schmeeckle et al 1999;Venditti & Bauer 2005;Stoesser et al 2008;Grigoriadis et al 2009;Omidyeganeh & Piomelli 2011), but the behaviour at the lobe is different. The separation streamline never reaches the wall: fluid coming from the saddle region near the wall displaces it upwards, and a saddle point (point C in Figure 3(a)) is formed at the beginning of the stoss side on the lobe plane.…”

“…Although flow over dunes has been extensively studied in field experiments (Matthes 1947;Jackson 1976;Flemming 1978;Gabel 1993;Kostaschuk & Church 1993;Bennett & Best 1995;Babakaiff & Hickin 1996;Kostaschuk & Villard 1996;Roden 1998;Carling et al 2000;Kostaschuk 2000;Best et al 2001), fixed 2D dunes have been the focus of the studies in laboratory experiments (Müller & Gyr 1986;Nelson et al 1993;Kadota & Nezu 1999;Schmeeckle et al 1999;Venditti & Bennett 2000;Hyun et al 2003;Balachandar et al 2007;Balachandar & Patel 2008), numerical simulations (Yoon & Patel 1996;Schmeeckle et al 1999;Yue et al 2005;Polatel et al 2006;Yue et al 2006;Stoesser et al 2008;Grigoriadis et al 2009;Omidyeganeh & Piomelli 2011), as well as theoretical studies (McLean & Smith 1986;Nelson & Smith 1989;McLean et al 1999). A comprehensive review of literature on dunes is given by Best (2005).…”

Large-eddy simulation of three-dimensional dunes in a steady, unidirectional flow. Part 2. Flow structures

“…Aider & Danet (2006) found the flapping frequency as well as the shedding frequency at St = 0.064 and 0.102, respectively. In the simulations over the two-dimensional dunes, similar shedding frequencies have been observed (St = 0.078 by Grigoriadis et al (2009), and St = 0.065 by Omidyeganeh & Piomelli (2011)). The shedding frequency is also in the range of the measurements by Venditti & Bauer (2005) as well as the range proposed by Jackson (1976), St = 0.04 0.11.…”

Morphodynamics of river dunes : suspended sediment transport along mobile dunes and dune development towards upper stage plane bed

“…Several time-averaged flow features over dunes are observed in Figure 3.7 that have been described in other studies [e.g., Raudkivi, 1966;Parsons et al, 2005;Venditti, 2007;Coleman et al, 2008;Grigoriadis et al, 2009;Shugar et al, 2010;Bradley et al, 2013]. This includes (1) a zone of lee side flow reversal or deceleration; (2) flow acceleration due to convergence on the stoss side of the dune towards the dune crest with largest mean streamwise velocities at the crest area; (3) flow deceleration due to expansion in the wake region with negative velocities in the flow separation zone; (4) an outer, near-surface region with higher velocities overlying the flow separation zone; and (5) development of an internal boundary layer starting on the stoss side of the dune towards the dune crest.…”