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Emergence of large-scale coherent structures in a shallow separating flow
Abstract
In rivers, the phenomenon of flow separation past obstacles often gives rise to large-scale coherent structures. This study focuses on quasi-2d coherent structures associated with shallow flow separation (vortex shedding). New insights about the physical mechanism governing vortex shedding have been obtained from largescale Particle Image Velocimetry (PIV) experiments on a Shallow Lateral Expansion (SLE) with a variable inflow width. Analysis of the acquired data stresses the crucial role of the secondary circulation cell, which is often present in shallow separation geometries. A sufficiently developed secondary circulation cell is significantly contributing to vortex shedding. Moreover, the interaction between primary and secondary circulation cells causes a "scale jump" in the horizontal length scale of the shed vortices. An analysis of Reynolds' stresses and the downstream development of conditional averaged eddies does clearly show this jump. Since the scale jump is essentially due to interaction of discrete horizontal eddies, 3D Large Eddy Simulations (LES) are performed in analogy with the measured PIV geometries. The obtained LES data will be used to develop a depth-averaged flow model that will reproduce the discrete horizontal eddy interaction in an accurate way, thus enabling researchers and engineers to predict vortex shedding in river geometries.
... Many previous works have investigated the spatio-temporal dynamics of Q2CS created by plane shear instabilities e.g. ( Chu and Babarutsi, 1988;Rhoads and Sukhodolov, 2004;Uijttewaal and Tukker, 1998 ), and have shown that due to the effects of bedfriction the spread/growth rate of a shallow mixing layer is modified. In an experimental study to investigate the effect of topographical forcing on a shallow flow, Talstra et al. (2006) found that unlike in a deep flow, ( Armaly et al., 1983 ), the shallow flow mixing layer bound a second counter rotating recirculation cell. They also found at the downstream edge of the first recirculation cell there was a sudden expansion in the mixing layer. ...
... The region where the point of incidence moves about coincides with the high Reynolds stresses as seen in Fig. 5 . This suggests that this mechanism of oscillation is associated with the sudden expansion of the mixing layer, as hypothesised by Talstra (2011) , andTalstra et al. (2006) . To investigate the turbulent structures associated with this mechanism, Fig. 13 shows a low-order reconstruction based upon the fluctuating vorticity, where dark grey is positive vorticity and light grey is negative vorticity. ...
... However, it is the interface between the two counter rotating recirculation cells that transports the second eddy into the mixing layer leading to the sudden expansion. It has previously been shown by Talstra (2011) , Talstra et al. (2006) and Safarzadeh and Brevis (2016) that the shallowness of the flow leads to the production of the dual recirculation cell. The occurrence of the sudden expansion of the mixing layer is a function of the flow depth. ...
The sudden expansion of the mixing layer created in the wake of a single groyne is investigated using Particle Image Velocimetry (PIV). In the region of the sudden expansion a patch of high Reynolds shear stresses are observed. Using low-order representations, created from a Dynamic Mode Decomposition and a search criteria based on a Proper Orthogonal Decomposition, the spatio-temporal mechanism of the sudden expansion is investigated. The present study demonstrates the sudden expansion is created by the periodic merging of eddies. These eddies originate from the upstream separation and the tip of the groyne and merge with recirculating eddies created, downstream of the groyne, at the interface of the mixing layer and the lateral wall.
... These data have been acquired from shallow flow experiments carried out using the measurement technique of Particle Image Velocimetry (PIV). These experiments are described in Talstra, Uijttewaal & Stelling (2006). The vortex shedding phenomenon, as indicated by the experimental data, is expected to be found back within the LES data. ...
... The latter type of structures is associated with the interaction with the secondary recirculation cell, while the first type is associated with lateral shear instabilities. From the experimental PIV study of Talstra, Uijttewaal & Stelling (2006), the difference between these two large eddy types can be clarified. The experimental setup (which is identical to the geometry of the 3D LES computations) will be described in Section 2.1. ...
Paper presented at The Seventh International Conference on HydroScience and Engineering (ICHE) hosted by the College of Engineering at Drexel Univeristy on September 10-13, 2006 in Philadelphia, Pennsylvania. The conference theme was IT in the Field of HydroSciences. It included several mini-symposia that emphasized IT topics in HydroSciences and the yearly meeting of the metadata group of the International Oceanographic Data and Information Exchange organization. In environmental shallow flows, the phenomenon of flow separation often gives rise to large-scale turbulent structures (vortex shedding). In this study, 3D LES computations of three Shallow Lateral Expansion geometries are performed. The resolved large-scale turbulent structures are studied in detail in order to allow a comparison with laboratory experiments, carried out using the Particle Image Velocimetry (PIV) technique. When LES is applied for practical cases involving flow separation, immersed boundaries are often an essential part of the geometry. These boundaries can cause problems with respect to the Navier Stokes solver used, especially regarding the pressure correction module. A solution to this problem, known as Immersed Boundary Method (IBM), is found by using body forces to ensure the impermeability of internal boundaries. The classical IBM formulation, however, makes a systematic error regarding momentum transfer in the vicinity of solid walls. In this study an adjusted IBM is proposed, based on momentum fluxes instead of body forces. The adjusted model is applied to Shallow Lateral Expansion geometries of various aspect ratios. In order to analyze the real-time large-scale turbulent structures, the vector potential function of the velocity field is computed. This is a very suitable tool to detect large-scale flow structures. The turbulence features observed in the 3D LES computation are compared with the PIV data, especially regarding the vortex shedding behaviour. An analysis of Reynolds stresses and the downstream development of eddy length scales reveals the existence of two different regimes in the vortex shedding behaviour. The difference can be explained by the interaction of shed vortices with the primary and secondary recirculation cells that are present.
... Due to the resulting adverse pressure gradient, the main flow separates shedding vortices from the obstacle head. Secondly, and depending on the flow shallowness, the separation gives rise to a main and secondary recirculation cells (Talstra et al., 2006). The lateral flow velocity difference between the recirculating regions and the main flow leads to the development of an intense shear region, resulting in an enhanced growing of the shear layer vortex. ...
... Due to the resulting adverse pressure gradient, the main flow separates shedding vortices from the obstacle head. Secondly, and depending on the flow shallowness, the separation gives rise to a main and secondary recirculation cells (Talstra et al., 2006). The lateral flow velocity difference between the recirculating regions and the main flow leads to the development of an intense shear region, resulting in an enhanced growing of the shear layer vortex. ...
In this work the performance of Reynolds Averaged Navier-Stokes (RANS) simulations to predict the flow structure developed by the presence of a sidewall obstacle in a uniform open-channel shallow flow is discussed. The tested geometry was selected due to its important role in several fluvial applications, such as the control of riverbank erosion and the creation of improved ecological conditions in river restoration applications. The results are compared against experimental laboratory velocity fields obtained after Large Scale Particle Image Velocimetry (LSPIV) measurements. It is shown that the length of reattachment of the separated shear layer generated by the obstacle is well predicted by a Reynolds Stress Model, while classical two-equation models show important limitations. All the performed RANS simulations are unable to properly predict the formation of a secondary gyre region, which develops immediately downstream the obstacle.
... For free surface flows, the same kind of large recirculation zones can occur in the presence of obstacles or expansions (Talstra et al., 2006). Stovin and Saul (1994) reported experiments performed in a detention tank. ...
We study the flow pattern in rectangular detention tanks experimentally and numerically. After the verification of the model, a large number of tanks are generated in order to study the transitions between the different kinds of flow (plug flow, symmetric reciculations, asymmetric recirculations, etc.). The effects of the length, breadth, water depth, inlet pipe dimension and location are investigated. We define non-dimensional geometrical parameters. The flow pattern can be predicted by calculating these parameters and comparing their values to the critical values that are given in this paper. Approximate formulas of the reattachment lengths are also given.
... River confluences include shear layers as a distinctive feature that defines initial mixing of waters with different temperatures, suspended sediment loads, or chemical compositions of dissolved matter [Best, 1987; Rhoads, 1996; Rhoads and Sukhodolov, 2008]. They also develop along river reaches with pronounced lateral heterogeneities of roughness, for instance, between a floodplain and a main channel [Alavian and Chu, 1985; Nadaoka and Yagi, 1998; van Prooijen et al., 2005], at the margins of recirculating flows of channel expansions [Babarutsi et al., 1989; Talstra, 2006], and along sequences of groynes in trained reaches [Uijttewaal et al., 2001; Sukhodolov et al., 2008]. [3] Hitherto, knowledge of lateral shear layers in fluvial systems has been provided mainly by experimental and analytical studies of shallow mixing layers [Chu and Babarutsi, 1988; Tukker, 1997; Uijttewaal and Booij, 2000; van Prooijen, 2004]. ...
Shallow lateral shear layers forming between flows with different velocities, though essential for mixing processes in natural streams, have been examined only in laboratory settings using smooth, fixed-bed channels. This paper reports the results of an experimental study of a shear layer in a straight reach of a natural river where the layer, in contrast to the two-dimensional structure observed in the laboratory, is highly three-dimensional. The study included pronounced transverse pressure gradients, which influenced shear layer structure compared to flume experiments. It also introduces an analysis that complements conventional theory on mixing layers. The lateral velocity gradient between the flows downstream from a splitter plate placed in the river, the principal controlling factor, was adjusted for three experimental runs to determine the influence of different gradients on shear-layer dynamics. In each run, detailed three-dimensional measurements of mean and turbulent characteristics were obtained at five cross sections downstream from the splitter plate. Although experimental results agreed with conventional mixing-layer theories with respect to turbulence, the dynamics of the shear layers were dominated by the mean lateral fluxes of momentum. After re-examining the governing equations, we developed a parabolic equation describing the shear layer evolution and several scaling relations for essential terms of the energy budget: mean and turbulent lateral fluxes of momentum, turbulent kinetic energy, and dissipation rates. The study also provides insight into the spectral dynamics of turbulence in the shear layer and clarifies previous observations reported for confluences in natural streams.
... Two regions with different streamwise velocities form a mixing layer at the interface between them (Uijttewaal & Booij 2000). With a uniform horizontal bed and a transversely uniform free-surface slope the velocity difference is disappearing gradually with downstream distance because the high-velocity side is decelerated by bed friction whereas the low velocity side is accelerated (Talstra et al. 2006). The eventual transversely uniform flow is established through friction and gravity rather than through a horizontal momentum exchange. ...
Shallow shear flows play an important role in the transverse transport of mass and momentum in rivers. In order to understand structure of the flow and the mechanism resulting in the particular turbulence properties, three types of shallow mixing layers are investigated each with a different cause for the velocity difference: inflow conditions, bed level and bed roughness. It is shown
that mixing layer properties are highly affected by the 3D turbulence generated in the bottom boundary layer. This implies that effects of subtle geometric properties like roughness variation and bed level changes should be incorporated in predictive models
The recirculating flow produced by a sudden widening of flow in a shallow open channel is computed using three turbulence models including (1) a constant-eddy-viscosity model; (2) a depth-averaged k-epsilon model; and (3) a two-length-scale model. The computational results demonstrate the existence of a friction-dominant regime. In this regime, all turbulence models give approximately the same recirculating length and the same recirculating flow rate despite the different levels of eddy viscosity determined by the models. The length of the recirculating zone obtained by the models is approximately equal to one frictional-length scale, and the recirculating flow rate equal to 2.5% of the frictional flow rate; these numerical results are in agreement with the experimental observations. The implication on the computation of the turbulent flow in natural waterways is discussed in light of these numerical results.
The Lagrangian second-moment method is used to compute the dye-concentration distribution in turbulent recirculating flow generated in a shallow open channel by a sudden widening of how in the transverse direction. The performance of the second-moment method is compared with the Eulerian numerical schemes of Upwind, QUICK, HLPA, and the semi-Lagrangian Hermite scheme. The results show that the Lagrangian second-moment method is an accurate and a very promising scheme for the computation of concentration distribution in flows dominated by advection. It minimizes the generation of numerical diffusion, is free from numerical oscillations, and is independent of the value of Courant number. Its efficiency in terms of computational time is high in flows where the mixing is confined to a small region of the solution domain and low in hows where the mixing is extended in the whole solution domain. In addition to an accurate numerical scheme, a necessary requirement for the accurate prediction of concentration field is a hydrodynamic model able to determine correctly the velocity held and the diffusion coefficient in shallow recirculating flows.