On shallow-water wakes: an analytical study

The generation and evolution of large-scale vortices with vertical axis (macro-vortices) in a straight compound channel under quasi-uniform flow conditions is investigated. We discuss possible similarities and clear differences with free shear layer flows induced by the meeting of shallow streams of different speeds. An experimental investigation based on particle image velocimetry (PIV) measurements of free-surface velocities forms the basis for an analysis of both the specific features of macro-vortices and of the related mean flow characteristics. Dynamical properties strongly depend on the ratio r h between the main channel flow depth (h * mc ) and the floodplain depth (h * fp ), and three flow classes can be identified. 'Shallow flows' (r h > 3) are dominated by strong shearing and large macro-vortices populating the transition region between the main channel and the floodplains. The mean streamwise velocity induced in 'intermediate flows'(2 6 r h 6 3) is characterized by a dip in the transition region, while it closely resembles that occurring in a rectangular channel in the case of 'deep flows' (r h < 2). For both the latter cases the shear in the transition region decreases and the macro-vortices are also generated in the wall boundary layer of the floodplains. The typical size of the quasi-two-dimensional macro-vortices, generated at the transition region, is found to be independent of the streamwise coordinate. This and the non-monotonic behaviour of the mean streamwise velocity suggest that in straight compound channels the topographic forcing is so dominant that conceptual models interpreting these flows as free shear layers may largely fail to describe the physics of compound channels flows.

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“…shallow wakes discussed in Negretti et al 2006), will allow for an analytical description of the mean flow.…”

Section: Discussionmentioning

confidence: 99%

Horizontal mixing of quasi-uniform straight compound channel flows

Stocchino¹,

Brocchini

2010

J. Fluid Mech.

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“…Further investigation about free and wall turbulence in shallow flows can be found in Negretti et al 15 The nondimensional horizontal eddy viscosity representing free turbulence which is generated by the gradient of horizontal velocities is given by In this paper, the wall turbulence is assumed to be generated only from the bottom, not from a side wall.…”

Section: A Dispersive Stress By the Velocity Fluctuation Uјmentioning

confidence: 99%

Turbulent mixing and passive scalar transport in shallow flows

Kim¹,

Lynett²

2011

Physics of Fluids

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A depth-integrated model including subgrid scale mixing effects for turbulent transport by long waves and currents is presented. A fully nonlinear, depth-integrated set of equations for weakly dispersive and rotational flow is derived by the long wave perturbation approach. The same approach is applied to derive a depth-integrated scalar transport model which can accommodate small vertical variation of a weakly unsteady scalar. The proposed equations are solved by a fourth-order accurate finite volume method. The depth-integrated flow and transport models are applied to typical problems which have different mixing mechanisms. From the simulations, several important conclusions are obtained. ͑i͒ From simulation of a mixing layer generated by internal transverse shear, it is revealed that the dispersive stress implemented with a stochastic backscatter model ͑BSM͒ can play an important role for energy transfer in a shallow mixing layer. ͑ii͒ From a comparison of the characteristic width of a scalar plume in shallow and uniform flow, the proposed depth-integrated transport model coupled with the depth-integrated flow model can predict the passive scalar transport physically-that is, based on the turbulent intensity-without relying on a coarse empirical constant. ͑iii͒ From the same simulation, the inherent limitation of the two-dimensional horizontal model to capture vertical structure is recognized in near field. ͑iv͒ If the main mechanism of flow instability originates from relatively large-scale bottom topography features, then the effects of the dispersive stresses ͑i.e., BSM͒ are less important.

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“…The separation lines can roll and form the so-called Karman vortices. In particular, the bottom friction affects the stability of the wake similar to viscosity in laminar flow [22]. The bottom friction and the vertical extent of the water depth play a significant role in the dynamics of shallow wakes [21].…”

Section: Shallow-water Flow Modelingmentioning

confidence: 99%

“…The bottom friction and the vertical extent of the water depth play a significant role in the dynamics of shallow wakes [21]. In particular, the bottom friction affects the stability of the wake similar to viscosity in laminar flow [22]. For shallow-water flows dominated by bottom friction, the regimes of the unsteady wake are interpreted in terms of a stability parameter S = c f D/ h, in which c f is the friction coefficient at the bed, D is the cylinder diameter, and h is the water depth [23].…”

Section: Shallow-water Flow Modelingmentioning

confidence: 99%

Numerical simulation of laminar flow past a circular cylinder with slip conditions

Seo

Song

2011

Numerical Methods in Fluids

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SUMMARY The no‐slip condition is an assumption that cannot be derived from first principles and a growing number of literatures replace the no‐slip condition with partial‐slip condition, or Navier‐slip condition. In this study, the influence of partial‐slip boundary conditions on the laminar flow properties past a circular cylinder was examined. Shallow‐water equations are solved by using the finite element method accommodating SU/PG scheme. Four Reynolds numbers (20, 40, 80, and 100) and six slip lengths were considered in the numerical simulation to investigate the effects of slip length and Reynolds number on characteristic parameters such as wall vorticity, drag coefficient, separation angle, wake length, velocity distributions on and behind the cylinder, lift coefficient, and Strouhal number. The simulation results revealed that as the slip length increases, the drag coefficient decreases since the frictional component of drag is reduced, and the shear layer developed along the cylinder surface tends to push the separation point away toward the rear stagnation point so that it has larger separation angle than that of the no‐slip condition. The length of the wake bubble zone was shortened by the combined effects of the reduced wall vorticity and wall shear stress which caused a shift of the reattachment point closer to the cylinder. The frequency of the asymmetrical vortex formation with partial slip velocity was increased due to the intrinsic inertial effect of the Navier‐slip condition. Copyright © 2011 John Wiley & Sons, Ltd.

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On shallow-water wakes: an analytical study

Cited by 22 publications

References 12 publications

Horizontal mixing of quasi-uniform straight compound channel flows

Horizontal mixing of quasi-uniform straight compound channel flows

Turbulent mixing and passive scalar transport in shallow flows

Numerical simulation of laminar flow past a circular cylinder with slip conditions

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