Integral model of shallow mixing layers

Booij, R.; Tukker, J.

doi:10.1080/00221680109499818

Cited by 19 publications

(13 citation statements)

References 13 publications

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“…The dipoles frequently observed in these flows have been widely studied and compared with theoretical 2D model. As shown recently by experiments carried out on mixing layers 13,14 and grid turbulence, 15 forced turbulent shallow flows can also develop a Q2D dynamics, characterized by emergence of large coherent vortices. These studies have revealed the simultaneous presence of large scale Q2D vortices and small scale 3D turbulence induced by bottom friction.…”

Section: Introductionmentioning

confidence: 64%

Turbulent vortex dipoles in a shallow water layer

2004

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Role of fluid density in shaping eruption currents driven by frontal particle blow-out Phys. Fluids 24, 066603 (2012) Reynolds number effect on the velocity increment skewness in isotropic turbulence Phys. Fluids 24, 015108 (2012) High-Reynolds-number turbulent-boundary-layer wall-pressure fluctuations with dilute polymer solutions Phys. Fluids 22, 085104 (2010) High-Reynolds shallow flow over an inclined sinusoidal bottom Phys. Fluids 22, 054110 (2010) Additional information on Phys. FluidsThis paper describes an experimental study on turbulent dipolar vortices in a shallow water layer. Dipoles are generated by an impulsive horizontal jet, by which a localized three-dimensional turbulent flow region is created. Dipole emergence is only controlled by the confinement number CϭͱQ/H 2 t inj whereas the jet Reynolds number ReϭͱQ/v has no influence in the studied range 50 000ϽReϽ75 000 ͑H is the water depth, v is the kinematical viscosity, Q the injected momentum flux and t inj the injection duration͒. When CϾ2, the flow becomes quasi-two-dimensional and a single vortex dipole emerges in most cases. By qualitative observations and application of particle image velocimetry, the main dipole features have been determined. The shallow water dipoles are characterized by the simultaneous presence of several scales of turbulence: A quasi-two-dimensional main flow at large scale and three-dimensional turbulent motions at small scale. A vertical circulation takes place in the dipole front. A theoretical model is presented and compared to experimental results. The three-dimensional turbulence production occurs mainly in the frontal circulation. A good agreement has been found between the model prediction and the measurements for the velocity evolution.

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Section: Introductionmentioning

confidence: 64%

Turbulent vortex dipoles in a shallow water layer

2004

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“…These authors consider that the agreement is satisfactory with their field measurements using a fixed spreading rate coefficient α=0.11. Note that Booij and Tukker (2001) The present shallow sudden expansions then consist in a fourth case. Regarding the outer velocity difference, the faster outer velocity U 1 (x) in the free stream is measured at y/d=1.5 for each section while U 2 (x) is the outer velocity on the recirculation side.…”

Section: Definitionsmentioning

confidence: 70%

Shallow Mixing Layer Downstream from a Sudden Expansion

2017

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The present paper aims at investigating the mixing layer located at the interface between the free stream and the recirculation zone downstream an open-channel, sudden, lateral expansion. Specific attention is paid on the interaction of the shallowness of the flow, characterized by the bed friction number, with the lateral confinement, due to the side wall. The velocity field for four flows, with the same geometry but very different bed friction numbers, is measured in detail in order to characterize the mean velocity fields and Reynolds stresses across the mixing layers and to evaluate the width of the mixing layers and their growth rates along with the typical oscillation frequencies. In the upstream region of the recirculation zone, the mixing layer characteristics for our configurations are analogous to the ones of classical-laterally unbounded-mixing layers. In this region, the shallowness modifies the shape of the streamwise velocity profiles, extends the mean velocity gradient magnitudes, lowers the Reynolds stress terms but hardly affects the mixing layer expansion rate. On the other hand, in the region near the flow reattachment, the mixing layer adopts a very different behavior, with an abrupt drop of the mixing layer expansion. This change in behavior is linked to the dynamics of the 2D vortices within the mixing layer. It is not due to a damping effect of the bed friction on these vortices as the local bed friction numbers remain much lower than the critical values reported in the literature. It is rather due to the interaction of the coherent structures with the side wall, the characteristics of this interaction being itself influenced

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“…The parameter S ml can be interpreted as a measure of the ratio of dissipation to production of kinetic energy contained in large eddies [ Socolofsky and Jirka , 2004; van Prooijen and Uijttewaal , 2002]. The critical value of S ml ( S mlc ) denotes equilibrium of dissipation and production; stability analyses indicate a value of S mlc between 0.06 and 0.12, whereas experimental work yields S mlc = 0.09 [ Booij and Tukker , 2001; Chu and Barbarutsi , 1988; Uijttewaal and Booij , 2000]. For S ml ≪ S mlc the effects of bottom friction on growth of instabilities are negligible and large turbulent structures develop within the mixing layer.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

“…Although has been used to analyze flow in shallow mixing layers, the number of terms usually is reduced to simplify its application to specific test cases. Experimental analysis [ Uijttewaal and Booij , 2000] and numerical modeling [ Booij and Tukker , 2001] of shallow mixing layers generally have neglected terms for turbulence and advective lateral fluxes of momentum (terms 2 and 3, left side ) and have viewed bed friction (term 2, right side ) as the dominant control of downstream decay in velocity differential between parallel flows. Analytical approaches to shallow wakes typically consider unidirectional flow past an isolated obstacle and attempt to define the influence of bed friction on wake evolution downstream of the obstacle [ Ghidaoui et al , 2006; Negretti et al , 2006].…”

Section: Theoretical Frameworkmentioning

confidence: 99%

Lateral momentum flux and the spatial evolution of flow within a confluence mixing interface

Rhoads

Sukhodolov

2008

Water Resources Research

132

111

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[1] Mixing interfaces at confluences have been viewed as analogous to shallow mixing layers in which lateral fluxes of momentum generally are viewed as unimportant. This investigation examines the spatial evolution of flow along a confluence mixing interface, focusing on lateral fluxes of momentum. Cross-stream profiles of depth-averaged mean velocities indicate that flow within the mixing interface has wake characteristics near the upstream junction corner, mixing-layer properties within the confluence, and attributes of a weak jet within the downstream channel. Convective acceleration of downstream velocity along the path of the mixing interface is influenced by lateral fluxes of momentum from the converging mean flow. These fluxes exceed turbulence lateral momentum fluxes by one to two orders of magnitude. Flow in the mixing interface is unstable, but lateral expansion of coherent turbulent vortices over distance is limited, possibly due to the inhibiting effects of the converging flow. Similar low-frequency oscillations in near-surface velocity fluctuations occur within the stagnation zone and along the mixing interface, suggesting that the dynamics of the stagnation-zone wake may influence low-frequency characteristics of flow in the downstream portion of the mixing interface. Patterns of turbulence kinetic energy (k) are influenced by lateral momentum fluxes, which progressively shift the zone of maximum k toward the outer bank. Overall the study shows that lateral momentum fluxes are important in the spatial evolution of flow within confluence mixing interfaces and need to be accounted for in theoretical treatments of these interfaces.

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Integral model of shallow mixing layers

Cited by 19 publications

References 13 publications

Turbulent vortex dipoles in a shallow water layer

Turbulent vortex dipoles in a shallow water layer

Shallow Mixing Layer Downstream from a Sudden Expansion

Lateral momentum flux and the spatial evolution of flow within a confluence mixing interface

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