An advanced experimental investigation of quasi-two-dimensional shear flow

Dolzhanskii, F. V.; Krymov, V. A.; Manin, D. Yu.

doi:10.1017/s0022112092002209

Cited by 60 publications

(43 citation statements)

References 9 publications

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“…19 As yet, it is not completely clear whether this approximation is valid in general for shallow water flows. It is worthwhile to note that it was shown by Dolzhanskii et al 14,15 that the 2D hydrodynamic equation with Rayleigh friction correctly describes the stability of shear flows in thin layers of homogeneous fluid.…”

Section: Introductionmentioning

confidence: 88%

“…[8][9][10] Besides the experiments on soap films, it is also possible to study Q2D flows in a thin layer of fluid inside a container, for example, the experiments on vortex interactions performed by Antonova et al 11 and the experiments on freely decaying Q2D turbulence by Tabeling et al 12 In the latter experiment, but also in several other studies of this type, the flow is forced electromagnetically. Other examples are the experiments on the interaction of allocated vortices performed by Danilov et al 13 and the experimental study of Q2D shear flows by Dolzhan-skii et al 14,15 In the experimental studies on thin-layer flows of this type, usually a single layer of fluid is used. Recently, in the experiments of Paret and Tabeling, 16 a system of saltstratified fluid layers was used.…”

Section: Introductionmentioning

confidence: 99%

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Three-dimensional structure and decay properties of vortices in shallow fluid layers

et al. 2001

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Recently, several laboratory experiments on vortex dynamics and quasi-two-dimensional turbulence have been performed in thin (stratified) fluid layers. Commonly, it is tacitly assumed that vertical motions, giving rise to a three-dimensional character of the flow, are inhibited by the limited vertical dimension. However, shallow water flows, which are vertically bounded by a no-slip bottom and a free surface, necessarily possess a three-dimensional structure due to the shear in the vertical direction. This shear may lead to significant secondary circulations. In this paper, the three-dimensional (3D) structure and the decay properties of vortices in shallow layers of fluid, both homogeneous and stratified, have been studied in detail by 3D direct numerical simulations. The quasi-two-dimensionality of these flows is an important issue if one is interested in a comparison of experiments of this type with purely two-dimensional theoretical models. The influence of several flow parameters, like the depth of the fluid and the Reynolds number, has been investigated. In general, it can be concluded that the flow loses its two-dimensional character for larger fluid depth and larger Reynolds number. Furthermore, it is possible to construct a regime diagram that allows the assessment of the parameter regime, where the flow can be considered as quasi-two-dimensional. It is found that the presence of secondary circulations within a planar vortex flow results in a deformation of the radial profile of axial vorticity. In the limiting case of quasi-two-dimensional flow, the vorticity profiles can be scaled according to a simple diffusion model. In a two-layer stratified system, the decay is reduced and three-dimensional motions are significantly inhibited compared to the corresponding flows in a homogeneous layer.

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Section: Introductionmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Three-dimensional structure and decay properties of vortices in shallow fluid layers

et al. 2001

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“…The forcing system is an adaptation of a well-known system commonly used for shallow-flow experiments, introduced by Sommeria (1986), and independently further developed by Tabeling et al (1991) and Dolzhanskii et al (1992). The system consists of a container filled with a layer of mercury (Sommeria, 1986) or NaCl solution (Tabeling et al, 1991, Dolzhanskii et al, 1992, and a constant current density field parallel to the bottom of the container.…”

Section: Electromagnetic Forcingmentioning

confidence: 99%

“…The system consists of a container filled with a layer of mercury (Sommeria, 1986) or NaCl solution (Tabeling et al, 1991, Dolzhanskii et al, 1992, and a constant current density field parallel to the bottom of the container. The current is provided by a power supply, and it is homogeneously distributed through the fluid via two electrodes placed along two opposite sides of the domain.…”

Section: Electromagnetic Forcingmentioning

confidence: 99%

Table-top rotating turbulence: an experimental insight through particle tracking

Castello

Clercx

Trieling

et al. 2009

Springer Proceedings in Physics

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“…Such vertical dependence of the horizontal flow field is consistent with the fact that the flow is dominated by bottom drag as will become clear later. From previous studies, 8,9 it was concluded that such flows relax quickly to a Poiseuille flow, which is usually modeled by a Rayleigh bottom friction term 10,11 as implied by (3) and (4) when substituted in (1). The pressure distribution inside the fluid layer is dictated by the following Poisson equation that results from taking the divergence of (1):…”

Section: Quasi-linear Theory Of Secondary Motion In Q2d Shallow Fmentioning

confidence: 99%

Strain-vorticity induced secondary motion in shallow flows

Kamp

2012

Physics of Fluids

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Deviations from two-dimensionality of a shallow flow that is dominated by bottom friction are quantified in terms of the spatial distribution of strain and vorticity as described by the Okubo-Weiss function. This result is based on a Poisson equation for the pressure in a quasi-horizontal (primary) flow. It is shown that the Okubo-Weiss function specifies vertical pressure gradients, which for their part drive vertical (secondary) motion. An asymptotic expansion of these gradients based on the smallness of the vertical to horizontal scale ratio demonstrates that the sign and magnitude of secondary circulation inside the fluid layer is dictated by the signs and magnitude of the Okubo-Weiss function. As a consequence of this, secondary motion as well as nonzero horizontal divergence do also depend on the strength, i.e., the Reynolds number of the primary flow. The theory is exemplified by two generic vortical structures (monopolar and dipolar structures). Most importantly, the theory can be applied to more complicated turbulent shallow flows in order to assess the degree of two-dimensionality using measurements of the free-surface flow only.

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An advanced experimental investigation of quasi-two-dimensional shear flow

Cited by 60 publications

References 9 publications

Three-dimensional structure and decay properties of vortices in shallow fluid layers

Three-dimensional structure and decay properties of vortices in shallow fluid layers

Table-top rotating turbulence: an experimental insight through particle tracking

Strain-vorticity induced secondary motion in shallow flows

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