Stability and vortex structures of quasi-two-dimensional shear flows

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

doi:10.3367/ufnr.0160.199007a.0001

Cited by 60 publications

(36 citation statements)

References 44 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: 99%

“…[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: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2001

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“…In conclusion, we would like to stress that the instability investigated in this paper differs fundamentally from that studied in the known works Nezlin and Snejkin (1990), as well as Doljanski et al (1990). In these papers a common shear instability was modeled (modified by rotation), provoked by the flows directed oppositely.…”

Section: Discussionmentioning

confidence: 99%

Topographic instability of flow in a rotating fluid

Patarashvili¹,

Tsakadze

Калашник³

et al. 2006

Nonlin. Processes Geophys.

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Abstract.Here are presented the results of experimental and theoretical studies on a stability of zonal geostrophic flows in the rotating layer of the shallow water. In the experiments, a special apparatus by Abastumani Astrophysical Observatory Georgian Academy of Science was used. This apparatus represents a paraboloid of rotation, which can be set in a regulable rotation around the vertical axis. Maximal diameter of the paraboloid is 1.2 m, radius of curvature in the pole is 0.698 m. In the paraboloid, water spreads on walls as a layer uniform on height under the period of rotation 1.677 s. Against a background of the rotating fluid, the zonal flows are formed by the source-sink system. It consists of two concentric circular perforations on the paraboloid bottom (width is 0.3 cm, radiuses are 8.4 and 57.3 cm, respectively); water can be pumped through them with various velocities and in all directions. It has been established that under constant vertical depth of the rotating fluid the zonal flows are stable. There are given the measurements of the radial profiles for the water level and velocity in the stationary regime. It has been found that zonal flows may lose stability under the presence of the radial gradient of full depth formed by a change of angular velocity of paraboloid rotation. An instability origin results in the loss of flow axial symmetry and in the appearance of self-excited oscillations in the zonal flow. At the given angular velocity of rotation, instability is observed only in the definite range of intensities of the source-sink system.The theoretical estimations are performed in the framework of the equations of the shallow water theory, including the terms describing the bottom friction. It has been shown that the instability of zonal flows found experimentally has a topographical nature and is related with non-monotone dependence of the potential vorticity on radius.Correspondence to: M. V. Kalashnik (lingel@obninsk.com)

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“…The mass source-sink method [2][3][4][5] is widely used to generate zonal flows under laboratory conditions. In the Coriolis force field the radial flow generated between the concentric mass source and sink is transformed into an azimuthal (zonal) flow.…”

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confidence: 99%

Formation of azimuthal flows driven by a mass source-sink system in a rotating paraboloid

Zhvaniya¹,

Калашник²,

Kakhiani³

et al. 2006

Fluid Dyn

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The process of formation of azimuthal flows generated by a mass source-sink system in a shallow water layer on the surface of a rotating paraboloid is investigated theoretically and experimentally. The calculations are carried out within the framework of the shallow-water equations with allowance for bottom friction. Asymptotic solutions describing the process of establishment of steadystate azimuthal flows which takes place after instantaneous initiation of the source-sink system are constructed. It is shown that theory and experiment are in satisfactory agreement.As follows from theory of hyperbolic equations, if we take the plus sign in Eq. (2.2) (source at the center), the boundary condition (2.3) must be imposed at the left end r = r 1 of the interval considered, if the minus

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Stability and vortex structures of quasi-two-dimensional shear flows

Cited by 60 publications

References 44 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

Topographic instability of flow in a rotating fluid

Formation of azimuthal flows driven by a mass source-sink system in a rotating paraboloid

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