Experimental evidence for a new instability of a 
vertical columnar vortex pair in a strongly stratified fluid

Billant, Paul; Chomaz, Jean‐Marc

doi:10.1017/s0022112000001154

Cited by 144 publications

(161 citation statements)

References 28 publications

(47 reference statements)

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“…The Lamb-Chaplygin vortex dipole was chosen because of its resemblance to horizontal slices of experimentally created dipolar vortices. 3,4,[16][17][18] The vertical Poiseuille-like structure was chosen since it seems to be a realistic profile for time-dependent shallow flows. 9 Due to the symmetry with respect to the vertical plane y = 0, only the evolution of one half of the dipole ͑y Ͼ 0͒ is simulated.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Dynamics and structure of decaying shallow dipolar vortices

et al. 2010

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The current work reports on a numerical and experimental study of the evolution of decaying dipolar vortices in a shallow fluid layer. The dynamics and the structure of such vortices are investigated as a function of both their Reynolds number Re and the aspect ratio of vertical and horizontal length scales ␦. By quantifying the strength of the secondary motions ͑vertical motions and nonzero horizontal divergence͒ with respect to the swirling motions of the primary vortex cores, it was found that the three-dimensionality of a shallow ͑␦ Ӷ 1͒ dipolar vortex only depends on a single parameter: ␦ 2 Re. Depending on the value of this parameter, three flow regimes are observed for shallow dipolar vortices: ͑1͒ a quasi-two-dimensional regime where the structure of the dipolar vortex remains almost unchanged throughout its lifetime, ͑2͒ a transitional regime where the structure presents some three-dimensional characteristics but remains coherent, and ͑3͒ a three-dimensional regime where the structure of the dipolar vortex acquires a complicated three-dimensional shape with a persistent spanwise vortex at its front.

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Section: Numerical Simulationsmentioning

confidence: 99%

Dynamics and structure of decaying shallow dipolar vortices

et al. 2010

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“…As a consequence, the instability of the principal vortex never resulted in a complete vortex breakdown but saturated. For small Froude numbers (F r<1) the zigzag instability (Billant and Chomaz, 2000a) was observed eventually.…”

Section: Observationsmentioning

confidence: 99%

An experimental investigation on elliptical instability of a strongly asymmetric vortex pair in a stable density stratification

Cariteau

Flór

2006

Nonlin. Processes Geophys.

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Abstract. We investigate the elliptical instability of a strongly asymmetric vortex pair in a stratified fluid, generated by the acceleration and deceleration of the rotation of a single flap. The dominant parameter is the Froude number, F r=U/(N R), based on the maximum azimuthal velocity, U , and corresponding radius, R, of the strongest vortex, i.e. the principal vortex, and buoyancy frequency N . For F r>1, both vortices are elliptically unstable while the instability is suppressed for F r<1. In an asymmetric vortex pair, the principal vortex is less -and the secondary vortex more -elliptical than the vortices in an equivalent symmetric dipolar vortex. The far more unstable secondary vortex interacts with the principal vortex and increases the strain on the latter, thus increasing its ellipticity and its instability growth rate. The nonlinear interactions render the elliptical instability more relevant. An asymmetric dipole can be more unstable than an equivalent symmetric dipole. Further, the wavelength of the instability is shown to be a function of the Froude number for strong stratifications corresponding to small Froude numbers, whereas it remains constant in the limit of a homogenous fluid.

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“…[17][18][19][20][21] In a frame co-moving with the dipole, the horizontal flow in a Lamb-Chaplygin dipole is described by the following stream function given in cylindrical coordinates (r, θ ): 22…”

Section: Vertical Motion Inside a Lamb-chaplygin Dipolementioning

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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Experimental evidence for a new instability of a vertical columnar vortex pair in a strongly stratified fluid

Cited by 144 publications

References 28 publications

Dynamics and structure of decaying shallow dipolar vortices

Dynamics and structure of decaying shallow dipolar vortices

An experimental investigation on elliptical instability of a strongly asymmetric vortex pair in a stable density stratification

Strain-vorticity induced secondary motion in shallow flows

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