Dynamics and structure of decaying shallow dipolar vortices

Abstract

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.

On the existence and evolution of a spanwise vortex in laminar shallow water dipoles

“…The maximum vorticity of this vortex is stronger than that of the primary vortices [Figs. 2(b) and 2(d)], as observed by Lacaze et al 18 and Duran-Matute et al 19 As seen in Fig. 2(d), this vortex intersects the horizontal plane (white line at z ¼ 2h=3) at the meeting point of the secondary vertical vorticity patches in the horizontal plane [ Fig.…”

“…Emphasis will be put on generating an initially Q2D vortex dipole in order to ascertain that the origin of the three-dimensionalization lies in the quasi-two dimensional nature of the flow. The forcing will thus be twodimensional as in Lacaze et al 18 The present experimental study also inspired a companion numerical parametric study presented in Duran-Matute et al, 19 hereafter referred to as DMA. This companion work also includes some experiments for comparison issued, however, from a vortex generation forcing which is vertically dependent and therefore different from the one presented here.…”

Strain-vorticity induced secondary motion in shallow flows

“…(23) and (24) clearly demonstrate that the degree of two-dimensionality of the primary quasi-horizontal flow not only depends on the shallowness (δ) of the fluid layer but also on the magnitude of this primary flow (Re). The scaling of w and ∇ H · v H with δ and Re, δ 3 Re, and δ 2 Re, respectively, is consistent with recent findings by Duran-Matute et al 8,14 for decaying monopolar and dipolar vortices. Moreover, Eqs.…”

“…This evolution is confirmed by recently obtained experimental results on the dynamics and structure of decaying shallow dipolar vortices. 14 …”

The evolution of a continuously forced shear flow in a closed rectangular domain

“…However, it must be recalled that detailed 3D flow measurements in similar experiments have shown that important vertical motions might occur during the flow evolution 3,4 (see also a general review on shallow-layer flow experiments 31 ). In order to justify the predominantly 2D motion in our experiments, we consider a recently proposed scaling to determine the two-dimensionality of a shallow flow, 5,32 which establishes that the crucial parameter is not the smallness of the vertical aspect ratio δ v , but the product δ 2 v Re < 6, with Re the Reynolds number representing the response of the flow to the forcing. These nondimensional numbers can be defined as…”