Nonlinear evolution of the zigzag instability in stratified fluids: a shortcut on the route to dissipation (original) (raw)
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Onset of secondary instabilities on the zigzag instability in stratified fluids
Journal of Fluid Mechanics, 2011
Recently, Deloncle, Billant & Chomaz (J. Fluid Mech., vol. 599, 2008, p. 229) and Waite & Smolarkiewicz (J. Fluid Mech., vol. 606, 2008, p. 239) have performed numerical simulations of the nonlinear evolution of the zigzag instability of a pair of counter-rotating vertical vortices in a stratified fluid. Both studies report the development of a small-scale secondary instability when the vortices are strongly bent if the Reynolds number Re is sufficiently high. However, the two papers are at variance about the nature of this secondary instability: it is a shear instability according to Deloncle et al. (J. Fluid Mech., vol. 599, 2008, p. 229) and a gravitational instability according to Waite & Smolarkiewicz (J. Fluid Mech., vol. 606, 2008, p. 239). They also profoundly disagree about the condition for the onset of the secondary instability: ReF2h > O(1) according to the former or ReFh > 80 according to the latter, where Fh is the horizontal Froude number. In order to understand...
Journal of Fluid Mechanics, 2000
This paper shows that a long vertical columnar vortex pair created by a double flap apparatus in a strongly stratified fluid is subjected to an instability distinct from the Crow and short-wavelength instabilities known to occur in homogeneous fluid. This new instability, which we name zigzag instability, is antisymmetric with respect to the plane separating the vortices. It is characterized by a vertically modulated twisting and bending of the whole vortex pair with almost no change of the dipole's cross- sectional structure. No saturation is observed and, ultimately, the vortex pair is sliced into thin horizontal layers of independent pancake dipoles. For the largest Brunt–Väisälä frequency N = 1.75 rad s−1 that may be achieved in the experiments, the zigzag instability is observed only in the range of Froude numbers: 0.13 < Fh0 < 0.21 (Fh0 = U0/NR, where U0 and R are the initial dipole travelling velocity and radius). When Fh0 > 0.21, the elliptic instability develop...
Journal of Fluid Mechanics, 2006
This paper investigates the three-dimensional stability of a pair of co-rotating vertical vortices in a rotating strongly stratified fluid. In a companion paper , we have shown that such a basic flow in a strongly stratified fluid is affected by a zigzag instability which bends the two vortices symmetrically. In the non-rotating flow, the most unstable wavelength of this instability scales as the buoyancy length and its growth rate scales as the external strain that each vortex induces on the other one. Here, we show that the zigzag instability remains active whatever the magnitude of the planetary rotation and is therefore connected to the tallcolumn instability in quasi-geostrophic fluids. Its growth rate is almost independent of the Rossby number. The most amplified wavelength follows the universal scaling λ = 2πF h b γ 1 /Ro 2 + γ 2 /Ro + γ 3 , where b is the separation distance between the two vortices, (γ 1 , γ 2 , γ 3 ) are constants, F h is the horizontal Froude number and Ro the Rossby number (F h = Γ /πa 2 N, Ro = Γ /πa 2 f , where Γ is the circulation of each vortex, a the vortex radius, N the Brunt-Väisälä frequency and f the Coriolis parameter). When Ro = ∞, the scaling λ ∝ F h b found in the companion paper Otheguy et al. is recovered. When Ro → 0, λ ∝ bf/N in agreement with the quasi-geostrophic theory. In contrast to previous results, the wavelength is found to depend on the separation distance between the two vortices b, and not on the vortex radius a.
Three-dimensional stability of a vertical columnar vortex pair in a stratified fluid
Journal of Fluid Mechanics, 2000
This paper investigates the three-dimensional stability of a Lamb–Chaplygin columnar vertical vortex pair as a function of the vertical wavenumber kz, horizontal Froude number Fh, Reynolds number Re and Schmidt number Sc. The horizontal Froude number Fh (Fh = U/NR, where U is the dipole travelling velocity, R the dipole radius and N the Brunt–Väisälä frequency) is varied in the range [0.033, ∞[ and three set of Reynolds-Schmidt numbers are investigated: {Re = 10 000, Sc = 1}, Re = 1000, Sc = 1}, {Re = 200, Sc = 637}. In the whole range of Fh and Re, the dominant mode is always antisymmetric with respect to the middle plane between the vortices but its physical nature and properties change when Fh is varied. An elliptic instability prevails for Fh > 0.25, independently of the Reynolds number. It manifests itself by the bending of each vortex core in the opposite direction to the vortex periphery. The growth rate of the elliptic instability is reduced by stratification effects but ...
Evolution and instability of monopolar vortices in a stratified fluid
Physics of Fluids, 2003
The evolution of initially axisymmetric shielded pancake-like vortices in a nonrotating linearly stratified fluid has been investigated experimentally and numerically. The evolution process and the shape of tripoles in laboratory experiments depend on the experimental parameter values. In order to investigate this phenomenon we have considered the influence of the Reynolds ͑Re͒ and Froude ͑F͒ numbers on the tripole formation process. Also, the role of the ͑absolute͒ ratio ␥ between the vorticity values of the satellite vortices and the core vortex on the tripole evolution has been investigated. Additionally, a set of numerical simulations has been performed to enable an examination of the role of Reynolds numbers ͑up to Reϭ10 000) and Froude numbers (Fϭ0.1, 0.2, 0.4, and 0.8͒ outside the experimentally accessible range. The steepness parameter ␣ was varied between 2 and 8 in order to estimate the relative importance of the different modes constituting the perturbation. From this study we conclude that tripole formation and dipole splitting in a linearly stratified fluid can be well described in terms of the parameter set (Re,F,␣).
Physics of Fluids, 2019
Analyzing a large database of high-resolution three-dimensional direct numerical simulations of decaying rotating stratified flows, we show that anomalous mixing and dissipation, marked anisotropy, and strong intermittency are all observed simultaneously in an intermediate regime of parameters in which both waves and eddies interact nonlinearly. A critical behavior governed by the stratification occurs at Richardson numbers of order unity and with the flow close to being in a state of instability. This confirms the central dynamical role, in rotating stratified turbulence, of large-scale intermittency, which occurs in the vertical velocity and temperature fluctuations, as an adjustment mechanism of the energy transfer in the presence of strong waves.