Evolution and instability of monopolar vortices in a stratified fluid (original) (raw)
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Numerical study of the evolution of vortices in a linerly stratified fluid
Il Nuovo Cimento C, 1999
This paper presents a numerical study in which the evolution of vortices in a stratified fluid is compared to the evolution of two-dimensional vortices. The influence of the Reynolds number and the Froude number are investigated, for the evolution of axisymmetric vortices, for their azimuthal instability and for the subsequent formation of tripoles. It is found that due to radial diffusion axisymmetric vortices with various initial vorticity profiles all evolve towards the same profile. This evolution reduces the growth of azimuthal instabilities which may lead to the formation of a tripole. For vortices in a stratified fluid the effect of the ambient stratification on the evolution of the vortices is investigated. It is found that a process of vortex stretching, which becomes more pronounced for increasing Froude numbers, leads to a weaker tripole formation.
The structure and dynamics of dipolar vortices in a stratified fluid
Journal of Fluid Mechanics, 2005
The three-dimensional structure and decay of a dipolar vortex in a linearly stratified fluid is investigated experimentally using a high-resolution three-dimensional scanning correlation image velocimetry system (SCIV). Comparisons with simple theoretical and numerical models are made for late times in the low-Froude-number regime. The relatively well-known stratified dipole, most of the time assumed to be quasitwo-dimensional, is revealed to have a complex three-dimensional vortex topology arising from its self-induced propagation. As the buoyancy scale u/N approaches zero the dynamics of such a structure are dominated by the horizontal velocity field, whereas the diffusion is mainly vertical. The evolution is then governed by an effective Reynolds number, Re eff , based on vertical diffusion and horizontal advection. At early times this effective Reynolds number is large, horizontal advection terms dominate and a decrease of aspect ratio of the structure is observed until Re eff reaches a critical value Re c eff ∼ O(1), independent of the initial condition and associated with a horizontal advection-vertical diffusion balance. Thereafter the evolution becomes purely diffusive with decay time Re c eff .
An experimental study of dipolar vortex structures in a stratified fluid
Journal of Fluid Mechanics, 1994
This paper describes laboratory experiments on dipolar vortex structures in a linearly stratified fluid. The dipoles are generated by a pulsed horizontal injection of a small volume of fluid, by which a localized three-dimensionally turbulent flow region is created. After the subsequent gravitational collapse the flow becomes approximately two-dimensional, and eventually a single vortex dipole emerges, as the result of the self-organizing properties of such flows. The flow evolution has been visualized both by dye and tracer particles, through which qualitative as well as quantitative information was obtained. By application of digital image analysis, the spatial distribution of the velocity ν, vorticity ω and stream function ψ were determined. It was found that dipoles in the turbulent-injection experiments are characterized by a nonlinear sinh-like relationship between ω and ψ, whereas in the case of laminar injection the (ω, ψ)-scatter plots of the dipoles reveal a linear relatio...
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...
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 ...
Horizontal jets and vortex dipoles in a stratified fluid
Journal of Fluid Mechanics, 1991
When a horizontal force is applied locally to some volume of a viscous densitystratified fluid, flows with high concentration of vertically oriented vorticity (vortex dipoles) are generated. The processes of generation and evolution with time of these unsteady flows in a stratified fluid are studied. A convenient way to produce and study these flows in the laboratory is to use a submerged horizontal jet as a ‘point’ source of momentum. The main governing parameter (the ‘force’) is easily controlled in this case. Two regimes were studied: starting jets with dipolar vortex fronts (the force acts continuously) and impulsive vortex dipoles (the force acts for a short period of time). A conductivity microprobe, aluminium powder, shadowgraph, thymol-blue and other techniques have been used to measure the velocity and density distributions in the flows. It is found that in both regimes the flows are self-similar: the lengthscale of the flows increases with time as t½ for starting jets and ...
5th AIAA Theoretical Fluid Mechanics Conference, 2008
An aircraft wake is made of counter-rotating vortices and is known to be affected by a long (Crow) and a short (elliptic) wavelength instabilities. Numerical investigations on the three-dimensionnal instabilities and transient growth of such dipole are performed. By means of a three-dimensionnal linear stability analysis, we retrieve the instability bands corresponding to the Crow and elliptic modes but we also observe less unstable oscillatory modes with very broad peaks. The transient growth of perturbations on this dipole, investigated by computing the optimal linear perturbations with a direct-adjoint technique, demonstrates the crucial role of the region of maximal strain at short time and of the hyperbolic point at intermediate time. Investigations on the three-dimensionnal dynamics of trailing vortices in stratified fluids are performed. The elliptic instability is almost unaffected by weak and moderate stratifications. Résumé : Le sillage d'un avion est constitué d'un paire de tourbillons contra-rotatifs et est affectée par une instabilité à grande (Crow) et à petite (elliptique) longueur d'onde. On réalise des études numériques sur les instabilités tridimensionnelles d'un tel dipole. Par une étude de stabilité linéaire tridimensionnelle, on retrouve les bandes d'instabilité correspondant aux modes de Crow et elliptiques mais on observe également des modes oscillants moins instables avec des pics très larges. Les croissances transitoires des perturbations sur ce dipole, qui sont étudiées en calculant les perturbations optimales linéaires par une technique direct-adjoint, démontrent le rôle crucial de la région où l'étirement est maximal aux temps courts et du point hyperbolique aux temps intermédiaires. Des études sur la dynamique tridimensionnelle des tourbillons de sillage d'avion en fluide stratifié sont réalisées. L'instabilité elliptique n'est pratiquement pas affectée par des stratifications faible et modérée.
Stratified turbulence forced with columnar dipoles: numerical study
Journal of Fluid Mechanics, 2015
This paper builds upon the investigation of Augier et al. (Phys. Fluids, vol. 26 (4), 2014) in which a strongly stratified turbulent-like flow was forced by 12 generators of vertical columnar dipoles. In experiments, measurements start to provide evidence of the existence of a strongly stratified inertial range that has been predicted for large turbulent buoyancy Reynolds numbers mathscrRt=itvarepsilon!K/(itnuN2)\mathscr{R}_{t}={\it\varepsilon}_{\!K}/({\it\nu}N^{2})mathscrRt=itvarepsilon!K/(itnuN2), where itvarepsilon!K{\it\varepsilon}_{\!K}itvarepsilon!K is the mean dissipation rate of kinetic energy, itnu{\it\nu}itnu the viscosity and NNN the Brunt–Väisälä frequency. However, because of experimental constraints, the buoyancy Reynolds number could not be increased to sufficiently large values so that the inertial strongly stratified turbulent range is only incipient. In order to extend the experimental results toward higher buoyancy Reynolds number, we have performed numerical simulations of forced stratified flows. To reproduce the experimental vortex generators, columnar di...
Three-dimensionnal instabilities and transient growth of trailing vortices
HAL (Le Centre pour la Communication Scientifique Directe), 2007
An aircraft wake is made of counter-rotating vortices and is known to be affected by a long (Crow) and a short (elliptic) wavelength instabilities. Numerical investigations on the three-dimensionnal instabilities and transient growth of such dipole are performed. By means of a three-dimensionnal linear stability analysis, we retrieve the instability bands corresponding to the Crow and elliptic modes but we also observe less unstable oscillatory modes with very broad peaks. The transient growth of perturbations on this dipole, investigated by computing the optimal linear perturbations with a direct-adjoint technique, demonstrates the crucial role of the region of maximal strain at short time and of the hyperbolic point at intermediate time. Investigations on the three-dimensionnal dynamics of trailing vortices in stratified fluids are performed. The elliptic instability is almost unaffected by weak and moderate stratifications. Résumé : Le sillage d'un avion est constitué d'un paire de tourbillons contra-rotatifs et est affectée par une instabilité à grande (Crow) et à petite (elliptique) longueur d'onde. On réalise des études numériques sur les instabilités tridimensionnelles d'un tel dipole. Par une étude de stabilité linéaire tridimensionnelle, on retrouve les bandes d'instabilité correspondant aux modes de Crow et elliptiques mais on observe également des modes oscillants moins instables avec des pics très larges. Les croissances transitoires des perturbations sur ce dipole, qui sont étudiées en calculant les perturbations optimales linéaires par une technique direct-adjoint, démontrent le rôle crucial de la région où l'étirement est maximal aux temps courts et du point hyperbolique aux temps intermédiaires. Des études sur la dynamique tridimensionnelle des tourbillons de sillage d'avion en fluide stratifié sont réalisées. L'instabilité elliptique n'est pratiquement pas affectée par des stratifications faible et modérée.