The goal of this study is to characterize the various breakdown states taking place in a swirling water jet as swirl ratio S and Reynolds number Re are varied. A pressure-driven discharges into large tank, being imparted by means motor which sets rotation honeycomb within settling chamber. experiments conducted for two distinct diameters varying while maintaining fixed range 300< <1200. Breakdown observed occur when reaches well defined threshold Sc ≈1.3–1.4 independent nozzle diameter...

Direct numerical simulations of stably and strongly stratified turbulent flows with Reynolds number Re ≫ 1 horizontal Froude F h ≪ are presented. The results interpreted on the basis a scaling analysis governing equations. suggests that there two different regimes according to parameter $\mathcal{R} \,{=}\, \hbox{\it Re} F^2_h$ . When \,{\gg}\, 1$ , viscous forces unimportant l v scales as ∼ U / N ( is characteristic velocity Brunt–Väisälä frequency) so dynamics flow inherently...

It is well-known that strongly stratified flows are organized into a layered pancake structure in which motions mostly horizontal but highly variable the vertical direction. However, what determines scale of motion remains an open question. In this paper, we propose scaling law for Lv when no lengthscales imposed by initial or boundary conditions and fluid stratified, i.e., Froude number small: Fh=U/NLh≪1, where U magnitude velocity, N Brunt–Väisälä frequency Lh lengthscale. Specifically,...

This paper shows that a long vertical columnar vortex pair created by double flap apparatus in strongly stratified fluid is subjected to an instability distinct from the Crow and short-wavelength instabilities known occur homogeneous fluid. new instability, which we name zigzag antisymmetric with respect plane separating vortices. It characterized vertically modulated twisting bending of whole almost no change dipole's cross- sectional structure. No saturation observed and, ultimately,...

The evolution of a Lamb–Oseen vortex is studied in stratified rotating fluid under the complete Coriolis force. In companion paper, it was shown that non-traditional force generates vertical velocity field and vorticity anomaly at critical radius when Froude number larger than unity. Below Rossby $\widetilde {Ro}$ , two-dimensional shear instability next triggered by anomaly. Here, we test robustness this against small three-dimensional perturbations. Direct numerical simulations (DNS) show...

The well-known Rayleigh criterion is a necessary and sufficient condition for inviscid centrifugal instability of axisymmetric perturbations. We have generalized this to disturbances any azimuthal wavenumber m by means large-axial-wavenumber WKB asymptotics. A free vortex with angular velocity real equal the inner cylinder radius. In sharp contrast, maximum growth rate non-axisymmetric then independent m.

This paper investigates the stability of a columnar vortex in an inviscid stratified fluid. By means WKBJ analysis for large axial wave number, we demonstrate that normal modes can be stable or unstable owing to emission internal waves from vortex. phenomenon is shown analogous radioactive decay nuclei quantum mechanics. The destabilized character associated with presence critical point radial structure mode. theoretical predictions frequency and growth rate are good agreement numerical...

A general theoretical account is proposed for the zigzag instability of a vertical columnar vortex pair recently discovered in strongly stratified experiment. The linear inviscid stability Lamb–Chaplygin analysed by multiple-scale expansion analysis small horizontal Froude number ( F h = U / L N , where magnitude velocity, lengthscale and Brunt–Väisälä frequency) v lengthscale) using scaling equations motion introduced Riley, Metcalfe & Weissman (1981). In limit 0, these reduce to...

A long-wavelength stability analysis of two co-rotating Gaussian vertical vortices in an inviscid strongly stratified fluid is conducted for separated by a large distance b compared to their radius ( ≫ ). This predicts and explains the zigzag instability found numerical companion paper (Otheguy, Chomaz & Billant, J. Fluid. Mech. vol. 553, 2006, p. 253). The results from coupling between bending perturbations each vortex external strain that one induces on other S = Γ/2 π 2 , where Γ...

We present high-resolution direct numerical simulations of the nonlinear evolution a pair counter-rotating vertical vortices in stratified fluid for various high Reynolds numbers Re and low Froude F h . The are bent by zigzag instability producing shear. There is no saturation so that exponential growth stopped only when viscous dissipation shear same order as horizontal transport, i.e. $Z^h_{\hbox{\it\scriptsize max}}$ / = O (1) where maximum enstrophy non-dimensionalized vortex turnover...

Abstract We investigate the spectral properties of turbulence generated during nonlinear evolution a Lamb–Chaplygin dipole in stratified fluid for high Reynolds number $Re= 28\hspace{0.167em} 000$ and wide range horizontal Froude ${F}_{h} \in [0. 0225~0. 135] $ buoyancy $\mathscr{R}= Re{{F}_{h} }^{2} [14~510] . The numerical simulations use weak hyperviscosity are therefore almost direct (DNS). After development zigzag instability, both shear gravitational instabilities develop lead to...

This paper investigates the three-dimensional stability of a Lamb–Chaplygin columnar vertical vortex pair as function wavenumber k z , horizontal Froude number F h Reynolds Re and Schmidt Sc . The ( = U / NR where is dipole travelling velocity, R radius N Brunt–Väisälä frequency) varied in range [0.033, ∞[ three set Reynolds-Schmidt numbers are investigated: { 10 000, 1}, 1000, 200, 637}. In whole dominant mode always antisymmetric with respect to middle plane between vortices but its...

This paper investigates the stability of an axisymmetric pancake vortex with Gaussian angular velocity in radial and vertical directions a continuously stratified-rotating fluid. The different instabilities are determined as function Rossby number $Ro$ , Froude $F_{h}$ Reynolds $Re$ aspect ratio ${\it\alpha}$ . Centrifugal instability is not significantly from case columnar due to its short-wavelength nature: it dominant when absolute $|Ro|$ large stabilized for small moderate generalized...

This paper investigates the three-dimensional stability of Lamb–Chaplygin vortex pair. Short-wavelength instabilities, both symmetric and antisymmetric, are found. The antisymmetric mode possesses largest growth rate is indeed one reported in a recent experimental study [J. Fluid Mech. 360, 85 (1998)]. rates, wave numbers maximum amplification, spatial eigenmodes these short-wavelength instabilities good agreement with predictions from elliptic instability theory. A long-wavelength similar...

The evolution of pancake dipoles different aspect ratio is studied in a stratified tank experiment. Two cases are reported here for values the dipole initial $\alpha_0 = L_v/L_h$ (where $L_v$ and $L_h$ vertical horizontal length scales, respectively) 0.4$ (case I) 1.2$ II). In first case, usual decay scenario observed where diffuses slowly with growing thickness decaying circulation. case II, we regime decreases circulation mid-plane vortices remains constant. We show that this scale can be...

We present a three-dimensional linear stability analysis of couple co-rotating vertical vortices in stratified fluid. When the fluid is non-stratified, two are unstable to elliptic instability owing deformation their core. These modes persist for weakly flow: . scaling laws and bending motion induced by this similar those zigzag counter-rotating vortex pair

This paper investigates the three-dimensional stability of a horizontal flow sheared horizontally, hyperbolic tangent velocity profile, in stably stratified fluid. In an homogeneous fluid, Squire theorem states that most unstable perturbation is two-dimensional. When stratified, this does not apply and we have performed numerical study to investigate characteristics flow. Froude number, F h , varied from ∞ 0.05, mode remains However, range vertical wavenumbers widens proportionally inverse...

In stratified and rotating fluids, pairs of columnar vertical vortices are subjected to three-dimensional bending instabilities known as the zigzag instability or tall-column in quasi-geostrophic limit. This paper presents a general asymptotic theory for these instabilities. The equations governing interactions between strain slow waves each vortex column fluids derived long wavelength when two well separated, i.e. radii R cores small compared separation distance b . These have same form...

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 vertical columnar dipoles. In experiments, measurements start to provide evidence existence inertial range that has been predicted for large turbulent buoyancy Reynolds numbers $\mathscr{R}_{t}={\it\varepsilon}_{\!K}/({\it\nu}N^{2})$ where ${\it\varepsilon}_{\!K}$ is mean dissipation rate kinetic energy, ${\it\nu}$...

This paper investigates the three-dimensional instabilities and transient growth of perturbations on a counter-rotating vortex pair. The two dimensional base flow is obtained by direct numerical simulation initialized Lamb–Oseen vortices that quickly adjust to with elliptic vortices. In present study, Reynolds number, ReΓ=Γ/ν, Γ circulation one ν kinematic viscosity, taken large enough for quasi steady assumption be valid. Both linearized Navier–Stokes equation its adjoint are solved...

The three-dimensional stability of vertical vortex pairs in stratified and rotating fluids is investigated using the analytical approach established Part 1 predictions are compared to results previous direct numerical analyses for co-rotating equal-strength Lamb–Oseen vortices new counter-rotating pairs. A very good agreement between theoretical generally found, thereby providing a comprehensive description zigzag instability. Co-rotating most unstable instability when Froude number F h =...

Abstract The stability of the flow between two concentric cylinders is studied numerically and analytically when fluid stably stratified. We show that such unstable angular velocity $\Omega (r)$ increases along radial direction, a regime never explored before. instability highly non-axisymmetric involves resonance families inertia–gravity waves like for strato-rotational instability. growth rate maximum only outer cylinder rotating goes to zero constant. sufficient condition linear, inviscid...

Abstract Swirling jets and vortices can both be unstable to the centrifugal instability but with a different wavenumber selection: most perturbations for swirling in inviscid fluids have an infinite azimuthal wavenumber, whereas, vortices, they are axisymmetric axial wavenumber. Accordingly, sufficient condition been derived asymptotically limits of large $m$ (Leibovich Stewartson, J. Fluid Mech. , vol. 126, 1983, pp. 335–356) dimensionless $k$ (Billant Gallaire, 542, 2005, 365–379). In this...

We present a novel experimental setup aimed at producing forced strongly stratified turbulent flow. The flow is by an arena of 12 vortex pair generators in large tank. continuous interactions the randomly produced pairs give rise to statistically stationary disordered contrast previous experiments where turbulence decaying. buoyancy frequency N set its highest value = 1.7 rad/s using salt as stratifying agent so that horizontal Froude number Fh Ω/N low, while Reynolds...