Jean-Marc Chomaz

Experimental study of vortex breakdown in swirling jets

The goal of this study is to characterize the various breakdown states taking place in a swirling water jet as the swirl ratio S and Reynolds number Re are varied. A pressure-driven water jet discharges into a large tank, swirl being imparted by means of a motor which sets into rotation a honeycomb within a settling chamber. The experiments are conducted for two distinct jet diameters by varying the swirl ratio S while maintaining the Reynolds number Re fixed in the range 300 Re <1200. Breakdown is observed to occur when S reaches a well defined threshold Sc ≈1.3–1.4 which is independent of Re and nozzle diameter used. This critical value is found to be in good agreement with a simple criterion derived in the same spirit as the first stage of Escudier & Kellers (1983) theory. Four distinct forms of vortex breakdown are identified: the well documented bubble state, a new cone configuration in which the vortex takes the form of an open conical sheet, and two associated asymmetric bubble and asymmetric cone states, which are only observed at large Reynolds numbers. The two latter configurations differ from the former by the precession of the stagnation point around the jet axis in a co-rotating direction with respect to the upstream vortex flow. The two flow configurations, bubble or cone, are observed to coexist above the threshold Sc at the same values of the Reynolds number Re and swirl parameter S . The selection of breakdown state is extremely sensitive to small temperature inhomogeneities present in the apparatus. When S reaches Sc , breakdown gradually sets in, a stagnation point appearing in the downstream turbulent region of the flow and slowly moving upstream until it reaches an equilibrium location. In an intermediate range of Reynolds numbers, the breakdown threshold displays hysteresis lying in the ability of the breakdown state to remain stable for S Sc once it has taken place. Below the onset of breakdown, i.e. when 0 S Sc , the swirling jet is highly asymmetric and takes the shape of a steady helix. By contrast above breakdown onset, cross-section visualizations indicate that the cone and the bubble are axisymmetric. The cone is observed to undergo slow oscillations induced by secondary recirculating motions that are independent of confinement effects.

Scaling analysis and simulation of strongly stratified turbulent flows

Direct numerical simulations of stably and strongly stratified turbulent flows with Reynolds number Re >> 1 and horizontal Froude number F-h > 1, viscous forces are unimportant and l(v) scales as l ...

Self-similarity of strongly stratified inviscid flows

It is well-known that strongly stratified flows are organized into a layered pancake structure in which motions are mostly horizontal but highly variable in the vertical direction. However, what determines the vertical scale of the motion remains an open question. In this paper, we propose a scaling law for this vertical scale Lv when no vertical lengthscales are imposed by initial or boundary conditions and when the fluid is strongly stratified, i.e., when the horizontal Froude number is small: Fh=U/NLh≪1, where U is the magnitude of the horizontal velocity, N the Brunt–Vaisala frequency and Lh the horizontal lengthscale. Specifically, we show that the vertical scale of the motion is Lv=U/N by demonstrating that the inviscid governing equations in the limit Fh→0, without any a priori assumption on the magnitude of Lv, are self-similar with respect to the variable zN/U, where z is the vertical coordinate. This self-similarity fully accounts for the layer characteristics observed in recent studies reportin...

Absolute/convective instabilities in the Batchelor vortex: a numerical study of the linear impulse response

The absolute/convective instability properties of the Batchelor vortex are determined by direct numerical simulation of the linear impulse response. A novel decomposition procedure is applied to the computed wavepacket in order to retrieve the complex wavenumber and frequency prevailing along each spatio-temporal ray. In particular, the absolute wavenumber and frequency observed in the laboratory frame are determined as a function of swirl parameter and external flow. The introduction of a moderate amount of swirl is found to strongly promote absolute instability. In the case of wakes, the transitional helical mode that rst undergoes a switch-over to absolute instability is found to be m = 1 without requiring any external counterflow. In the case of jets, the transitional helical mode is very sensitive to swirl and varies in the range 56 m6 1. Only a slight amount of external counterflow (1:5% of centreline velocity) is then necessary to trigger absolute instability. The results of this numerical procedure are in good qualitative and quantitative agreement with those obtained by direct application of the Briggs{Bers criterion to the inviscid dispersion relation (Olendraru et al. 1996). Implications for the dynamics of swirling jets and wakes are discussed.

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

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 dipoles 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–Vaisala 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 F h 0 F h 0 = U 0 / NR , where U 0 and R are the initial dipole travelling velocity and radius). When F h 0 > 0.21, the elliptic instability develops resulting in three-dimensional motions which eventually collapse into a relaminarized vortex pair. Irregular zigzags are then also observed to grow. The threshold for the inhibition of the elliptic instability F h 0 = 0.2±0.01 is independent of N and in good agreement with the theoretical study of Miyazaki & Fukumoto (1992). Complete stabilization for F h 0 < 0.13 is probably due to viscous effects since the associated Reynolds number is low, Re 0 < 260. In geophysical flows characterized by low Froude numbers and large Reynolds numbers, we conjecture that this viscous stabilization will occur at much lower Froude number. It is tentatively argued that this new type of instability may explain the layering widely observed in stratified turbulent flows.

Mode selection in swirling jet experiments: a linear stability analysis

The primary goal of the study is to identify the selection mechanism responsible for the appearance of a double-helix structure in the pre-breakdown stage of so-called screened swirling jets for which the circulation vanishes away from the jet. The family of basic flows under consideration combines the azimuthal velocity profiles of Carton & McWilliams (1989) and the axial velocity profiles of Monkewitz (1988). This model satisfactorily represents the nozzle exit velocity distributions measured in the swirling jet experiment of Billant et al. (1998). Temporal and absolute/convective instability properties are directly retrieved from numerical simulations of the linear impulse response for different swirl parameter settings. A large range of negative helical modes, winding with the basic flow, are destabilized as swirl is increased, and their characteristics for large azimuthal wavenumbers are shown to agree with the asymptotic analysis of Leibovich & Stewartson (1983). However, the temporal study fails to yield a clear selection principle. The absolute/convective instability regions are mapped out in the plane of the external axial flow and swirl parameters. The absolutely unstable domain is enhanced by rotation and it remains open for arbitrarily large swirl. The swirling jet with zero external axial flow is found to first become absolutely unstable to a mode of azimuthal wavenumber

The effect of swirl on jets and wakes: Linear instability of the Rankine vortex with axial flow

m\,{=}\,{-}2

The structure of the near wake of a sphere moving horizontally in a stratified fluid

, winding with the jet. It is suggested that this selection mechanism accounts for the experimental observation of a double-helix structure.

Spiral vortex breakdown as a global mode

The effect of swirl on jets and wakes is investigated by analyzing the inviscid spatiotemporal instability of the Rankine vortex with superimposed plug flow axial velocity profile. The linear dispersion relation is derived analytically as a function of two nondimensional control parameters: the swirl ratio S and the external axial flow parameter a (a>−0.5 for jets, a<−0.5 for wakes). For each azimuthal wave number m, there exists a single unstable Kelvin–Helmholtz mode and an infinite number of neutrally stable inertial waveguide modes. Swirl decreases the temporal growth rate of the axisymmetric Kelvin–Helmholtz mode (m=0), which nonetheless remains unstable for all axial wave numbers. For helical modes (m≠0), small amounts of swirl lead to the widespread occurrence of direct resonances between the unstable Kelvin–Helmholtz mode and the inertial waveguide modes. Such interactions generate, in the low wave number range, neutrally stable wave number bands separated by bubbles of instability. As S increases...

Direct numerical simulations of round jets: Vortex induction and side jets

We present experimental results for the wake structure of spheres moving in homogeneous and stratified fluid. In homogeneous fluid, the results of Kim & Durbin (1988) are confirmed and it is shown that the two characteristic frequencies of the wake correspond to two instability modes, the Kelvin-Helmholtz instability and a spiral instability. For the stratified wake four general regimes have been identified, depending principally on the Froude number F. For F > 4.5 the near wake is similar to the homogeneous case, and for F < 0.8 it corresponds to a triple-layer flow with two lee waves, of amplitude linear in F, surrounding a layer dominated by quasi-twodimensional motion. Froude numbers close to one (F~]0.8,1.5[ ) give rise to a saturated lee wave of amplitude equal to half the sphere radius, which suppresses the separation region or splits it into two. Between F = 1.5 and 4.5 a more complex regime exists where the wake recovers progressively its behaviour in homogeneous fluid: the axisymmetry of the recirculating zone, the Kelvin-Helmholtz instability and, finally, the spiral instability.