Jérôme Fontane

Rare gas flow structuration in plasma jet experiments

Modifications of rare gas flow by plasma generated with a plasma gun (PG) are evidenced through simultaneous time-resolved ICCD imaging and schlieren visualization. The geometrical features of the capillary inside which plasma propagates before in-air expansion, the pulse repetition rate and the presence of a metallic target are playing a key role on the rare gas flow at the outlet of the capillary when the plasma is switched on. In addition to the previously reported upstream offset of the laminar to turbulent transition, we document the reverse action leading to the generation of long plumes at moderate gas flow rates together with the channeling of helium flow under various discharge conditions. For higher gas flow rates, in the l min−1 range, time-resolved diagnostics performed during the first tens of ms after the PG is turned on, evidence that the plasma plume does not start expanding in a laminar neutral gas flow. Instead, plasma ignition leads to a gradual laminar-like flow build-up inside which the plasma plume is generated. The impact of such phenomena for gas delivery on targets mimicking biological samples is emphasized, as well as their consequences on the production and diagnostics of reactive species.

The combined Lagrangian advection method

We present and test a new hybrid numerical method for simulating layerwise-two-dimensional geophysical flows. The method radically extends the original Contour-Advective Semi-Lagrangian (CASL) algorithm [5] by combining three computational elements for the advection of general tracers (e.g. potential vorticity, water vapor, etc.): (1) a pseudo-spectral method for large scales, (2) Lagrangian contours for intermediate to small scales, and (3) Lagrangian particles for the representation of general forcing and dissipation. The pseudo-spectral method is both efficient and highly accurate at large scales, while contour advection is efficient and accurate at small scales, allowing one to simulate extremely fine-scale structure well below the basic grid scale used to represent the velocity field. The particles allow one to efficiently incorporate general forcing and dissipation.

Stochastic forcing of the Lamb-Oseen vortex

The aim of the present paper is to analyse the dynamics of the Lamb–Oseen vortex when continuously forced by a random excitation. Stochastic forcing is classically used to mimic external perturbations in realistic configurations, such as variations of atmospheric conditions, weak compressibility effects, wing-generated turbulence injected in aircraft wake, or free-stream turbulence in wind tunnel experiments. The linear response of the Lamb–Oseen vortex to stochastic forcing can be decomposed in relation to the azimuthal symmetry of the perturbation given by the azimuthal wavenumber m. In the axisymmetric case m = 0, we find that the response is characterised by the generation of vortex rings at the outer periphery of the vortex core. This result is consistent with recurrent observations of such dynamics in the study of vortex-turbulence interaction. When considering helical perturbations m = 1, the response at large axial wavelengths consists of a global translation of the vortex, a feature very similar to the phenomenon of vortex meandering (or wandering) observed experimentally, corresponding to an erratic displacement of the vortex core. At smaller wavelengths, we find that stochastic forcing can excite specific oscillating modes of the Lamb–Oseen vortex. More precisely, damped critical-layer modes can emerge via a resonance mechanism. For perturbations with higher azimuthal wavenumber m > 2, we find no structure that clearly dominates the response of the vortex.

The Rayleigh-Taylor instability of two-dimensional high-density vortices

We investigate the stability of variable-density two-dimensional isolated vortices in the frame of incompressible mixing under negligible gravity. The focus on a single vortex flow stands as a first step towards vortex interactions and turbulent mixing. From heuristic arguments developed on a perturbed barotropic vortex, we find that highdensity vortices are subject to a Rayleigh–Taylor instability. The basic mechanism relies on baroclinic vorticity generation when the density gradient is misaligned with the centripetal acceleration field. For Gaussian radial distributions of vorticity and density, the intensity of the baroclinic torque due to isopycnic deformation is shown to increase with the ratio δ/δρ of the vorticity radius to the density radius. Concentration of mass near the vortex core is confirmed to promote the instability by the use of an inviscid linear stability analysis. We measure the amplification rate for the favoured azimuthal wavenumbers m=2, 3 on the whole range of positive density contrasts between the core and the surroundings. The separate influence of the density-contrast and the radius ratio is detailed for modes up to m=6. For growing azimuthal wavenumbers, the two-dimensional structure of the eigenmode concentrates on a ring of narrowing radial extent centred on the radius of maximum density gradient. The instability of the isolated high-density vortex is then explored beyond the linear stage based on high-Reynolds-number numerical simulations for modes m=2,3 and a moderate density contrast Cρ =0.5. Secondary roll-ups are seen to emerge from the nonlinear evolution of the vorticity and density fields. The transition towards m smaller vortices involves vorticity exchange between initially-rotating dense fluid particles and the irrotational less-dense medium. It is shown that baroclinic enstrophy production is associated with the centrifugal mass ejection away from the vortex centre.

The stability of the variable-density Kelvin-Helmholtz billow

We perform a three-dimensional stability analysis of the Kelvin-Helmholtz billow, developing in a shear-layer between two fluids with different density. We begin with two-dimensional simulations of the temporally evolving mixing-layer yielding the unsteady base flow fields. The Reynolds number is 1500 while the Schmidt and Froude numbers are infinite. Then exponentially unstable modes are extracted from a linear stability analysis performed at the saturation of the primary mode kinetic energy. The spectrum of the least stable modes exhibits two main classes. The first class comprises three-dimensional core-centred and braid-centred modes already present in the homogeneous case. The baroclinic vorticity concentration in the braid lying on the light side of the KH-billow turns the flow into a sharp vorticity ridge holding high shear levels. The hyperbolic modes benefit from the enhanced level of shear in the braid while elliptic ones remain quite insensitive to the modifications of the base flow. In the second class, we found typical two-dimensional modes resulting from a shear instability of the curved vorticity-enhanced braid. For a density contrast of 0.5, the wavelength of the two-dimensional instability is about ten times shorter than the one of the primary wave. Its amplification rate competes well against the ones of the hyperbolic three-dimensional modes. The vorticity-enhanced braid thus becomes the preferred location for the development of secondary instabilities. This stands as the key feature of the transition of the variable-density mixing layer. We carry out a fully resolved numerical continuation of the nonlinear development of the two-dimensional braid-mode. Secondary roll-ups due to a small-scale Kelvin-Helmholtz mechanism are promoted by the underlying strain field and develop rapidly in the compression part of the braid. Originally analysed in Reinaud et al. (2000) from two-dimensional non-viscous numerical simulations, this instability is shown to substantially increase the mixing.

Fractal Kelvin–Helmholtz breakups

The Kelvin–Helmholtz billow developing in an infinite- Schmidt number mixing layer at Re=1500 between two density-contrasted fluids experiences a two-dimensional shear instability. Secondary Kelvin–Helmholtz billows are seen to emerge on the light side of the primary structure, and then are advected towards the core of the main billow as the wave overturns. Due to the inertial baroclinic vorticity production, the braid region turns into a sharp vorticity ridge holding high shear levels and is thus sensitized to the Kelvin–Helmholtz instability. We carry out numerical simulations of the temporal development of the secondary mode when the flow is seeded at t=18 with the perturbation obtained from a linear stability analysis of the primary billow.

Evidence of the Influence of Plasma Jets on a Helium Flow into Open Air

Microplasma jets propagating in a helium flow surrounded by open air at ambient temperature have attracted the attention of many researchers for their putative ability to deliver high fluxes of reactive oxygen and nitrogen species to a target situated some centimeters away. This is of particular interest in biomedical applications. In this paper, we use Schlieren images to show that ignition of the plasma jet causes a reduction in the length of the laminar zone of the helium flow.

Vortical control of forced two-dimensional turbulence

A new numerical technique for the simulation of forced two-dimensional turbulence [D. Dritschel and J. Fontane, “The combined Lagrangian advection method,” J. Comput. Phys. 229, 5408–5417 (2010)10.1016/j.jcp.2010.03.048] is used to examine the validity of Kraichnan-Batchelor scaling laws at higher Reynolds number than previously accessible with classical pseudo-spectral methods, making use of large simulation ensembles to allow a detailed consideration of the inverse cascade in a quasi-steady state. Our results support the recent finding of Scott [R. Scott, “Nonrobustness of the two-dimensional turbulent inverse cascade,” Phys. Rev. E 75, 046301 (2007)10.1103/PhysRevE.75.046301], namely that when a direct enstrophy cascading range is well-represented numerically, a steeper energy spectrum proportional to k−2 is obtained in place of the classical k−5/3 prediction. It is further shown that this steep spectrum is associated with a faster growth of energy at large scales, scaling like t−1 rather than Kraichna...

The HyperCASL algorithm

This paper outlines a major new extension to the diabatic Contour-Advective Semi-Lagrangian (CASL) algorithm (Dritschel and Ambaum, 1997, 2006). The extension, called the ‘HyperCASL’ (HCASL) algorithm, advects material potential vorticity contours like in CASL, but treats diabatic forcing or damping with a Vortex-In-Cell (VIC) algorithm. As a result, HCASL is fully Lagrangian regarding advection. A conventional underlying grid is used as in CASL for ‘inversion’, namely for obtaining the advecting velocity from the potential vorticity.