International audienceDirect numerical simulations of stably and strongly stratified turbulent flows with Reynolds number Re " 1 and horizontal Froude number Fh Gt; 1 are presented. The results are interpreted on the basis of a scaling analysis of the governing equations. The analysis suggests that there are two different strongly stratified regimes according to the parameter R = ReFh2. When R " 1, viscous forces are nimportant and lv scales as lv ~ U/N (U is a characteristic horizontal velocity and N is the Brunt - Väis¨alä frequency) so that the dynamics of the flow is inherently three-dimensional but strongly anisotropic. When R " 1, vertical viscous shearing is important so that lv ~ lh/Re1/2 (lh is a characteristic horizontal length scale). The parameter R is further shown to be related to the buoyancy Reynolds number and proportional to (lO/?) 4/3, where lO is the Ozmidov length scale and ? the Kolmogorov length scale. This implies that there are simultaneously two distinct ranges in strongly stratified turbulence when R " 1: the scales larger than lO are strongly influenced by the stratification while those between lO and ? are weakly affected by stratification. The direct numerical simulations with forced large-scale horizontal two-dimensional motions and uniform stratification cover a wide Re and Fh range and support the main parameter controlling strongly stratified turbulence being R. The numerical results are in good agreement with the scaling laws for the vertical length scale. Thin horizontal layers are observed independently of the value of R but they tend to be smooth for R > 1, while for R > 1 small-scale three-dimensional turbulent disturbances are increasingly superimposed. The dissipation of kinetic energy is mostly due to vertical shearing for R > 1 but tends to isotropy as R increases above unity. When R > 1, the horizontal and vertical energy spectra are very steep while, when R > 1, the horizontal spectra of kinetic and potential energy exhibit an pproximate kh-5/3-power-law range and a clear forward energy cascade is observed. © 2007 Cambridge University Press

International audienceIt 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 Lu 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-Vïsälä 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?O, without any a priori assumption on the magnitude of Lu, 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 reporting spontaneous layering from an initially vertically uniform flow. For such a fine vertical scale, vertical gradients are large, O(1/FhLh). Therefore, even if the magnitude of the vertical velocity is small and scales like FhU, the leading order governing equations of these strongly stratified flows are not two-dimensional in contradiction with a previous conjecture. The self-similarity further suggests that the vertical spectrum of horizontal kinetic energy of pancake turbulence should be of the form E(kz)?N2kz-3, giving an alternative explanation for the observed vertical spectra in the atmosphere and oceans. © 2001 American Institute of Physics

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 & Keller's (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.

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 crosssectional structure. No saturation is observed and, ultimately, the vortex pair is sliced into thin horizontal layers of independent pancake dipoles. For the largest BruntVäisälä 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 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 h0 =0.2 ± 0.01 is independent of N and in good agreement with the theoretical study of Miyazaki & Fukumoto (1992). Complete stabilization for F h0 < 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. IntroductionFluid motions in the atmosphere and oceans are often strongly affected by stable density stratification. In these flows, large vertical motions are inhibited by the buoyancy force, leaving only two possible modes of motion: internal gravity waves and vortices with vertical axis (Riley, Metcalfe & Weissman 1981). Laboratory experiments (Lin & Pao 1979;Hopfinger 1987;Chomaz et al. 1993;Fincham, Maxworthy & Spedding 1996;Spedding, Browand & Fincham 1996;Spedding 1997;Bonnier, Eiff & Bonneton 2000), numerical simulations (Riley et al. 1981;Kimura & Herring 1996) and oceanic measurements (Gregg 1987) have revealed that these vortices never have a large vertical extent, but are † Present address:

The well-known Rayleigh criterion is a necessary and sufficient condition for inviscid centrifugal instability of axisymmetric perturbations. We have generalized this criterion to disturbances of any azimuthal wavenumber m by means of large-axialwavenumber WKB asymptotics. A sufficient condition for a free axisymmetric vortex with angular velocity Ω(r) to be unstable to a three-dimensional perturbation of azimuthal wavenumber m is that the real part of the growth rateis positive at the complex radius r = r 0 where ∂σ(r)/∂r =0, i.e.where φ =(1/r 3 )∂r 4 Ω 2 /∂r is the Rayleigh discriminant, provided that some ap o s t e r i o r ichecks are satisfied. The application of this new criterion to various classes of vortex profiles shows that the growth rate of non-axisymmetric disturbances decreases as m increases until a cutoff is reached. The criterion is in excellent agreement with numerical stability analyses of the Carton & McWilliams (1989) vortices and allows one to analyse the competition between the centrifugal instability and the shear instability. The generalized criterion is also valid for a vertical vortex in a stably stratified and rotating fluid, except that φ becomes φ =(1/r 3 )∂r 4 (where Ω b is the background rotation about the vertical axis. The stratification is found to have no effect. For the Taylor-Couette flow between two coaxial cylinders, the same criterion applies except that r 0 is real and equal to the inner cylinder radius. In sharp contrast, the maximum growth rate of non-axisymmetric disturbances is then independent of m.

Anthracnose, caused by the hemibiotrophic fungal pathogen Colletotrichum lindemuthianum is a devastating disease of common bean. Resistant cultivars are economical means for defense against this pathogen. In the present study, we mapped resistance specificities against 7 C. lindemuthianum strains of various geographical origins revealing differential reactions on BAT93 and JaloEEP558, two parents of a recombinant inbred lines (RILs) population, of Meso-american and Andean origin, respectively. Six strains revealed the segregation of two independent resistance genes. A specific numerical code calculating the LOD score in the case of two independent segregating genes (i.e. genes with duplicate effects) in a RILs population was developed in order to provide a recombination value (r) between each of the two resistance genes and the tested marker. We mapped two closely linked Andean resistance genes (Co-x, Co-w) at the end of linkage group (LG) B1 and mapped one Meso-american resistance genes (Co-u) at the end of LG B2. We also confirmed the complexity of the previously identified B4 resistance gene cluster, because four of the seven tested strains revealed a resistance specificity near Co-y from JaloEEP558 and two strains identified a resistance specificity near Co-9 from BAT93. Resistance genes found within the same cluster confer resistance to different strains of a single pathogen such as the two anthracnose specificities Co-x and Co-w clustered at the end of LG B1. Clustering of resistance specificities to multiple pathogens such as fungi (Co-u) and viruses (I) was also observed at the end of LG B2.

International audienceThis paper investigates the three-dimensional stability of a horizontal flow sheared horizontally, the hyperbolic tangent velocity profile, in a stably stratified fluid. In an homogeneous fluid, the Squire theorem states that the most unstable perturbation is two-dimensional. When the flow is stably stratified, this theorem does not apply and we have performed a numerical study to investigate the three-dimensional stability characteristics of the flow. When the Froude number, Fh, is varied from 8 to 0.05, the most unstable mode remains two-dimensional. However, the range of unstable vertical wavenumbers widens proportionally to the inverse of the Froude number for Fh " 1. This means that the stronger the stratification, the smaller the vertical scales that can be destabilized. This loss of selectivity of the two-dimensional mode in horizontal shear flows stratified vertically may explain the layering observed numerically and experimentally. © 2007 Cambridge University Press

We present high-resolution direct numerical simulations of the nonlinear evolution of a pair of counter-rotating vertical vortices in a stratified fluid for various high Reynolds numbers Re and low Froude numbers F h . The vortices are bent by the zigzag instability producing high vertical shear. There is no nonlinear saturation so that the exponential growth is stopped only when the viscous dissipation by vertical shear is of the same order as the horizontal transport, i.e. when Z h max /Re = O(1) where Z h max is the maximum horizontal enstrophy non-dimensionalized by the vortex turnover frequency. The zigzag instability therefore directly transfers the energy from large scales to the small dissipative vertical scales. However, for high Reynolds number, the vertical shear created by the zigzag instability is so intense that the minimum local Richardson number Ri decreases below a threshold of around 1/4 and small-scale Kelvin-Helmholtz instabilities develop. We show that this can only occur when ReF 2h is above a threshold estimated as 340. Movies are available with the online version of the paper.