Conformal invariance in three-dimensional rotating turbulence

We examine three--dimensional turbulent flows in the presence of solid-body rotation and helical forcing in the framework of stochastic Schramm-L\"owner evolution curves (SLE). The data stems from a run on a grid of $1536^3$ points, with Reynolds and Rossby numbers of respectively 5100 and 0.06. We average the parallel component of the vorticity in the direction parallel to that of rotation, and examine the resulting $_\textrm{z}$ field for scaling properties of its zero-value contours. We find for the first time for three-dimensional fluid turbulence evidence of nodal curves being conformal invariant, belonging to a SLE class with associated Brownian diffusivity $\kappa=3.6\pm 0.1$. SLE behavior is related to the self-similarity of the direct cascade of energy to small scales in this flow, and to the partial bi-dimensionalization of the flow because of rotation. We recover the value of $\kappa$ with a heuristic argument and show that this value is consistent with several non-trivial SLE predictions.Comment: 4 pages, 3 figures, submitted to PR

Statistical mechanics of Beltrami flows in axisymmetric geometry: Equilibria and bifurcations

We characterize the thermodynamical equilibrium states of axisymmetric Euler-Beltrami flows. They have the form of coherent structures presenting one or several cells. We find the relevant control parameters and derive the corresponding equations of state. We prove the coexistence of several equilibrium states for a given value of the control parameter like in 2D turbulence [Chavanis and Sommeria, J. Fluid Mech. 314, 267 (1996)]. We explore the stability of these equilibrium states and show that all states are saddle points of entropy and can, in principle, be destabilized by a perturbation with a larger wavenumber, resulting in a structure at the smallest available scale. This mechanism is therefore reminiscent of the 3D Richardson energy cascade towards smaller and smaller scales. Therefore, our system is truly intermediate between 2D turbulence (coherent structures) and 3D turbulence (energy cascade). We further explore numerically the robustness of the equilibrium states with respect to random perturbations using a relaxation algorithm in both canonical and microcanonical ensembles. We show that saddle points of entropy can be very robust and therefore play a role in the dynamics. We evidence differences in the robustness of the solutions in the canonical and microcanonical ensembles. A scenario of bifurcation between two different equilibria (with one or two cells) is proposed and discussed in connection with a recent observation of a turbulent bifurcation in a von Karman experiment [Ravelet et al., Phys. Rev. Lett. 93, 164501 (2004)].Comment: 25 pages; 16 figure

Geometrical statistics of the vorticity vector and the strain rate tensor in rotating turbulence

We report results on the geometrical statistics of the vorticity vector obtained from experiments in electromagnetically forced rotating turbulence. A range of rotation rates $\Omega$ is considered, from non-rotating to rapidly rotating turbulence with a maximum background rotation rate of $\Omega=5$ rad/s (with Rossby number much smaller than unity). Typically, in our experiments ${\rm{Re}}_{\lambda}\approx 100$. The measurement volume is located in the centre of the fluid container above the bottom boundary layer, where the turbulent flow can be considered locally statistically isotropic and horizontally homogeneous for the non-rotating case, see van Bokhoven et al., Phys. Fluids 21, 096601 (2009). Based on the full set of velocity derivatives, measured in a Lagrangian way by 3D Particle Tracking Velocimetry, we have been able to quantify statistically the effect of system rotation on several flow properties. The experimental results show how the turbulence evolves from almost isotropic 3D turbulence ($\Omega\lesssim 0.2$ rad/s) to quasi-2D turbulence ($\Omega\approx 5.0$ rad/s) and how this is reflected by several statistical quantities. In particular, we have studied the orientation of the vorticity vector with respect to the three eigenvectors of the local strain rate tensor and with respect to the vortex stretching vector. Additionally, we have quantified the role of system rotation on the self-amplification terms of the enstrophy and strain rate equations and the direct contribution of the background rotation on these evolution equations. The main effect is the strong reduction of extreme events and related (strong) reduction of the skewness of PDFs of several quantities such as, for example, the intermediate eigenvalue of the strain rate tensor and the enstrophy self-amplification term.Comment: 17 pages, 6 figures, 3 table

Dual Cascades in Axisymmetric Turbulence

International audienceA spectral analysis of strictly axisymmetric turbulence is performed. We investigate in particular by direct numerical simulation the possible cascades of energy and helicity. Decaying and forced flows at moderate Reynolds numbers are considered. A dual cascade, in which energy is transferred to the large scales and helicity to the small ones, is first evidenced in helical flows. A similar scenario is then shown to hold in the absence of a net helicity: in this case, energy also cascades to the largest scales, and positively and negatively polarized helicity are transferred to the small ones

Analysis of an ordinal outcome in a multicentric randomized controlled trial: application to a 3-arm anti- malarial drug trial in Cameroon

Background: Malaria remains a burden in Sub-Saharan Countries. The strategy proposed by the World Health Organization (WHO) is to systematically compare the therapeutic efficacy of antimalarial drugs using as primary outcome for efficacy, a four-category ordered criterion. The objective of the present work was to analyze the treatment effects on this primary outcome taking into account both a center-effect and individual covariates. A three-arm, three-centre trial of Amodiaquine (AQ), sulfadoxine-pyrimethamine (SP) and their combination (AQ + SP), conducted by OCEAC-IRD in 2003, in 538 children with uncomplicated Plasmodium falciparum malaria, is used as an illustration. Methods: Analyses were based on ordinal regression methods, assuming an underlying continuous latent variable, using either the proportional odds (PO) or the proportional hazards (PH) models. Different algorithms, corresponding to both frequentist- and bayesian-approaches, were implemented using the freely available softwares R and Winbugs, respectively. The performances of the different methods were evaluated on a simulated data set, and then they were applied on the trial data set. Results: Good coverage probability and type-1 error for the treatment effect were achieved. When the methods were applied on the trial data set, results highlighted a significance decrease of SP efficacy when compared to AQ (PO, odds ratio [OR] 0.14, 95% confidence interval [CI] 0.04-0.57; hazard ratio [HR] 0.605, 95% CI 0.42-0.82), and an equal effectiveness between AQ + SP and AQ (PO, odds ratio [OR] 1.70, 95% confidence interval [CI] 0.25-11.44; hazard ratio [HR] 1.40, 95% CI 0.88-2.18). The body temperature was significantly related to the responses. The patient weights were marginally associated to the clinical response. Conclusion: The proposed analyses, based on usual statistical packages, appeared adapted to take into account the full information contained in the four categorical outcome in malaria trials, as defined by WHO, with the possibility of adjusting on individual and global covariates

Cross-helicity in rotating homogeneous shear-stratified turbulence

International audienceWe consider homogeneous shear-stratified turbulence in a rotating frame, that exhibits complex nonlinear dynamics. Since the analysis of relative orientation between coupled fluctuating fields helps us to understand turbulence dynamics, we focus on the alignment properties of both the velocity and gravity fields with the potential vorticity gradient. With the help of statistical mechanics, we define a vector field which plays a role in the analogous so-called cross-helicity in magnetohydrodynamics. High-resolution direct numerical simulations of developed homogeneous baroclinic turbulence are performed, and a detailed analysis of probability density functions for cross-helicity is provided. A net preference for positive cross-helicity is shown to be related to a new alignment mechanism. We argue that the analysis of cross-helicity is crucial for understanding the dynamics of buoyancy driven flows