Alexandre Delache

On the two-dimensionalization of quasistatic magnetohydrodynamic turbulence

We analyze the anisotropy of turbulence in an electrically conducting fluid in the presence of a uniform magnetic field, for low magnetic Reynolds number, using the quasistatic approximation. In the linear limit, the kinetic energy of velocity components normal to the magnetic field decays faster than the kinetic energy of component along the magnetic field [H. K. Moffatt, “On the suppression of turbulence by a uniform magnetic field,” J. Fluid Mech. 28, 571 (1967)]. However, numerous numerical studies predict a different behavior, wherein the final state is characterized by dominant horizontal energy. We investigate the corresponding nonlinear phenomenon using direct numerical simulations. The initial temporal evolution of the decaying flow indicates that the turbulence is very similar to the so-called two-and-a-half-dimensional flow [D. Montgomery and L. Turner, “Two-and-a-half-dimensional magnetohydrodynamic turbulence,” Phys. Fluids 25, 345 (1982)] and we offer an explanation for the dominance of hori...

Scale by scale anisotropy in freely decaying rotating turbulence

We analyse the anisotropy present at different scales in rotating homogeneous turbulence. The Zeman wavenumber kΩ [O. Zeman, “A note on the spectra and decay of rotating homogeneous turbulence,” Phys. Fluids 6, 3221 (1994)] was introduced to quantify the effect of nonlinearity compared to the Coriolis force, and was proposed as a threshold to separate the anisotropic subrange, at scales k≪kΩ (largest scales), from the isotropic subrange at k≫kΩ. We study the nature of anisotropy and the role of the Zeman wavenumber using high resolution direct numerical simulations of freely decaying rotating turbulence, for various initial Rossby numbers. The anisotropy is analysed scale-by-scale by considering the angle-dependent energy spectrum, which characterizes directional anisotropy as a tendency to selectively accumulate energy towards the transverse waveplane k∥ = 0. This ring-to-ring anisotropy is shown to develop in a non-monotonic way from small to large wavenumbers, first increasing, then decreasing. The Zem...

Mechanical action of the blood onto atheromatous plaques: influence of the stenosis shape and morphology

The vulnerability of atheromatous plaques in the carotid artery may be related to several factors, the most important being the degree of severity of the endoluminal stenosis and the thickness of the fibrous cap. It has recently been shown that the plaque length can also affect the mechanical response significantly. However, in their study on the effect of the plaque length, the authors did not consider the variations of the plaque morphology and the shape irregularities that may exist independently of the plaque length. These aspects are developed in this paper. The mechanical interactions between the blood flow and an atheromatous plaque are studied through a numerical model considering fluid–structure interaction. The simulation is achieved using the arbitrary Lagrangian–Eulerian scheme in the COMSOL TM commercial finite element package. The stenosis severity and the plaque length are, respectively, set to 45% and 15 mm. Different shapes of the stenosis are modelled, considering irregularities made of several bumps over the plaque. The resulting flow patterns, wall shear stresses, plaque deformations and stresses in the fibrous cap reveal that the effects of the blood flow are amplified if the slope upstream stenosis is steep or if the plaque morphology is irregular with bumps. More specifically, the maximum stress in the fibrous cap is 50% larger for a steep slope than for a gentle slope. These results offer new perspectives for considering the shape of plaques in the evaluation of the vulnerability.

Modelling of fluid–structure interactions in stenosed arteries: effect of plaque deformability

This paper deals with the study of fluid structure interactions in stenosed arteries. Stenoses in arteries are usually induced by the formation of an atheromatous plaque. This is a major issue of public health. Diagnoses based on simple image analysis (measurement of stenosis severity) are currently insufficient for reducing the impact of the cardio-vascular diseases, which may provoke a decrease of life expectancy for the 25-45 generation in the near future. Improved diagnoses should be devised for avoiding this issue. Therefore, there is a real medical and economical interest in developing tools and systems for determining and understanding the mechanical response of plaques in the arteries

Dimensionality of Anisotropic Homogeneous Turbulence With Distortions: Compared Effects Between the Coriolis Force and the Lorentz Force

We consider initially isotropic homogeneous turbulence which is submitted to an external force, in statistically axisymmetric configurations. First, we study hydrodynamical turbulence in a rotating frame, in which case the Coriolis force modifies the structure and dynamics of the flow, thus creating elongated structures along the axis of rotation, corresponding to an accumulation of energy in the neighbourhood of the equatorial spectral plane. Secondly, a very similar configuration is that of magnetohydrodynamics (MHD) of a conducting fluid within an externally applied space uniform magnetic field, in which case the Lorentz force also concentrates energy to the same spectral equatorial manifold, but creates axially extending current sheets, along the magnetic field. We more specifically consider the quasi-static limit at small magnetic Reynolds number, in which the induction equation is analytically solved. We study the anisotropy of each turbulent flow using progressively refined statistics applied to results of direct numerical simulations, and we show that an accurate characterization of the flow structure requires advanced two-point statistics, which are available easily only in spectral space.Copyright

Toroidal/Poloidal Modes Dynamics in Anisotropic Turbulence

Isotropic turbulence receives a continuous effort for an increasingly refined description, but complex effects modify the dynamics of turbulence, and are poorly understood. Instances of distorted turbulence by external body forces are present throughout natural and industrial flows, as in geophysical flows submitted to the Earth’s rotation, and to density or temperature stratification. We focus here on the effects of stable stratification and solid body rotation on the dynamics and structure of homogeneous turbulence.We perform high resolution Direct Numerical Simulations (DNS), to characterize the 3D structure of anisotropic turbulence and its statistical properties. Vertical structures appear in rotating turbulence, or a layering in stably stratified turbulence, depending on the rotation rate and the density gradient, parameters that are varied in our simulations (see [8]).