Daniel Margerit

A computational code EZ-vortex* is developed for the motion of slender vortex filaments of closed or open shape. The integro-differential equations governing the motion of the vortex centre lines are either the Callegari and Ting equations, which are the leading order solution of a matched asymptotic analysis, or equivalent forms of these equations...

The dynamics of axial core-variations of axisymmetric shape on a vortex filament is derived from the Navier-Stokes equations in the slenderness limit. The core of the vortex is of similar, Rankine, or bubble type with a centerline of any shape. In this limit, a two-time-scale asymptotic approach is used to study the dynamics of the axial core-varia...

Algebraic formulas predicting the frequencies and shapes of waves in a reaction-diffusion model of excitable media are presented in the form of four recipes. The formulas themselves are based on a detailed asymptotic analysis (published elsewhere) of the model equations at leading order and first order in the asymptotic parameter. The importance of...

Three-dimensional scroll waves are considered in a reaction-diffusion model of excitable media in the large excitability limit. Coordinates based on the scroll filament are defined and shown to provide a natural extension of the coordinates used for two-dimensional spiral waves. The leading-order free-boundary equations for interface motion in thre...

The selection of shape and rotation frequency for scroll waves in reaction-diffusion equations modeling excitable media is investigated. For scrolls with uniform twist about straight filaments, asymptotic methods are used to derive free-boundary equations at leading and first order. Both orders are validated against full solutions of the reaction-d...

The Method of Matched Asymptotic Expansion of Singular Integrals (MAESI) is used to expand the Biot-Savart law in terms of different parameters. This method is first used to find, in terms of the small distance r to a line vortex, the first orders of the known expansion of the potential flow induced by this line vortex. This method is also used to...

In this paper, the idea of Prandtl’s boundary layer is exported to a field other than fluid dynamics. Excitable media, such as nerve fibers and heart tissue, are typically modelled with reaction-diffusion equations containing two chemical species that evolve on very different time scales. In three dimensions solutions of these equations take the fo...

The long bending distortions of the central line of a perturbed circular slender vortex ring with an axial velocity component are studied with the equation of motion of Callegari and Ting [1] rather than with the equation due to a cut-off method as in Widnall and Sullivan [2]. The link between the evolution of the perturbation and the inner structu...

We perform a comparison between the equation of motion of the central line of a slender vortex filament deduced from a matched asymptotic expansion, and the expansion of the equation of motion by using ad-hoc cut-off methods with cut-off length as small asymptotic parameter. The comparison justifies the cut-off methods and gives a link between the...

Equations for the axisymmetric part of the velocity field and for the equation of motion of a non circular slender vortex ring are given at first order. This is the correction to the known leading order given by Callegari and Ting [2].

Un filament tourbillon est un cas particulier d’écoulement rotationnel, pour lequel lavorticité se trouve uniquement autour d’une courbe tridimensionnel, dite fibre centrale dufilament. Calculer l’écoulement, c’est déterminer l’évolution de cette zone de vorticité, ditefilament tourbillon, c’est à dire trouver le mouvement de la fibre centrale. Cet...

In the context of vortex dynamics, and more specifically of complex interactions between vortex tubes, we present the validation tests for a code based on a Vortex Particle formulation and its detailed comparison with a pseudo-spectral code. For the test cases we have chosen the classical Crow geometry with different resolutions and a vortical reyn...

The potential hazard related to the two-vortex aircraft wake induces separation distances between aircrafts and associated delays at landing and take-off. Rennich and Lele (1998) have shown that the destruction of aircraft wake vortices can be accelerated by adding two flap-vortices between the trailing-edge vortices. Their results were obtained fr...