Agnès Maurel

Comparison between an experimental turbulent vortex and the Lundgren vortex

In a recent letter (Cuypers Y et al 2003 Phys. Rev. Lett. 91 194502), the authors presented experimental results on a structure resulting from a vortex burst. The temporal evolution of this structure results in the k  − 5/3 Kolmogorov spectrum and some common features with the Lundgren theoretical vortex have been shown. The purpose of the present paper is to go further in the comparison with the Lundgren model by a parallel analysis of the experimental structure and of a Lundgren single spiral vortex, whose evolution is numerically obtained based on the calculations of Pullin et al (1993 Phys. Fluids A 5 126; 1994 Phys. Fluids 6 3010).

Experimental and theoretical inspection of the phase-to-height relation in Fourier transform profilometry

The measurement of an objects shape using projected fringe patterns needs a relation between the measured phase and the objects height. Among various methods, the Fourier transform profilometry proposed by Takeda and Mutoh [Appl. Opt.22, 3977-3982 (1983)] is widely used in the literature. Rajoub et al. have shown that the reference relation given by Takeda is erroneous [J. Opt. A. Pure Appl. Opt.9, 66-75 (2007)]. This paper follows from Rajoubs study. Our results for the phase agree with Rajoubs results for both parallel- and crossed-optical-axes geometries and for either collimated or noncollimated projection. Our two main results are: (i) we show experimental evidence of the error in Takedas formula and (ii) we explain the error in Takedas derivation and we show that Rajoubs argument concerning Takedas error is not correct.

Lamb wave propagation in elastic waveguides with variable thickness

The problem of Lamb wave propagation in waveguides with varying height is treated by a multimodal approach. The technique is based on a rearrangement of the equations of elasticity that provides a new system of coupled mode equations preserving energy conservation. These coupled mode equations avoid the usual problem at the cut-offs with zero wavenumber. Thereafter, we define an impedance matrix that is governed by a Riccati equation yielding a stable numerical computation of the solution. Incidentally, the versatility of the multimodal method is exemplified by treating analytically the case of slowly varying guide and by showing how to get easily the Green tensor in any geometry. The method is applied for a waveguide whose height is described by a Gaussian function and the energy conservation in verified numerically. We determine the Green tensor in this geometry.

Lamb wave propagation in inhomogeneous elastic waveguides

The problem of Lamb wave propagation in an axially multi–layered waveguide is treated by a multi–modal approach. A general formalism is proposed that avoids the numerical divergence due to evanescent modes and that is based on an impedance matrix. To describe the fields, we choose a 4–vector composed of the displacements and the horizontal stresses. Due to symmetry properties of the right– and left–going modes, this 4–vector can be split into two 2–vectors described by only two sets of modal components. Moreover, the modal 2–vectors have a biorthogonality relation that allows us to express the fields continuity at the interface between two media in a simple manner. Formally, this approach permits us to extend the multi–modal formalism from fluidic to elastic waveguides. In this context, the impedance matrix is defined as the linear operator that links the two sets of modal components. As in the fluidic case, the impedance matrix has the advantage of avoiding numerical divergence, and can be used to obtain the reflection and transmission matrices, as well as the wave fields. The technique is validated in the case of two semi–infinite elastic plates bounded along their lateral faces (succession of two media) and is also applied to a thick bonding (succession of three media) and to a periodic waveguide (succession of multiple media).

Scattering matrix properties with evanescent modes for waveguides in fluids and solids

Reciprocity, energy conservation, and time-reversal invariance are three general properties of the wave fields that imply algebraic scattering matrix properties. In this paper, these scattering matrix properties are established for waveguides when evanescent modes are taken into account. The situations correspond to guided acoustic pressure waves in fluids and Lamb waves in solids treated with the same formalism. The relations between the three properties verified by the scattering matrix are then discussed, and it is found that, as soon as two properties are verified, the third is also verified.

Experimental study on water-wave trapped modes

We present an experimental study on the trapped modes occurring around a vertical surface-piercing circular cylinder of radius a placed symmetrically between the parallel walls of a long but finite water waveguide of width 2 d . A wavemaker placed near the entrance of the waveguide is used to force an asymmetric perturbation into the guide, and the free-surface deformation field is measured using a global single-shot optical profilometric technique. In this configuration, several values of the aspect ratio a / d were explored for a range of driving frequencies below the waveguides cutoff. Decomposition of the obtained fields in harmonics of the driving frequency allowed for the isolation of the linear contribution, which was subsequently separated according to the symmetries of the problem. For each of the aspect ratios considered, the spatial structure of the trapped mode was obtained and compared to the theoretical predictions given by a multipole expansion method. The waveguide–obstacle system was further characterized in terms of reflection and transmission coefficients, which led to the construction of resonance curves showing the presence of one or two trapped modes (depending on the value of a / d ), a result that is consistent with the theoretical predictions available in the literature. The frequency dependency of the trapped modes with the geometrical parameter a / d was determined from these curves and successfully compared to the theoretical predictions available within the frame of linear wave theory.

Estimating the dynamic effective mass density of random composites

The effective mass density of an inhomogeneous medium is discussed. Random configurations of circular cylindrical scatterers are considered, in various physical contexts: fluid cylinders in another fluid, elastic cylinders in a fluid or in another solid, and movable rigid cylinders in a fluid. In each case, time-harmonic waves are scattered, and an expression for the effective wavenumber due to Linton and Martin [J. Acoust. Soc. Am. 117, 3413-3423 (2005)] is used to derive the effective density in the low frequency limit, correct to second order in the area fraction occupied by the scatterers. Expressions are recovered that agree with either the Ament formula or the effective static mass density, depending upon the physical context.

MEAN-FLOW CORRECTION AS NON-LINEAR SATURATION MECHANISM

We are interested in identifying the mean-flow correction in the development of an instability. In the presented configuration (a 2D jet confined in a rectangular cavity that presents an oscillating instability), numerical simulations allow the identification of this mean-flow correction. We show that this distortion contributes to the non-linear saturation of the instability and that it is itself generated by the instability development: the action of the Reynolds tensor due to oscillating terms produces the mean-flow change.

Characterization of an experimental turbulent vortex in the physical and spectral spaces

We present an experiment where a stretched vortex is experiencing quasi-periodical turbulent bursts inside a laminar environment. In previous studies (Cuypers et al., 2003 Phys. Rev. Lett., 91, 194502, Cuypers et al., 2004 J. Turb., 5), the classical k−5/3 decay of the spectrum resulting from the evolution of this burst has been characterized and interpreted in the framework of Lundgrens mechanism (Lundgren 1982 Phys. Fluids 25 2193). In this paper, the flow is further characterized in both the physical and the spectral spaces using a statistical exploitation of phase averaged particle image velocimetry measurements.

Scattering of an elastic wave by a single dislocation

The scattering amplitude for the scattering of anti-plane shear waves by screw dislocations, and of in-plane shear and acoustic waves by edge dislocations are computed within the framework of elasticity theory. The former case reproduces well-known results obtained on the basis of an electromagnetic analogy. The latter case involves four scattering amplitudes in order to fully take into account mode conversion, and an adequately generalized optical theorem for vector waves is provided. In contrast to what happens for scattering by obstacles, the scattering amplitude increases with wavelength, and, in general, mode conversion in the forward direction does not vanish.