M lefranc, S. Boccaletti, B. Gluckman, C. Grebogi, J. K¨ Urths, L. Pecora

In flows with sufficiently high pressure gradients, a strong peak of turbulent kinetic energy have been observed and not yet fully explained. Through the analysis of a DNS database of a converging-diverging channel, the origine of intense coherent structures was identified and linked to the linear instability of the flow. The instability of the normal profile of the mean streamwise velocity is not satisfactory to fully explain the generation of the coherent vortices observed in the DNS. However, the linear stability analysis of the spanwise varying average streak (which is the most energetic long structure in the vicinity of the wall) superimposed to the normal profile is able to predict both the streamwise location and the shape of the coherent structures. These structures quickly evolve according to the non-linearity of the Navier Stokes equations to elongated vortical structures which are able to redistribute the turbulent kinetic energy in the three directions.

The drawback of the DNS is the limitation in term of Reynolds number. On the other hand, the progress on experimental tools for flow characterization are significant as quantitative analysies in three dimensions are now possible. However, the accuracy and the spatial resolution of methods such as tomographic Particles Image Velocimetry are not yet satisfactory for careful investigations of near wall turbulent structures

.

Instabilities of conducting fluid flows in cylindrical shells under external forcing [40]

Javier Burguete & Montserrat Miranda-Galceran

Depto. Fisica y Mat Aplicada, Universidad de Navarra, Irunlarrea 1, E-31008 Pamplona, Spain [e-mail]

Flows created in neutral conducting flows remain one of the topics less studied of fluid dynamics. But there is a great variety of unexplained behaviours in these systems, with strong consequences both in fundamental research (dynamo action, MHD instabilities, turbulence suppression) and applications (casting, aluminium production, biophysics).

Having in mind a biological application, in this experiment we present the effect of a time-dependent magnetic field parallel to the axis of an annular cavity. Due to the Lenz’s law, a current is induced in the bulk when the magnetic field increases or decreases, producing a radial force that alternatively changes its orientation. This force produces the destabilization of the static fluid layer, and a flow is created.

The geommetry of the experimental cell is a cylindrical layer with external and internal diameters 94 and 84 mm respectively. The layer is 20mm depth, and we use as conducting fluid an In-Ga-Sn alloy. There is no external current applied on the problem, only an external magnetic field. This field evolves harmonically with a frequency up to 10Hz, small enough to not to observe skin depth effects. The magnitude ranges from 0 to 0.1 T. With a threshold of 0.01T a dynamical behaviour is observed, and the main characteristics of this flow have been determined.

Previous works have shown that very thin layers (extended drops) destabilize from a circular shape to starlike or labyrinth shapes. With these geometries, induced currents can be interrupted, and there is no dynamical behaviour. Here, we deal with a shallow layer and bulk forces caused by the induced currents cannot disappear.

10

4

Convection in a binary ferrofluid [41]

David Laroze1;2& Harald Pleiner2

1

2Instituto de Alta Investigaci ´ on, Universidad de Tarapac ´ a, Casilla 7D, Arica, Chile

Max Planck Institute for Polymer Research, Ackermannweg 10, D 55128 Mainz, Germany [e-mail]

We report theoretical and numerical results on convection for a magnetic fluid. The binary mixture effect is taken into account. We focus in the stationary and oscillatory convection for idealized boundary conditions. We obtain explicit expressions of convective thresholds in terms of the control parameters of the system. Close to bifurcation, the coefficients of the corresponding amplitude equations are determined. Finally, the secondary instabilities are performed.

10

5

A model for bubbling dynamics [42]

Felipe Pereira1, Jos ´ e Sartorelli1, & Eduardo Colli

21

2Instituto de F ´ isica, Universidade de S ˜ ao Paulo, Caixa Postal 66318, 05314-970 S ˜ ao Paulo, Brazil

n

This work was supported by the Brazilian agencies FAPESP and CNPq.

10

6Instituto de Matem ´ atica e Estat ´ istica, Universidade de S ˜ ao Paulo, R. do Mat ˜ ao 1010, CEP 05508-090 S ˜ ao Paulo, Brazil [e-mail]

We have studied air bubbles formation in water/glycerol solution with the bubbles generated in a nozzle at the bottom of a cylindrical container. For narrow metallic nozzle (seringe needle) the system presents period adding cascade and bistability having the air flux as a control parameter. The maximum periodicity depends also on the hose length that connects the nozzle to the air supplier (See [1]). We have obtained three different type of simultaneous data: a) the time between successive bubbles (T) by detecting the pulses induced in a phototransistor when the bubble is crossing a laser beam placed a little above the nozzle; b) the pressure wave in the hose conection with microphones placed close to the nozzle; c) the evolution of the bubble profiles by recording the images with a high speed camera. Therefore, these data allowed us to develop a model based on physical principles that reproduces the period adding cascade and bistability, and also explains why the hose length and the nozzle width are essential parameters.

References

1. E. Colli, V. S. M. Piassi, A. Tufaile, J. C. Sartorelli, Bistability in bubble formation, Phys. Rev. E 70, 066215, 2004

.

Modulated waves in the Couette-Taylor system submitted to a high radial temperature gradient [43]

Arnaud Prigent, Rapha ¨ el Guillerm, & Innocent Mutabazi

LOMC - FRE 3102 CNRS, Universit ´ e du Havre, 53 Rue Prony, 76 058 Le Havre Cedex, France [e-mail]

This experimental work focus on the study of the flow induced by the coupling between the centrifugal force and thermal effects in a Couette-Taylor system submitted to a high radial temperature gradient [1-3]. For this purpose, we have developed a non-intrusive velocity and temperature fields measurement technique using thermochromic liquid crystals [4, 5]. It allows us to fully characterize the flow produced in a narrow gap and large aspect ratio Couette-Taylor system with aspect ratio and radius ratio respectively equal to 112 and 0:8. For such a system, the control parameters are the Grashof number Gr, related to the radial temperature gradient, and the Taylor number Ta, related to the rotation of the inner cylinder. Here, Gris fixed and Tais gradually increased.

For small values of the Taylor number, the base flow is composed of the circular Couette flow and a vertical flow corresponding to a convective cell induced by the radial temperature gradient. Above a critical value of the Taylor number, the base flow becomes unstable. For small values of the Grashof number, it is replaced by an inclined co-rotating vortex flow pattern present on the bottom of the system [3]. For large values of the Grashof number, the base flow is replaced by a modulated wave present along the entire length of the system and rotating at the mean angular velocity of the flow. The pattern takes the form of wave packets we have studied the envelope. It can be modeled as A(t) = Amax:cosh1[(ttmax)=Tmod] where Ais the maximum value of the amplitude of a packet, tmaxthe time at which this maximum is reached and Tmaxmodthe period of the modulation which also corresponds to the length of a packet.

Bibliography 1. H.A. Snyder, S.K.F. Karlsson, Experiments on the stability of Couette motion with a radial thermal gradient,

Phys. Fluids, 7 (10) (1964). 2. D.C. Kuo, K.S. Ball, Taylor-Couette flow with buoyancy : Onset of spiral flow, Phys. Fluids, 9 (10), 2872-

2884 (1997). 3. V. Lepiller, A. Goharzadeh, A. Prigent, I. Mutabazi, Weak temperature gradient effect on the stability of the

circular Couette flow, Euro. Phys. J. B, 61, 479-501 (2008). 4. N. Akino, T. Kunugi, M. Ueda et A. Kurosawa, Liquid crystal thermometry based on automatic colour

evaluation and applications to measure turbulent heat transfer, Transport phenomena in turbulent flows (New York: Hemisphere), pp. 807-827 (1989).

5. J.L. Hay, D.K. Hollingsworth, Calibration of micro-encapsulated liquid crystals using hue angle and a dimensionless temperature, Experimental thermal and fluid science, 18, 251-257 (1998).

10

7

Modeling of volcanomagnetic dynamics by recurrent orthogonal least-squares learning systems [44]

Stanislaw Jankowski1, Gilda Currenti2, Rosalba Napoli2, Zbigniew Szymanski1, Luigi Fortuna2, Ciro Del Negro, & Marek Dwulit1

31

2

3Warsaw University of Technology,Poland

Istituto Nazionale di Geofisica e Vulcanologia, Sezione di Catania,Italy

10

8Dipartimento Di Ingegneria Elettrica Elettronica e dei Sistemi Universit ` a di Catania,Italy [e-mail]

We present a new model of volcanomagnetic dynamics created by means of recurrent orthogonal least squares. The advantages of our approach are: low complexity algorithm as compared to recurrent kernel machines and parsimonious representation of observed dynamical system that enables physical interpretation. The observations of the geomagnetic time series from the magnetic network on Etna volcano are analyzed to investigate the dynamical behavior of magnetic anomalies. The predictability of the geomagnetic time series was evaluated to establish a possible low-dimensional deterministic dynamics. The analysis of the 10-minutes differences at PDN station with respect to the reference station located far away from the volcano edifice shows prominent peaks centered around diurnal components at the period of 8, 12 and 24 h. After having removed the dominant periodic components, the filtered differences appear to be aperiodic and broadband. We attempt to explain the mechanism generating the time dependent variations by constructing the recurrent learning system. The data from PDN station was normalized to the range [-1,1]. We used a learning data set from 7th to 13th January 2008. The testing data set spans from 15th to 21st January 2008. The idea of recurrent model of nonlinear dynamical system is based on the general NARMAX form. The idea is to find the mapping rule between the past values of the observed process and its prediction. Hence, the learning algorithm consists of 2 phases. In the phase 1 the model state inputs are delayed measured output values of the process for the input-output representation. In the learning phase 2 the measured output values are replaced by the estimated output values of the predictor before performing the new learning phase. The performed model has the form of linear combination of RBF functions selected by Gram-Schmidt orthogonalisation from the hierarchical basis function system. The result of embedding analysis shows that the geomagnetic time series is 3rd order dynamical system. The recurrent orthogonal least squares system was first used as model of the Chua circuit dynamics and applied to predict the Etna geomagnetic time series. The obtained models are accurate enough to explain the chaotic mechanism of observed processes and to distinguish various modes of behavior. As compared to the recurrent least-squares support vector machines tested on the same data sets, the orthogonal least squares systems require 10 times less number of regressors at higher accuracy due to the ability to explore RBF basis functions with flexible width parameters

.

Observation of Hamiltonian phase space structure in geospace plasmas [45]

Richard Martin, Daniel Holland, Hiroshi Matsuoka, & Morgan Presley

Illinois State University, Normal, Illinois, USA [e-mail]

We consider Hamiltonian dynamics of charged particles in a sharp magnetic feild reversal (a current sheet), modeling a broad region in the geomagnetic tail region of the magnetosphere. Theory and simulations have predicted an energy resonance related to the symmetry of the particle phase space partitions (into regular, chaotic, and transient regions). The resonance manifests itself a series of peaks in the ion velocity distribution function, which have been observed in in-situ data from two different spacecraft during periods of low to moderate magnetic activity. The observed peaks scale as the fourth root of the normalized particle energy, in agreement with the theoretical resonance structure. In this paper, we summarize these results and present new results from the multi-spacecraft Cluster mission, which allow us to better utilize the resonances to remote sense properties of the magnetotail current sheet that are difficult to determine otherwise.

10

9

Penetration of sound into rough marine sediments: numerical analysis and statistics [46]

Vladislav Aleshin1, Laurent Guillon2, & Ali Khenchaf

31

2IEMN - UMR 8520, av. Poincar ´ e, BP 60069, 59652 Villeneuve d’Ascq cedex

Ecole Navale, BP600, 29240 Lanv ´ eoc Poulmi

c3ENSIETA, 2 rue Franc¸ois Verny, 29806 Brest Cedex 9 [e-mail]

The problem of acoustical scattering by rough (rippled) sediments is important for many applications, such as buried objects detection, seafloor characterization, AUV navigation, etc. The presented numerical analysis concerns a general case of an arbitrary grazing angle that can be as low as 5 -10 and a realistic ratio between the height and the quasi-period of roughness. We use the Boundary Element Method (BEM) in 2D geometry to obtain the scattered pressure field in water and in sediment and compare these results to the well-known HelmholtzKirchhoff (HK) approximation. Further development of the BEM (accelerated BEM) has been realized by means of numerical implementation of an exact analytical solution to the Helmholtz equation in the discretized matrix form; an acceleration factor of 10 is easily obtained. Using a Monte-Carlo technique, we evaluate the distribution of the pressure field together with its essential characteristics, such as average and standard deviation. A regime in which a Gaussian distribution for the real and imaginary parts of the penetrated field is found which means that the penetrated field is a result of interference of many statistically independent components scattered from the surface. Another observation is depth independence of the averaged penetrated field that appears below some minimum depth in lossless sediment, whereas this phenomenon is not observed for a single roughness realization. Interpretation of these results could help building up a theoretical description for penetration at low grazing angles and high frequency.

11

0

Granular and bacterial motors [47]

Alessio Guarino1;

21Laboratoire de Physique de l’Ecole Normale Superieure de Lyon, France

2Universit ´ e de la Polyn ´ esie Francaise, Tahiti, French Polynesia [e-mail]

If the spatial and temporal symmetries are broken, it is then possible to extract work from a thermalized gas. In our experiment, an asymmetric ratchet is immersed in a 2D granular Gas. We show that the work extracted from the granular gas depend on the energy dissipation in ratchet-gas collisions and on the ratchet mass. We also show experiments performed with self-propelled particles, which are supposed to simulate the dynamics of a bacterial motor.

11

1

Collective motion of spherical particles induced by horizontal vibration [48]

Feifang Chung & Sy-Sang Liaw

Department of Physics, National Chung-Hsing University, 250 Guo-Kuang Road, Taichung 402, Taiwan [e-mail]

The study measures experimentally the kinetic energy of N spherical particles moving on a horizontal plane. The plane is bounded by rectangular wall and shaken horizontally. A CCD camera above the system is used to record the motion of every particle so that the kinetic energy of the system can be analyzed by tracking the trajectory of each particle. We find that the motions of the spherical particles change from pure rolling to sliding at a certain filling fraction and the change of motion is accompanied by the abrupt change of the kinetic energy. We determine the critical value of the filling fraction and find it is a linear decreasing function of the driven amplitude. By considering the conditions for all particles moving collectively in resonance with the external drive, we propose a model that can well explain the linear relation between the critical filling fraction and the amplitude.

11

2

Interaction of a bouncing ball with a sinusoidally vibrating table [49]

Elbert Macau1, Marcus V. Carneiro2, & Joaquim J. Barroso

31

2

3Computing and Applied Mathematics Laboratory / National Institute for Space Research (INPE) / 12227-010 - Sao Jose dos Campos - SP - Brazil

Swiss Federal Institute of Technology (ETH-Z ¨ urich)

Associated Plasma Laboratory / National Institute for Space Research (INPE) / 12227-010 - Sao Jose dos Campos - SP Brazi

[e-mail]

Exploring all its ramifications, this presentation gives an overview of the simple yet fundamental bouncing ball problem, which consists of a ball bouncing vertically on a sinusoidally vibrating table under the action of gravity. The dynamics is modeled on the basis of a discrete map of difference equations, which numerically solved fully reveals a rich variety of nonlinear behaviors, encompassing irregular non-periodic orbits, subharmonic and chaotic motions, chattering mechanisms, and also unbounded non-periodic orbits. For periodic motions, the corresponding conditions for stability and bifurcation are determined from analytical considerations of a reduced map. Through numerical examples, it is shown that a slight change in the initial conditions makes the ball motion switch from periodic to chaotic orbits bounded by a velocity strip v =  =(1  ), where is the non-dimensionalized shaking acceleration and e the coefficient of restitution which quantifies the amount of energy lost in the ball-table collision. Moreover, a detailed numerical discussion of the excitation of the unstable 1-periodic mode and the ensuing transition to its stable counterpart mode is also given.

11

3

Airflow caused by a ball impacting on soft sand [50]

Sylvain Joubaud1, Tess Homan2, Deveraj van der Meer2, & Detlef Lohse

21

2Laboratoire de Physique de Ecole Normale Superieure de Lyon, UMR5672 CNRS et Universite de Lyon, 46 Allee d Italie, 69007 Lyon, France.

11

4Physics of Fluids group, University of Twente P.O. Box 217, 7500 AE Enschede, The Netherlands [e-mail]

When a ball is dropped on a loosely packed sand bed, a surprisingly energetic jet shoots out of the bed. It is already known that the interstitial air plays an important role during the series of events caused by the impacting ball: splash and penetration, jet formation, and granular eruption. During the impact, air is pushed through the bed creating a pressure difference over the sand bed. We measure this difference as a function of time for different sets of parameters (ambient air pressure, impact velocity, ...). From this measurement, the flow of air through the bed is evaluated

.

Chaos in foams with grains [51]

Alberto Tufaile & Adriana Tufaile

Escola de Artes, Ci ˆ encias e Humanidades, Soft Matter Laboratory, Universidade de S ˜ ao Paulo, 03828-000 S ˜ ao Paulo, SP, Brazil

[e-mail]

We have observed some features of foams and granular materials in Hele-Shaw cells. When a liquid containing a surfactant is shaken in the presence of air, there is the formation of a foam by the action of deformation and stretching of the air/liquid interface. If this foam is left to rest, the interface evolves towards a minimal surface by a minimization process of energy. If the motion persists, the liquid flows through the interstitial spaces between bubbles, along with the rearrangement of the bubble structure. We consider the following question: what are the descriptions from the point of view of dynamical systems theory applicable to the complex spatio-temporal behavior of the foam evolution? We have described the stretching and folding mechanism present in foams obtained from an experiment of a Hele-Shaw cell containing liquid detergent and air [1]. We have reported the evolution of liquid and air for some sequences of upside-down flips, with a detailed description of the phenomenology involved, such as the snowball effect and vertex creation. We also have found that the general evolution of the foam in the presence of the granular material is different from the case without grains, while the foam structure in the stationary state in both cases is almost the same, with their fractal dimensions close to the values obtained from Random Apollonian Packing. Our results indicate that granular materials can alter some aspects of pattern formation in foams, such as the emergence of nodes with degree four. This work was supported by Conselho Nacional de Desenvolvimento Cient ´ ifico e Tecnol ´ ogico (CNPq), and Instituto Nacional de Ci ˆ encia e Tecnologia de Fluidos Complexos (INCTFCx). [1] A. Tufaile, A. P. B. Tufaile, Stretching and folding mechanism in foams, Physics Letters A 372, (2008) 6381-6385. [2] A. Tufaile, A. P. B. Tufaile, T. A. S. Haddad, Mixing foams and grains in Hele-Shaw cells, Journal of Physics, accepted for publication.

11

5

Pattern formation in a magnetic nanowire at fixed temperature [52]

Omar Suarez1& David Laroze2;3

1

2

3Departamento de Fisica, Universidad Tecnica Federico Santa Maria, Casilla 110-V, Valparaiso, Chile

Max Planck Institute for Polymer Research, Ackermannweg 10, D 55128 Mainz, Germany

Instituto de Alta Investigacion, Universidad de Tarapaca, Casilla 7-D, Arica, Chile [e-mail]

Magnetic nanoarrays are important due to possible technological applications, such us in data storage devices or in biomedicine. Here, we study the effect of the temperature in an anisotropic magnetic nanowire when an external magnetic field is applied. We use the continuous approximation to describe the wire in the framework of Landau Lifshitz Bloch equation. The linear stability analysis is achieved and the threshold is calculated. Close to the bifurcation, the weakly nonlinear analysis is performed; and the corresponding amplitude equation is derived. We find that different types of patterns are formed depending on the ratio between of the magnetic field and the temperature.