Control of vortex breakdown in a closed cylinder with a rotating lid

The flow within a closed cylinder with a rotating lid is considered as a prototype for fundamental studies of vortex breakdown. Numerical simulations for various parameter values have been carried out to reproduce the known effect of a thin rotating rod positioned along the center axis as well as analyze the influence of local vorticity sources. As expected, the results show that the breakdown bubbles in the steady axisymmetric flow can be affected dramatically, i.e., fully suppressed or significantly enhanced, by rotating the rod. The main contribution of this article is to show that the observed behavior can be explained by the vorticity generated by the rod locally near the rotating lid and near the fixed lid, as analogous behavior is caused by the introduction of local vorticity sources in the flow without a rod. Moreover, we describe the influence on the breakdown bubbles of the vorticity sources by an analytical model. In addition to improving our understanding, this finding should also open the door to other types of flow control devices capable of generating localized vorticity.     

A note on pseudo-symplectic Runge-Kutta methods

Aubry and Chartier introduced (1998) the concept of pseudo-symplecticness in order to construct explicit Runge-Kutta methods, which mimic symplectic ones. Of particular interest are methods of order (p, 2p), i.e., of orderp and pseudo-symplecticness order 2p, for which the growth of the global error remains linear. The aim of this note is to show that the lower bound for the minimal number of stages can be achieved forp=4 andp=5.     

Spatio-temporal symmetries and bifurcations via bi-orthogonal decompositions

Summary A tool for analyzing spatio-temporal complex physical phenomena was recently proposed by the authors, Aubry et al. [5]. This tool consists in decomposing a spatially and temporally evolving signal into orthogonal temporal modes (temporal “structures”) and orthogonal spatial modes (spatial “structures”) which are coupled. This allows the introduction of a temporal configuration space and a spatial one which are related to each other by an isomorphism. In this paper, we show how such a tool can be used to analyze space-time bifurcations, that is, qualitative changes in both space and time as a parameter varies. The Hopf bifurcation and various spatio-temporal symmetry related bifurcations, such as bifurcations to traveling waves, are studied in detail. In particular, it is shown that symmetry-breaking bifurcations can be detected by analyzing the temporal and spatial eigenspaces of the decomposition which then lose their degeneracy, namely their invariance under the symmetry. Furthermore, we show how an extension of the theory to “quasi-symmetries” permits the treatment of nondegenerate signals and leads to an exponentially decreasing law of the energy spectrum. Examples extracted from numerically obtained solutions of the Kuramoto-Sivashinsky equation, a coupled map lattice, and fully developed turbulence are given to illustrate the theory.     

Flexible Wiper System Dynamic Instabilities: Modelling and Experimental Validation

The optimization of wiper systems under various conditions and the creation of a product which is as robust as possible are the main objectives for an equipment supplier. However, in certain conditions, instabilities can appear and generate wiping defects due to the rubber-glass contact. To improve wiping quality and to reduce the number of test stages for design, this study proposes a wiper system modeling method. The wiper system is represented by a rigid blade holder on which a rubber blade is fitted. This rigid blade system is used on a flat test bench at constant wiping velocity. The model is based on modal synthesis methods and will be validated through comparison with experimental tests under various conditions. The right correlation obtained allows the same modelling method to be applied to the new generation of flexible wiper blades which take account of the degree of freedom of the wiper blade flexions. So, a new computation tool will be developed and validated through experimentation on a specific test bench.     

Synthesis and foaming properties of new anionic surfactants based on a renewable building block: sodium dodecyl isosorbide sulfates

Two agro-based anionic surfactants containing an isosorbide moiety have been synthesized and their amphiphilic properties evaluated. Since isosorbide is now considered as an important platform chemical of the starch industry, these compounds could represent bio-sourced alternatives to the alkyl ether sulfates (notably lauryl ether sulfate, LES) that are based on petroleum-derived ethylene oxides. As isosorbide is an asymmetric diol, two isomers can be prepared (2-O-dodecyl isosorbide sulfate and 5-O-dodecyl isosorbide sulfate) that show significantly different aqueous properties as regards to their Krafft temperatures and critical micellar concentrations. 5-O-dodecyl isosorbide sulfate is the most soluble and the most efficient surfactant. It possesses a much lower critical micelle concentration (cmc) than sodium dodecyl sulfate, SDS, leading to comparable foaming properties with a three times lower concentration. Its behavior compares well with the one of pure diethoxylated dodecyl sulfate that has also been prepared and evaluated in this work.     

Spatiotemporal and statistical symmetries

The notion of symmetries, either statistical or deterministic, can be useful for the characterization of complex systems and their bifurcations. In this paper, we investigate the connection between the (microscopic) spatiotemporal symmetries of a space-time functionu(x, t), on the one hand, and the (macroscopic) symmetries of statistical quantities such as the spatial (resp. temporal) two-point correlations and the spatial (resp. temporal) average, on the other hand. We show, how, under certain conditions, these symmetries are related to the symmetries of the orbits described byu(x, t) in the characteristic (phase) spaces. We also determine the largest group of spatiotemporal symmetries (in the sense introduced in our earlier work) satisfied by a given space-time functionu(x, t) and indicate how to extract the subgroups of point symmetries, namely those directly implemented on the space and time variables. Conversely, we determine all the functions invariant by a given space-time symmetry group. Finally, we illustrate all the previous points with specific examples.