Effects of rotation on temperature fluctuations in turbulent thermal convection on a hemisphere.

Rotation is present in many physical and geophysical systems and its role in determining flow properties and modifying turbulent fluctuations is of crucial importance. Here we focus on the role of rotation on temperature fluctuations in turbulent thermal convection. The system used consists of a rotating half soap bubble heated from below. This system has features, curvature and a quasi two dimensional character, which are reminiscent of atmospheric and planetary systems. Our experiments and numerical simulations show that rotation changes the nature of turbulent fluctuations and a new scaling regime is obtained for the temperature field. This change in the scaling behavior of temperature fluctuations, due to rotation, is put forth by studying the so called second moment of temperature differences across different scales. For high enough rotation rates, these temperature differences display a transition from Bolgiano Obukhov scaling to a new scaling regime. This scaling is at odds with expectations from theory, numerics, and experiments in three dimensions, suggesting that the effects of rotation on turbulent flows depend strongly on geometry and spatial dimension.

Intensity of vortices: from soap bubbles to hurricanes.

By using a half soap bubble heated from below, we obtain large isolated single vortices whose properties as well as their intensity are measured under different conditions. By studying the effects of rotation of the bubble on the vortex properties, we found that rotation favors vortices near the pole. Rotation also inhibits long life time vortices. The velocity and vorticity profiles of the vortices obtained are well described by a Gaussian vortex. Besides, the intensity of these vortices can be followed over long time spans revealing periods of intensification accompanied by trochoidal motion of the vortex center, features which are reminiscent of the behavior of tropical cyclones. An analysis of this intensification period suggests a simple relation valid for both the vortices observed here and for tropical cyclones.

Non-linear oscillatory rheological properties of a generic continuum foam model: comparison with experiments and shear-banding predictions.

The occurrence of shear bands in a complex fluid is generally understood as resulting from a structural evolution of the material under shear, which leads (from a theoretical perspective) to a non-monotonic stationary flow curve related to the coexistence of different states of the material under shear. In this paper we present a scenario for shear-banding in a particular class of complex fluids, namely foams and concentrated emulsions, which differs from other scenarios in two important ways. First, the appearance of shear bands is shown to be possible both without any intrinsic physical evolution of the material (e.g. via a parameter coupled to the flow such as concentration or entanglements) and without any finite critical shear rate below which the flow does not remain stationary and homogeneous. Secondly, the appearance of shear bands depends on the initial conditions, i.e. the preparation of the material. In other words, it is history dependent. This behaviour relies on the tensorial character of the underlying model (2D or 3D) and is triggered by an initially inhomogeneous strain distribution in the material. The shear rate displays a discontinuity at the band boundary whose amplitude is history dependent and thus depends on the sample preparation.

An elasto-visco-plastic model for immortal foams or emulsions.

A variety of complex fluids consists in soft, round objects (foams, emulsions, assemblies of copolymer micelles or of multilamellar vesicles--also known as onions). Their dense packing induces a slight deviation from their preferred circular or spherical shape. As a frustrated assembly of interacting bodies, such a material evolves from one conformation to another through a succession of discrete, topological events driven by finite external forces. As a result, the material exhibits a finite yield threshold. The individual objects usually evolve spontaneously (colloidal diffusion, object coalescence, molecular diffusion), and the material properties under low or vanishing stress may alter with time, a phenomenon known as aging. We neglect such effects to address the simpler behaviour of (uncommon) immortal fluids: we construct a minimal, fully tensorial, rheological model, equivalent to the (scalar) Bingham model. Importantly, the model consistently describes the ability of such soft materials to deform substantially in the elastic regime (be it compressible or not) before they undergo (incompressible) plastic creep--or viscous flow under even higher stresses.

Experiments and direct numerical simulations of two-dimensional turbulence.

Experiments and direct numerical simulations reveal the coexistence of two cascades in two-dimensional grid turbulence. Several features of this flow such as the energy density and the scalar spectra are found to be consistent with well known theoretical predictions. The energy transfer function displays the expected up-scale energy transfers. The vorticity correlation function is logarithmic and thus consistent with recently proposed models.

Numerical study of grid turbulence in two dimensions and comparison with experiments on turbulent soap films.

Numerical simulations of two dimensional channel flow behind an array of cylinders are carried out for high Reynolds numbers. Results for the energy density and enstrophy spectra, as well as for velocity and vorticity differences, are presented. The results compare favorably with recent experiments carried out with turbulent soap films. Some marked deviations from expected behavior are found for the enstrophy spectrum and for moments of vorticity increments.