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We analyze the reversals of the large-scale flow in Rayleigh-Bénard convection both through particle image velocimetry flow visualization and direct numerical simulations of the underlying Boussinesq equations in a (quasi-) two-dimensional, rectangular geometry of aspect ratio 1. For medium Prandtl number there is a diagonal large-scale convection roll and two smaller secondary rolls in the two remaining corners diagonally opposing each other. These corner-flow rolls play a crucial role for the largescale wind reversal: They grow in kinetic energy and thus also in size thanks to plume detachments from the boundary layers up to the time that they take over the main, large-scale diagonal flow, thus leading to reversal. The Rayleigh vs Prandtl number space is mapped out. The occurrence of reversals sensitively depends on these parameters.

a b s t r a c tA new simulation method for solving fluid-structure coupling problems has been developed. All the basic equations are numerically solved on a fixed Cartesian grid using a finite difference scheme. A volume-of-fluid formulation [Hirt, Nichols, J. Comput. Phys. 39 (1981) 201], which has been widely used for multiphase flow simulations, is applied to describing the multi-component geometry. The temporal change in the solid deformation is described in the Eulerian frame by updating a left Cauchy-Green deformation tensor, which is used to express constitutive equations for nonlinear Mooney-Rivlin materials. In this paper, various verifications and validations of the present full Eulerian method, which solves the fluid and solid motions on a fixed grid, are demonstrated, and the numerical accuracy involved in the fluid-structure coupling problems is examined.

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Non-Oberbeck-Boussinesq (NOB) effects on the flow organization in two-dimensional Rayleigh-Bénard turbulence are numerically analyzed. The working fluid is water. We focus on the temperature profiles, the center temperature, the Nusselt number, and on the analysis of the velocity field. Several velocity amplitudes (or Reynolds numbers) and several kinetic profiles are introduced and studied; these together describe the various features of the rather complex flow organization. The results are presented both as functions of the Rayleigh number Ra (with Ra up to 10 8 ) for fixed temperature difference ∆ between top and bottom plates and as functions of ∆ ("non-Oberbeck-Boussinesqness") for fixed Ra with ∆ up to 60K. All results are consistent with the available experimental NOB data for the center temperature T c and the Nusselt number ratio N u N OB /N u OB (the label OB meaning that the Oberbeck-Boussinesq conditions are valid). For the temperature profiles we find -due to plume emission from the boundary layers -increasing deviations from the extended Prandtl-Blasius boundary layer theory presented in (Ahlers et al. 2006 J. Fluid Mech. 569, 409-445) with increasing Ra, while the center temperature itself is surprisingly well predicted by that theory. For given non-Oberbeck-Boussinesqness ∆ both the center temperature T c and the Nusselt number ratio N u N OB /N u OB only weakly depend on Ra.Beyond Ra ≈ 10 6 the flow consists of a large diagonal center convection roll and two smaller rolls in the upper and lower corners, respectively ("corner flows"). In the NOB case the center convection roll is still characterized by only one velocity scale. In contrast, the top and bottom corner flows are then of different strengths, the bottom one being a factor 1.3 larger (for ∆ = 40K) than the top one, due to the lower viscosity in the hotter bottom boundary layer. Under NOB conditions the enhanced lower corner flow as well as the enhanced center roll lead to an enhancement of the volume averaged energy based Reynolds number Re E = 1 2 u 2 1/2 L/ν of about 4% to 5% for ∆ = 60K. Moreover, we find Re E N OB /Re E OB ≈ (β(T c )/β(T m )) 1/2 , with β the thermal expansion coefficient and T m the arithmetic mean temperature between top and bottom plate temperatures. This corresponds to the ratio of the free fall velocities at the respective temperatures. By artificially switching off the temperature dependence of β in the numerics, the NOB † Present Address: K. Sugiyama et al.modifications of Re E is less than 1% even at ∆ = 60K, revealing the temperature dependence of the thermal expansion coefficient as the main origin of the NOB effects on the global Reynolds number in water.

We compute the continuum thermo-hydrodynamical limit of a new formulation of lattice kinetic equations for thermal compressible flows, recently proposed in [Sbragaglia et al., J. Fluid Mech. 628 299 (2009)]. We show that the hydrodynamical manifold is given by the correct compressible FourierNavier-Stokes equations for a perfect fluid. We validate the numerical algorithm by means of exact results for transition to convection in Rayleigh-Bénard compressible systems and against direct comparison with finite-difference schemes. The method is stable and reliable up to temperature jumps between top and bottom walls of the order of 50% the averaged bulk temperature. We use this method to study Rayleigh-Taylor instability for compressible stratified flows and we determine the growth of the mixing layer at changing Atwood numbers up to At ∼ 0.4. We highlight the role played by the adiabatic gradient in stopping the mixing layer growth in presence of high stratification and we quantify the asymmetric growth rate for spikes and bubbles for two dimensional RayleighTaylor systems with resolution up to Lx × Lz = 1664 × 4400 and with Rayleigh numbers up to Ra ∼ 2 × 10 10 .

We investigate the effect of microbubbles on Taylor-Couette flow by means of direct numerical simulations. We employ an Eulerian-Lagrangian approach with a gas-fluid coupling based on the point-force approximation. Added mass, drag, lift, and gravity are taken into account in the modeling of the motion of the individual bubble. We find that very dilute suspensions of small non-deformable bubbles (volume void fraction below 1%, zero Weber number and bubble Reynolds number 10) induce a robust statistically steady drag reduction (up to 20%) in the wavy vortex flow regime (Re = 600 -2500). The Reynolds number dependence of the normalized torque (the so-called Torque Reduction Ratio (TRR) which corresponds to the drag reduction) is consistent with a recent series of experimental measurements performed by Murai et al. (J. Phys. Conf. Ser. 14, 143 (2005)). Our analysis suggests that the physical mechanism for the torque reduction in this regime is due to the local axial forcing, induced by rising bubbles, that is able to break the highly dissipative Taylor wavy vortices in the system. We finally show that the lift force acting on the bubble is crucial in this process. When neglecting it, the bubbles preferentially accumulate near the inner cylinder and the bulk flow is less efficiently modified.

The shape of velocity and temperature profiles near the horizontal conducting plates in turbulent Rayleigh-Bénard convection are studied numerically and experimentally over the Rayleigh number range 10 8Ra 3 × 10 11 and the Prandtl number range 0.7 P r 5.4. The results show that both the temperature and velocity profiles well agree with the classical Prandtl-Blasius laminar boundary-layer profiles, if they are re-sampled in the respective dynamical reference frames that fluctuate with the instantaneous thermal and velocity boundary-layer thicknesses.