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The effects of the plates thermal properties on the heat transfer in turbulent thermal convection are investigated by direct numerical simulations of the Navier–Stokes equations with the Boussinesq approximation. It has been found that the governing parameter is the ratio of the thermal resistances of the fluid layer Rf and the plates Rp; when this ratio is smaller than a threshold value (Rf/Rp≈300 arbitrarily defined by requiring that the actual heat transfer differs by less than 2% from its ideal value), the finite conductivity of the plates limits the heat transfer in the cell. In addition, since Rf decreases for increasing Rayleigh numbers, any experimental apparatus is characterized by a threshold Rayleigh number that cannot be exceeded if the heat transfer in the cell has not to be influenced by the thermal properties of the plates. It has been also shown that the plate effects cannot be totally corrected by subtracting the temperature drop occurring within the plates from the measured total tempera...

The evolution of initially axisymmetric shielded pancake-like vortices in a nonrotating linearly stratified fluid has been investigated experimentally and numerically. The evolution process and the shape of tripoles in laboratory experiments depend on the experimental parameter values. In order to investigate this phenomenon we have considered the influence of the Reynolds (Re) and Froude (F) numbers on the tripole formation process. Also, the role of the (absolute) ratio [gamma] between the vorticity values of the satellite vortices and the core vortex on the tripole evolution has been investigated. Additionally, a set of numerical simulations has been performed to enable an examination of the role of Reynolds numbers (up to Re = 10 000) and Froude numbers (F = 0.1, 0.2, 0.4, and 0.8) outside the experimentally accessible range. The steepness parameter [alpha] was varied between 2 and 8 in order to estimate the relative importance of the different modes constituting the perturbation. From this study we conclude that tripole formation and dipole splitting in a linearly stratified fluid can be well described in terms of the parameter set (Re,F, [alpha] ).

In this work a statistical model for the prediction of the intermittency exponents in fully developed isotropic turbulence, recently proposed by Camussi and Verzicco [Phys. Fluids 12, 676 (2000)] is clarified and improved. It was found, in fact, that the same results as those found by Camussi and Verzicco can be obtained by a neater and more general formulation. This is achieved starting from a reliable statistical description of the velocity difference probability density function (pdf). A new and more general predictive formula is obtained and the dependence on the free parameters describing the pdf shape is discussed. It is shown that for the technically measurable exponents, the results are not very sensitive to the shape of the pdf. This indicates that, within the present limitations of experimental measurements and numerical simulations, the analysis of the velocity difference statistics is not a sufficiently accurate tool for studying in detail the intermittency in turbulence.

The transitions from the onset of convection to fully developed turbulence of a Rayleigh–Benard flow, in a low-aspect-ratio cell and in mercury, are studied through three-dimensional numerical simulation of the Navier–Stokes equations. The calculation of the growth rate of the azimuthal energy modes permitted the accurate determination of the critical Rayleigh number for the establishment of the convective regime (Rac=3750) which is in good agreement with analytical and other numerical results. Increasing the Rayleigh number, the flow remained steady up to Ra≃2.11×104 when an oscillatory instability was observed. Further increases in the Rayleigh produced a chaotic state through the period doubling mechanism and finally the turbulent state was achieved. It is shown that for Ra⩾Rac the mean flow consists of a large-scale convective cell which persists in the whole range of studied Rayleigh numbers (Ra⩽106). The dependence of the Nusselt number over the Rayleigh number is also analyzed and, for Ra⩾3.75×104,...

This study deals with the instabilities that arise in the flow generated in a rotating tank by the evolution of a two-layer density stratified fluid. Numerical investigations have been performed by direct simulation of the Navier-Stokes equations for axisymmetric and fully three-dimensional flows. In the former case results have shown the attainment, in a very short time, of an equilibrium position and the formation of an anticyclonic structure in the upper light layer and a cyclonic one in the lower layer, consistently with the observation of Griffiths and Linden. In the long term, however, the Ekman layer at the bottom damps out the cyclone and a steady state with only an anticyclone in the upper layer is reached. In three-dimensions the flow is unstable to azimuthal disturbances and the steady state is no longer achieved. In particular a ring of cyclonic vorticity, surrounding the anticyclone, by the combined effects of baroclinic and barotropic processes, breaks, entrains vorticity from the anticyclon...

We present a numerical study of incremental spin-up of a thermally stratified fluid enclosed within a right circular cylinder with rigid bottom and side walls and stress-free upper surface. This investigation reveals a feasibility for transition from an axisymmetric initial circulation to nonaxisymmetric flow patterns, and it is motivated by the desire to compare the spin-up for Dirichlet and Neumann thermal boundary conditions. The numerical simulations demonstrate that the destabilizing mechanism is not purely baroclinic but that vertical and horizontal shears may contribute to the instability. By characterizing the azimuthal instabilities without introducing any simplification, we were able to assess to what extent an insulating boundary condition changes the time-dependent emergence of the instability. Our results agree with previous experimental data and provide a framework for understanding the role played by the baroclinic vorticity in the development of instabilities in thermally stratified incremental spin-up flows

In search for the cheapest but still reliable numerical simulation, a systematic study on the effect of the computational domain ("box") size on direct numerical simulations of Taylor-Couette flow was performed. Four boxes, with varying azimuthal and axial extents were used. The radius ratio between the inner cylinder and the outer cylinder was fixed to $\eta=r_i/r_o=0.909$, and the outer was kept stationary, while the inner rotated at a Reynolds number $Re_i=10^5$. Profiles of mean and fluctuation velocities are compared, as well as autocorrelations and velocity spectra. The smallest box is found to accurately reproduce the torque and mean azimuthal velocity profiles of larger boxes, while having smaller values of the fluctuations than the larger boxes. The axial extent of the box directly reflects on the Taylor-rolls and plays a crucial role on the correlations and spectra. The azimuthal extent is also found to play a significant role, as larger boxes allow for azimuthal wave-like patterns in the Taylor rolls to develop, which affects the statistics in the bulk region. For all boxes studied, the spectra does not reach a box independent maximum.

Numerical simulations of the Stokes boundary layer over a three‐dimensional wavy wall are performed in order to investigate the role played by infinitesimal wall imperfections in triggering transition to turbulence. Our results show flow patterns qualitatively similar to those experimentally detected. In particular the laminar, disturbed‐laminar and intermittent turbulent regimes are recovered. The characteristics of the above flow regimes are analyzed.

The mixing process in the formation of an axisymmetric vortex ring is analyzed by direct numerical simulation. After the initial phase, when the impulse is imparted to the fluid, the mixing increases linearly in time with a slope that is directly proportional to the vortex circulation (Γ) and to reactants diffusivity to the power −1/3 (Pe−0.33). In addition, for reacting flows with equivalence ratio (s) different from 1, it has been found that as s decreases the mixing first decreases and then increases. An explanation for this behavior is given.

We report on the results of a combined experimental and numerical study on the fluid motion generated by the controlled approach and arrest of a solid sphere moving towards a solid wall at moderate Reynolds number. The experiments are performed in a small tank filled with water for a range of Reynolds numbers for which the flow remains axisymmetric. The fluid agitation of the fluid related to the kinetic energy is obtained as function of time in the experiment in a volume located around the impact point. The same quantities are obtained from the numerical simulations for the same volume of integration as in the experiments and also for the entire volume of the container. As shown in previous studies, this flow is characterized by a vortex ring, initially in the wake of the sphere, that spreads radially along the wall, generating secondary vorticity of opposite sign at the sphere surface and wall. It is also observed that before the impact, the kinetic energy increases sharply for a small period of time and then decreases gradually as the fluid motion dies out. The measure of the relative agitation of the collision is found to increase weakly with the Reynolds number Re. The close agreement between the numerics and experiments is indicative of the robustness of the results. These results may be useful in light of a potential modelling of particle-laden flows. Movies illustrating the spatio-temporal dynamics are provided with the online version of this paper