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The bifurcations of penetrative Rayleigh-Benard convection in cylindrical containers are studied by the linear stability analysis (LSA) combined with the direct numerical simulation (DNS) method. The working fluid is cold water near 4 degrees C, where the Prandtl number Pr is 11.57, and the aspect ratio (radius/height) of the cylinder ranges from 0.66 to 2. It is found that the critical Rayleigh number increases with the increase in the density inversion parameter (m). The relationship between the normalized critical Rayleigh number (Ra-c((m))/Ra-c(0)) and (m) is formulated, which is in good agreement with the stability results within a large range of (m). The aspect ratio has a minor effect on Ra-c((m))/Ra-c(0). The bifurcation processes based on the axisymmetric solutions are also investigated. The results show that the onset of axisymmetric convection occurs through a trans-critical bifurcation due to the top-bottom symmetry breaking of the present system. Moreover, two kinds of qualitatively different steady axisymmetric solutions are identified.

For a fixed geometric configuration, hydrodynamic instabilities and bifurcation processes of laminar isothermal planar opposed jet flows with symmetric and slightly asymmetric inlet boundary conditions are investigated numerically using a high-resolution approach based on spectral element method. In current configuration, when inlet boundary conditions are symmetric, in the range of the Reynolds number considered (Re <= 200), multiple new symmetry-breaking bifurcations are observed and four new flow patterns are identified. Their hydrodynamic characteristics are analyzed, in particular their symmetries. In addition, the case that inlet boundary conditions are slightly asymmetric is investigated. It is found that bifurcation processes are extremely sensitive to this small symmetry-breaking imperfection and much different from those in the symmetric case. Furthermore, model equations are constructed by symmetry consideration to explain the numerical results based on hydrodynamic equations.

Flow reversals in two-dimensional Rayleigh-Benard convection led by non-Oberbeck-Boussinesq (NOB) effects due to large temperature differences arc studied by direct numerical simulation. Perfect gas is chosen as the working fluid and the Prandtl number is 0.71 for the reference state. 11 NOB effects are included, the flow pattern P-11 with only one dominant roll often becomes unstable by the growth of the cold corner roll, which sometimes results in cession-led flow reversals. By exploiting the vorticity transport equation, it is found that the asymmetries of buoyancy and viscous forces are responsible for the growth of the cold corner roll because both such asymmetries cause an imbalance between the corner rolls and the large-scale circulation (I.SC). The buoyancy force near the cold wall increases and decreases near the hot wall originating from the temperature-dependent isobaric thermal expansion coefficient alpha = 1/T if NOB effects are included; Moreover, the decreased dissipation due to lower viscosity is favourable for the growth of the cold corner roll, while the increased viscosity further suppresses the growth of the hot corner roll. Finally, it is found that the boundary layer near the cold wall plays an important role in the mass transport from LSC to corner rolls subject to mass conservation.

We report on a three-dimensional direct numerical simulation study of flow structure and heat transport in the annular centrifugal Rayleigh-Bdnard convection (ACRBC) system, with cold inner and hot outer cylinders corotating axially, for the Rayleigh number range Ra is an element of [10(6), 10(8)] and radius ratio range eta = R-i/R-o is an element of [0.3, 0.9] (R-i and R-o are the radius of the inner and outer cylinders, respectively). This study focuses on the dependence of flow dynamics, heat transport and asymmetric mean temperature fields on the radius ratio eta. For the inverse Rossby number Ro(-1) = 1, as the Coriolis force balances inertial force, the flow is in the inertial regime. The mechanisms of zonal flow revolving in the prograde direction in this regime are attributed to the asymmetric movements of plumes and the different curvatures of the cylinders. The number of roll pairs is smaller than the circular roll hypothesis as the convection rolls are probably elongated by zonal flow. The physical mechanism of zonal flow is verified by the dependence of the drift frequency of the large-scale circulation (LSC) rolls and the space- and time-averaged azimuthal velocity on eta. The larger eta is, the weaker the zonal flow becomes. We show that the heat transport efficiency increases with eta. It is also found that the bulk temperature deviates from the arithmetic mean temperature and the deviation increases as eta decreases. This effect can be explained by a simple model that accounts for the curvature effects and the radially dependent centrifugal force in ACRBC.

We perform a numerical study of the heat transfer and flow structure of Rayleigh-Benard (RB) convection in (in most cases regular) porous media, which are comprised of circular, solid obstacles located on a square lattice. This study is focused on the role of porosity in the flow properties during the transition process from the traditional RB convection with (so no obstacles included) to Darcy-type porous-media convection with approaching 0. Simulations are carried out in a cell with unity aspect ratio, for Rayleigh number from to and varying porosities , at a fixed Prandtl number , and we restrict ourselves to the two-dimensional case. For fixed , the Nusselt number is found to vary non-monotonically as a function of ; namely, with decreasing , it first increases, before it decreases for approaching 0. The non-monotonic behaviour of originates from two competing effects of the porous structure on the heat transfer. On the one hand, the flow coherence is enhanced in the porous media, which is beneficial for the heat transfer. On the other hand, the convection is slowed down by the enhanced resistance due to the porous structure, leading to heat transfer reduction. For fixed , depending on , two different heat transfer regimes are identified, with different effective power-law behaviours of versus , namely a steep one for low when viscosity dominates, and the standard classical one for large . The scaling crossover occurs when the thermal boundary layer thickness and the pore scale are comparable. The influences of the porous structure on the temperature and velocity fluctuations, convective heat flux and energy dissipation rates are analysed, further demonstrating the competing effects of the porous structure to enhance or reduce the heat transfer.

We study the translational and rotational dynamics of neutrally buoyant finite-size spheroids in hydrodynamic turbulence by means of fully resolved numerical simulations. We examine axisymmetric shapes, from oblate to prolate, and the particle volume dependences. We show that the accelerations and rotations experienced by non-spherical inertial-scale particles result from volume filtered fluid forces and torques, similar to spherical particles. However, the particle orientations carry signatures of preferential alignments with the surrounding flow structures, which are reflected in distinct axial and lateral fluctuations for accelerations and rotation rates. The randomization of orientations does not occur even for particles with volume-equivalent diameter size in the inertial range, here up to 60 dissipative units (eta) at Taylor-scale Reynolds number Re-lambda = 120. Additionally, we demonstrate that the role of fluid boundary layers around the particles cannot be neglected in reaching a quantitative understanding of particle statistical dynamics, as they affect the intensities of the angular velocities and the relative importance of tumbling with respect to spinning rotations. This study brings to the fore the importance of inertial-scale flow structures in homogeneous and isotropic turbulence and their impacts on the transport of neutrally buoyant bodies with sizes in the inertial range.

This paper presents a numerical study of the Rayleigh-Benard convection (RBC) in two-dimensional cells with asymmetric (ratchet) roughness distributed on the top and bottom surfaces. We consider two aspect ratios of roughness gamma = 1, 2 and the range of the Rayleigh number 1.0 x 10(6) <= Ra <= 2.0 x 10(10) with the Prandtl number Pr = 4. The influences of the roughness on the heat transfer and the flow structure are found to be strongly dependent on both Ra and the roughness geometry. We find that the roughness can have a significant influence on the organization of the secondary corner rolls, and the corner rolls are evidently suppressed by the roughness for intermediate values of Ra. In the presence of the roughness, a sharp jump of the Nu values is identified as the Ra value is slightly increased, accompanied with the dramatic changes of the large-scale flow structure and the plume dynamics. The influences of the ratchet orientation on the heat transfer and the flow structure are discussed and analyzed.

In this numerical study on Rayleigh-Benard convection, we seek to improve the heat transfer by passive means. To this end we introduce a single tilted conductive barrier centered in an aspect ratio one cell, breaking the symmetry of the geometry and to channel the ascending hot and descending cold plumes. We study the global and local heat transfer and the flow organization for Rayleigh numbers 10(5) <= Ra <= 10(9) for a fixed Prandtl number of Pr = 4.3. We find that the global heat transfer can be enhanced up to 18%, and locally around 800%. The averaged Reynolds number is always decreased when a barrier is introduced, even for those cases where the global heat transfer is increased. We map the entire parameter space spanned by the orientation and the size of a single barrier for Ra = 10(8).

We report a numerical study of Rayleigh-Benard convection through random porous media using pore-scale modelling, focusing on the Lagrangian dynamics of fluid particles and heat transfer for varied porosities . Due to the interaction between the porous medium and the coherent flow structures, the flow is found to be highly heterogeneous, consisting of convection channels with strong flow strength and stagnant regions with low velocities. The modifications of flow field due to porous structure have a significant influence on the dynamics of fluid particles. Evaluation of the particle displacement along the trajectory reveals the emergence of anomalous transport for long times as is decreased, which is associated with the long-time correlation of Lagrangian velocity of the fluid. As porosity is decreased, the cross-correlation between the vertical velocity and temperature fluctuation is enhanced, which reveals a mechanism to enhance the heat transfer in porous-media convection.

The influences of non-Oberbeck-Boussinesq (NOB) effects on flow instabilities and bifurcation characteristics of Rayleigh-Benard convection are examined. The working fluid is air with reference Prandtl number Pr = 0.71 and contained in two-dimensional rigid cavities of finite aspect ratios. The fluid flow is governed by the low-Mach-number equations, accounting for the NOB effects due to large temperature difference involving flow compressibility and variations of fluid viscosity and thermal conductivity with temperature. The intensity of NOB effects is measured by the dimensionless temperature differential epsilon. Linear stability analysis of the thermal conduction state is performed. An epsilon(2) scaling of the leading-order corrections of critical Rayleigh number Ra-cr and disturbance growth rate sigma due to NOB effects is identified, which is a consequence of an intrinsic symmetry of the system. The influences of weak NOB effects on flow instabilities are further studied by perturbation expansion of linear stability equations with regard to epsilon, and then the influence of aspect ratio A is investigated in detail. NOB effects are found to enhance (weaken) flow stability in large (narrow) cavities. Detailed contributions of compressibility, viscosity and buoyancy actions on disturbance kinetic energy growth are identified quantitatively by energy analysis. Besides, a weakly nonlinear theory is developed based on centre-manifold reduction to investigate the NOB influences on bifurcation characteristics near convection onset, and amplitude equations are constructed for both codimension-one and -two cases. Rich bifurcation regimes are observed based on amplitude equations and also confirmed by direct numerical simulation. Weakly nonlinear analysis is useful for organizing and understanding these simulation results.