相关论文: Route to hyperchaos in Rayleigh-Benard convection
We study the Rayleigh-B{\'e}nard convection in a 2-D rectangular domain with no-slip boundary conditions for the velocity. The main mathematical challenge is due to the no-slip boundary conditions, since the separation of variables for the…
In wall-bounded flows, the laminar regime remain linearly stable up to large values of the Reynolds number while competing with nonlinear turbulent solutions issued from finite amplitude perturbations. The transition to turbulence of plane…
We present results from a numerical study of particle dispersion in the weakly nonlinear regime of Rayleigh-B\'enard convection of a fluid with Prandtl number around unity, where bi-stability between ideal straight convection rolls and weak…
Large-scale patterns, which are well-known from the spiral defect chaos regime of thermal convection at Rayleigh numbers $Ra < 10^4$, continue to exist in three-dimensional numerical simulations of turbulent Rayleigh-B\'{e}nard convection…
Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant Lyapunov vectors have been proposed as…
We explore the chaotic dynamics of Rayleigh-B\'enard convection using large-scale, parallel numerical simulations for experimentally accessible conditions. We quantify the connections between the spatiotemporal dynamics of the leading-order…
We test the ability of a low-dimensional turbulence model to predict how dynamics of large-scale coherent structures such as convection rolls change in different cell geometries. We performed Rayleigh-B\'enard convection experiments in a…
We investigate the large-scale circulation (LSC) in a turbulent Rayleigh-B\'enard convection flow in a cubic closed convection cell by means of direct numerical simulations at a Rayleigh number $Ra=10^6$. The numerical studies are conducted…
We investigate instabilities and chaos near the onset of Rayleigh-B\'{e}nard convection (RBC) of electrically conducting fluids with free-slip, perfectly electrically and thermally conducting boundary conditions in presence of uniform…
We study numerically a succession of transitions in pipe Poiseuille flow that leads from simple travelling waves to waves with chaotic time-dependence. The waves at the origin of the bifurcation cascade possess a shift-reflect symmetry and…
Numerous study on natural and man made systems including rotating convection report the phenomena of supercritical and subcritical transitions from one state to another with the variation of relevant control parameters. However, the…
The study of the transitions among different regimes in thermal convection has been an issue of paramount importance in fluid mechanics. While the bifurcations at low Rayleigh number, when the flow is laminar or moderately chaotic, have…
We present three-dimensional direct numerical simulations of turbulent Rayleigh-B\'enard convection in a closed rectangular box whose width $L_y$ and length $L_x$ are 0.8 and 2.4 times the height $H$, respectively. The Rayleigh number $Ra$…
The transition of the flow in a duct of square cross-section is studied. Like in the similar case of the pipe flow, the motion is linearly stable for all Reynolds numbers; this flow is thus a good candidate to investigate the 'bypass' path…
Asymptotically large Reynolds number hydrodynamic turbulence is characterized by multi-scaling of moments of velocity increments and spatial derivatives. With decreasing Reynolds number toward $R_{\lambda}=R^{tr}_{\lambda}\approx 9.0$, the…
The Boussinesq equations for Rayleigh-Benard convection are simulated for a cylindrical container with an aspect ratio near 1.5. The transition from an axisymmetric stationary flow to time-dependent flows is studied using nonlinear…
The progress in our understanding of several aspects of turbulent Rayleigh-Benard convection is reviewed. The focus is on the question of how the Nusselt number and the Reynolds number depend on the Rayleigh number Ra and the Prandtl number…
A numerical investigation of an asymptotically reduced model for quasi-geostrophic Rayleigh-B\'enard convection is conducted in which the depth-averaged flows are numerically suppressed by modifying the governing equations. The Reynolds…
A Rayleigh-B\'enard cell has been designed to explore the Prandtl (Pr) dependence of turbulent convection in the cross-over range $0.7<Pr<21$ and for the full range of soft and hard turbulences, up to Rayleigh number $Ra\simeq 10^{11}$. The…
Turbulent superstructures in horizontally extended three-dimensional Rayleigh-B\'enard convection flows are investigated in controlled laboratory experiments in water at Prandtl number $Pr = 7$. A Rayleigh-B\'enard cell with square…