Related papers: One dimensional models for supercritical and subcr…
The classical Rayleigh-B\'{e}nard convection (RBC) system is known to exhibit either subcritical or supercritical transition to convection in the presence or absence of rotation and/or magnetic field. However, the simultaneous exhibition of…
A pure and incompressible material is confined between two plates such that it is heated from below and cooled from above. When its melting temperature is comprised between these two imposed temperatures, an interface separating liquid and…
Numerical simulations of rotating Rayleigh-B\'enard convection are presented for both no slip and free slip boundaries. The goal is to find a criterion distinguishing convective flows dominated by the Coriolis force from those nearly…
We investigate by direct numerical simulation Rayleigh-B\'enard convection in a rotating rectangular cell with rotation vector and gravity perpendicular to each other. The flow is two dimensional near the onset of convection with convection…
The previous investigation on Rayleigh-B\'enard convection of a dilute classical gas [T. Kita: J. Phys. Soc. Jpn. {\bf 75} (2006) 124005] is extended to calculate entropy change of the convective transition with the rigid boundaries. We…
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…
The main objective of this article is to study the three-dimensional Rayleigh-Benard convection in a rectangular domain from a pattern formation perspective. It is well known that as the Rayleigh number crosses a critical threshold, the…
A coupled map lattice for convection is proposed, which consists of Eulerian and Lagrangian procedures. Simulations of the model not only reproduce a wide-range of phenomena in Rayleigh-B\'{e}nard convection experiments but also lead to…
The possibility of subcritical behaviour in the geostrophic turbulence regime of rapidly rotating thermally driven convection is explored. In this regime a non-local inverse energy transfer may compete with the more traditional and local…
Rayleigh-Benard convection in a cylindrical container can take on many different spatial forms. Motivated by the results of Hof, Lucas and Mullin [Phys. Fluids 11, 2815 (1999)], who observed coexistence of several stable states at a single…
Buoyancy-induced (Rayleigh-Benard) convection of a fluid between two horizontal plates is a central paradigm for studying the transition to complex spatiotemporal dynamics in sustained nonequilibrium systems. To improve the analysis of…
Solid state convection can take place in the rocky or icy mantles of planetary objects and these mantles can be surrounded above or below or both by molten layers of similar composition. A flow toward the interface can proceed through it by…
A detailed study of the Rayleigh-B\'enard convection in two-dimensions with free-slip boundaries is presented. Pseudo-spectral method has been used to numerically solve the system for Rayleigh number up to $3.3 \times 10^7$. The system…
The main objective of this article is part of a research program to link the dynamics of fluid flows with the structure and its transitions in the physical spaces. As a prototype of problem and to demonstrate the main ideas, we study the…
The transition to turbulence in Rayleigh-Benard convection with phase changes and the resulting convective patterns are studied in a three-dimensional Galerkin model. Our study is focused to the conditionally unstable regime of moist…
The dynamics of heat transfer in a model system of Rayleigh-B\'enard (RB) convection reduced to its essential, here dubbed Burgers-Rayleigh-B\'enard (BRB), is studied. The system is spatially one-dimensional, the flow field is compressible…
We investigate the stability and dynamics of natural convection in two dimensions, subject to inhomogeneous boundary conditions. In particular, we consider a Rayleigh-B\`enard (RB) cell, where the horizontal top boundary contains a periodic…
We study the evolution of a melting front between the solid and liquid phases of a pure incompressible material where fluid motions are driven by unstable temperature gradients. In a plane layer geometry, this can be seen as classical…
The initial bifurcations in rotating Rayleigh-B\'enard convection are studied in the range of dimensionless rotation rate $0 < \Omega < 2150$ for an aspect-ratio-2.5 cylindrical cell. We used simultaneous optical shadowgraph, heat transport…
Numerical simulations of dynamos in rotating Rayleigh-B\'enard convection in plane layers are presented. Two different types of dynamos exist which obey different scaling laws for the amplitude of the magnetic field. The transition between…