Related papers: Pattern dynamics near homoclinic bifurcation in Ra…
We present results of direct numerical simulations on homoclinic gluing and ungluing bifurcations in low-Prandtl-number ($ 0 \leq Pr \leq 0.025 $) Rayleigh-B\'{e}nard system rotating slowly and uniformly about a vertical axis. We have…
In the inclined layer convection system, thermal convection in a Rayleigh--B\'enard cell tilted against gravity, the flow is subject to competing buoyancy and shear forces. For varying inclination angle ($\gamma$) and Rayleigh number…
The main objective of this article is to study the three-dimensional Rayleigh-Benard convection in a rectangular domain from a pattern formation perspective. It is well known that as the Rayleigh number crosses a critical threshold, the…
A six-dimensional reversible normal form system occurs in B{\'e}nard-Rayleigh convection between parallel planes, when we look for domain walls intersecting orthogonally (see Buffoni et al [1]). On the truncated system, we prove…
We study the Rayleigh-B{\'e}nard convection in a 2-D rectangular domain with no-slip boundary conditions for the velocity. The main mathematical challenge is due to the no-slip boundary conditions, since the separation of variables for the…
A low-dimensional model of large Prandtl-number ($P$) Rayleigh B\'{e}nard convection is constructed using some of the important modes of pseudospectral direct numerical simulations. A detailed bifurcation analysis of the low-dimensional…
In B{\'e}nard-Rayleigh convection we consider the pattern defect in orthogonal domain walls connecting a set of convective rolls with another set of rolls orthogonal to the first set. This is understood as an heteroclinic orbit of a…
A model for three-dimensional Rayleigh-B\'{e}nard convection in low-Prandtl-number fluids near onset with rigid horizontal boundaries in the presence of a uniform vertical magnetic field is constructed and analyzed in detail. The kinetic…
We use direct numerical simulations to study convection in rotating Rayleigh-B\'enard convection in horizontally confined geometries of a given aspect ratio, with the walls held at fixed temperatures. We show that this arrangement is…
We use nonlinear signal processing techniques, based on artificial neural networks, to construct an empirical mapping from experimental Rayleigh-Benard convection data in the quasiperiodic regime. The data, in the form of a one-parameter…
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…
We present a detailed bifurcation structure and associated flow patterns for low-Prandtl number ($P=0.0002, 0.002, 0.005, 0.02$) Rayleigh-B\'{e}nard convection near its onset. We use both direct numerical simulations and a 30-mode…
We present the detailed bifurcation structure and associated flow patterns near the onset of zero Prandtl number Rayleigh B\'enard convection. We employ both direct numerical simulation and a low-dimensional model ensuring qualitative…
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…
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…
We summarize our findings about laterally periodic convection structures in binary mixtures in the Rayleigh-Benard system for positive Soret effect. Stationary roll, square, and crossroll solutions and their stability are determined with a…
Numerical simulations of the time-dependent Swift-Hohenberg equation are used to test predictions of Cross [Phys. Rev. A 25:1065-1076 (1982)] that Rayleigh-Benard convection in the form of straight rolls or of an array of dislocations may…
We investigate the origin of various convective patterns using bifurcation diagrams that are constructed using direct numerical simulations. We perform two-dimensional pseudospectral simulations for a Prandtl number 6.8 fluid that is…
We report experimental results for convection near onset in a thin layer of a homeotropically aligned nematic liquid crystal heated from below as a function of the temperature difference $\Delta T$ and the applied vertical magnetic field…
Effects of a uniform magnetic field on homoclinic bifurcations in Rayleigh-B\'{e}nard convection in a fluid of Prandtl number $Pr = 0.01$ are investigated using direct numerical simulations (DNS). A uniform magnetic field is applied either…