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The parameter dependence of the various attractive solutions of the three variable nonlinear Lorenz model equations for thermal convection in Rayleigh-B\'enard flow is studied. Its bifurcation structure has commonly been investigated as a…
In a range of physical systems, the first instability in Rayleigh-Bernard convection between nearly thermally insulating horizontal plates is large scale. This holds for thermal convection of fluids saturating porous media. Large-scale…
We study shallow moist Rayleigh-Benard convection in the Boussinesq approximation in three-dimensional direct numerical simulations. The thermodynamics of phase changes is approximated by a piecewise linear equation of state close to the…
We report for the first time the pattern dynamics in the vicinity of an inverse homoclinic bifurcation in an extended dissipative system. We observe, in direct numerical simulations of three dimensional Rayleigh-B\'{e}nard convection, a…
The convective instability in a plane liquid layer with time-dependent temperature profile is investigated by means of a general method suitable for linear stability analysis of an unsteady basic flow. The method is based on a non-normal…
We present a theoretical study on pattern formation occurring in miscible fluids reacting by a second-order reaction $A + B \to S$ in a vertical Hele-Shaw cell under constant gravity. We have recently reported that concentration-dependent…
This work is devoted to the theoretical study of the stability of two superposed horizontal liquid layers bounded by two solid planes and subjected to a horizontal temperature gradient. The liquids are supposed to be immiscible with a…
The spontaneous convective patterns induced by evaporation of a pure liquid layer are studied experimentally. A volatile liquid layer placed in a cylindrical container is left free to evaporate into air at rest under ambient conditions. The…
Relationship between a surface pattern and vertical convections is studied in a condition of Rayleigh-Taylor instability. The vertical convections change with the case configuration and the aspect ratio r / h of the case, where r and h show…
Inertial modes have been observed on the Sun at low longitudinal wavenumbers. These modes probe the dynamics and structure of the solar convection zone down to the tachocline. While linear analysis allows the complex eigenfrequencies and…
Despite the presence of strong fluctuations, many turbulent systems such as Rayleigh-B\'{e}nard convection and Taylor-Couette flow display self-organized large-scale flow patterns. How do small-scale turbulent fluctuations impact the…
We study the dynamics associated with the extension of turbulent convective motions from a convection zone (CZ) into a stable region (RZ) that lies below the latter. For that purpose, we have run a series of three-dimensional direct…
Melting and, conversely, solidification processes in the presence of convection are key to many geophysical problems. An essential question related to these phenomena concerns the estimation of the (time-evolving) melting rate, which is…
We investigate a number of complex patterns driven by the electro-convection instability in a planarly aligned layer of a nematic liquid crystal. They are traced back to various secondary instabilities of the ideal roll patterns bifurcating…
Context. The one-dimensional treatment of turbulent convection had large successes until the early 2000s. However, the recent abundance and precision of observational data shows that this problem is far from solved. A modern approach should…
Horizontally-periodic Boussinesq Rayleigh-B\'enard Convection (RBC) is a simple model system to study the formation of large-scale structures in turbulent convective flows. We performed a suite of 2D numerical simulations of RBC between…
We present a numerical study of double-diffusive convection characterized by a stratification unstable to thermal convection while at the same time a mean molecular weight (or solute concentration) difference between top and bottom…
Gravity-driven convection of fluid at parameters near its thermodynamic critical point inside a porous layer heated from below (Rayleigh-Darcy convection) is studied. The fluid having the temperature slightly above the critical one is…
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…
This work studies two-dimensional fixed-flux Rayleigh-B\'enard convection with periodic boundary conditions in both horizontal and vertical directions and analyzes its dynamics using numerical continuation, secondary instability analysis…