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Nonlinear convection structures are investigated in quantitative detail as a function of Rayleigh number for several negative and positive Soret coupling strengths (separation ratios) and different Lewis and Prandtl numbers characterizing…
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…
Spatially confined solutions of traveling convection rolls are determined numerically for binary mixtures like ethanol-water. The appropriate field equations are solved in a vertical crossection of the rolls perpendicular to their axes…
Vertical thermal convection system exhibits weak turbulence and spatio-temporally chaotic behaviour. In this system, we report seven equilibria and 26 periodic orbits, all new and linearly unstable. These orbits, together with four…
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…
We describe an interpretation of convection in binary fluid mixtures as a superposition of thermal and solutal problems, with coupling due to advection and proportional to the separation parameter S. Many properties of binary fluid…
We study the convective instability of the melt during the initial transient in a directional solidification experiment in a vertical configuration. We obtain analytically the dispersion relation, and perform an additional asymptotic…
We examine the steady state of turbulent flows in thin layers using direct numerical simulations. It is shown that when the layer thickness is smaller than a critical height, an inverse cascade arises which leads to the formation of a…
An eigenvalue equation, for linear instability modes involving large scales in a convective hydromagnetic system, is derived in the framework of multiscale analysis. We consider a horizontal layer with electrically conducting boundaries,…
Vertical convection is the fluid motion that is induced by the heating and cooling of two opposed vertical boundaries of a rectangular cavity (see e.g. Wang et al. 2021). We consider the linear stability of the steady two-dimensional flow…
Volatile viscous fluids on partially-wetting solid substrates can exhibit interesting interfacial instabilities and pattern formation. We study the dynamics of vapor condensation and fluid evaporation governed by a one-sided model in a low…
A one-dimensional turbulent convection model in the form of a time-dependent diffusion equation for the turbulent energy is incorporated into our numerical pulsation code. The effect of turbulent convection on the structural rearrangement…
We show the possibility of quasiperiodic waves at the onset of thermal convection in a thin horizontal layer of slowly rotating zero-Prandtl number Boussinesq fluid confined between stress-free conducting boundaries. Two independent…
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…
A ubiquitous arrangement in nature is a free-flowing fluid coupled to a porous medium, for example a river or lake lying above a porous bed. Depending on the environmental conditions, thermal convection can occur and may be confined to the…
Oscillatory double-diffusive convection in horizontal cavity with Soret and Dufour effects is investigated numerically based on SIMPLE algorithm with QUICK scheme in non-uniform staggered grid system. The results show that double-diffusive…
We perform linear and nonlinear stability analysis for thermal convection in a fluid overlying a saturated porous medium. We use a coupled system, with the Navier-Stokes equations and Darcy's equation governing the free-flow and the porous…
In this note, we investigate a doubly nonlinear diffusion equation in the slow diffusion regime. We prove stability of the pressure of solutions that are close to traveling wave solutions in a homogeneous Lipschitz sense. We derive…
We study the (local) propagation of plane waves in a relativistic, non-dissipative, two-fluid system, allowing for a relative velocity in the "background" configuration. The main aim is to analyze relativistic two-stream instability. This…
Zonal flows are often found in rotating convective systems. Not only are these jet-flows driven by the convection, they can also have a profound effect on the nature of the convection. In this work the cylindrical annulus geometry is…