Related papers: Influence of through-flow on linear pattern format…
We investigate theoretically the nonlinear state of ideal straight rolls in the Rayleigh-B\'enard system of a fluid layer heated from below with a porous medium using a Galerkin method. Applying the Oberbeck-Boussinesq approximation, binary…
We hypothesize that dynamical systems concepts used to study the transition to turbulence in shear flows are applicable to other transition phenomena in fluid mechanics. In this paper, we consider a finite air bubble that propagates within…
Rayleigh-B\'{e}nard convection is studied and quantitative comparisons are made, where possible, between theory and experiment by performing numerical simulations of the Boussinesq equations for a variety of experimentally realistic…
We study the emergence of a velocity-dip phenomenon in turbulent mixed convection in open Poiseuille-Rayleigh-B\'enard (PRB) channels with a free-slip upper boundary. Three-dimensional direct numerical simulations (DNS) are performed for…
We analyse the process of convective mixing in two-dimensional, homogeneous and isotropic porous media with dispersion. We considered a Rayleigh-Taylor instability in which the presence of a solute produces density differences driving the…
The stability of two-dimensional Poiseuille flow and plane Couette flow for concentrated suspensions is investigated. Linear stability analysis of the two-phase flow model for both flow geometries shows the existence of a convectively…
The mixed convection flow in a plane channel with adiabatic boundaries is examined. The boundaries have an externally prescribed relative velocity defining a Couette-like setup for the flow. A stationary flow regime is maintained with a…
We consider the solution to the 2D Navier-Stokes equations around the Poiseuille flow $(y^2,0)$ on $\mathbb{T}\times\mathbb{R}$ with small viscosity $\nu>0$. Via a hypocoercivity argument, we prove that the $x-$dependent modes of the…
The current study is a pioneering work in presenting the boundary layer equations for the two-dimensional flow and heat transfer of the Cross fluid over a linearly stretching sheet. The system of partial differential equations is turned…
Nonlinear, spatially localized structures of traveling convection rolls are investigated in quantitative detail as a function of Rayleigh number for two different Soret coupling strengths (separation ratios) with Lewis and Prandtl numbers…
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 the above paper the authors treat the boundary layer flow along a stationary, vertical, permeable, flat plate within a vertical free stream. Fluid is sucked or injected through the vertical plate. The fluid species concentration at the…
Linear and nonlinear properties of convection in binary fluid layers heated from below are investigated, in particular for gas parameters. A Galerkin approximation for realistic boundary conditions that describes stationary and oscillatory…
A simple model to explain numerically observed behaviour of chaotically varying stripes and square patterns in zero Prandtl number convection in Boussinesq fluid is presented. The nonlinear interaction of mutually perpendicular sets of wavy…
The stability of plane Poiseuille flow of a viscous Newtonian fluid in a multilayer channel with anisotropic porous walls is analyzed using the classical modal analysis, the energy method, and the non-modal analysis. The influence of porous…
Convection in an infinite fluid layer is often modelled by considering a finite box with periodic boundary conditions in the two horizontal directions. The translational invariance of the problem implies that any solution can be translated…
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…
Turbulent shear flows driven by a combination of a pressure gradient and buoyancy forcing are investigated using direct numerical simulations. Specifically, we consider the setup of a differentially heated vertical channel subject to a…
This paper investigates the generation of free-surface waves in a liquid layer driven by linear instabilities in Couette-Poiseuille (quadratic) shear flows. The base velocity profiles are characterized by a curvature parameter, and…
In this paper we derive consistent shallow water equations for thin films of power law fluids down an incline. These models account for the streamwise diffusion of momentum which is important to describe accurately the full dynamic of the…