Analytical and numerical stability analysis of Soret-driven convection in a horizontal porous layer

We present an analytical and numerical stability analysis of Soret-driven convection in a porous cavity saturated by a binary fluid. Both the mechanical equilibrium solution and the monocellular flow obtained for particular ranges of the physical parameters of the problem are considered. The porous cavity, bounded by horizontal infinite or finite boundaries, is heated from below or from above. The two horizontal plates are maintained at different constant temperatures while no mass flux is imposed. The influence of the governing parameters and more particularly the role of the separation ratio, characterizing the Soret effect and the normalized porosity, are investigated theoretically and numerically. From the linear stability analysis, we find that the equilibrium solution loses its stability via a stationary bifurcation or a Hopf bifurcation depending on the separation ratio and the normalized porosity of the medium. The role of the porosity is important, when it decreases, the stability of the equilibrium solution is reinforced. For a cell heated from below, the equilibrium solution loses its stability via a stationary bifurcation when the separation ratio >0(Le,), while for 0, while a stationary or an oscillatory bifurcation occurs if mono the monocellular flow loses stability via a Hopf bifurcation. As the Rayleigh number increases, the resulting oscillatory solution evolves to a stationary multicellular flow. For a cell heated from above and <0, the monocellular flow remains linearly stable. We verified numerically that this problem admits other stable multicellular stationary solutions for this range of parameters

The dynamism of salt crust patterns on playas

Playas are common in arid environments and can be major sources of mineral dust that can influence global climate. These landforms typically form crusts that limit evaporation and dust emission, modify surface erosivity and erodibility, and can lead to over prediction or under prediction of (1) dust-emission potential and (2) water and heat fluxes in energy balance modeling. Through terrestrial laser scanning measurements of part of the Makgadikgadi Pans of Botswana (a Southern Hemisphere playa that emits significant amounts of dust), we show that over weeks, months, and a year, the shapes of these surfaces change considerably (ridge thrusting of &gt;30 mm/week) and can switch among continuous, ridged, and degraded patterns. Ridged pattern development changes the measured aerodynamic roughness of the surface (as much as 3 mm/week). The dynamic nature of these crusted surfaces must be accounted for in dust entrainment and moisture balance formulae to improve regional and global climate models

Anomalous Scaling and Solitary Waves in Systems with Non-Linear Diffusion

We study a non-linear convective-diffusive equation, local in space and time, which has its background in the dynamics of the thickness of a wetting film. The presence of a non-linear diffusion predicts the existence of fronts as well as shock fronts. Despite the absence of memory effects, solutions in the case of pure non-linear diffusion exhibit an anomalous sub-diffusive scaling. Due to a balance between non-linear diffusion and convection we, in particular, show that solitary waves appear. For large times they merge into a single solitary wave exhibiting a topological stability. Even though our results concern a specific equation, numerical simulations supports the view that anomalous diffusion and the solitary waves disclosed will be general features in such non-linear convective-diffusive dynamics.Comment: Corrected typos, added 3 references and 2 figure

Effect of a finite external heat transfer coefficient on the Darcy-Benard instability in a vertical porous cylinder

The onset of thermal convection in a vertical porous cylinder is studied by considering the heating from below and the cooling from above as caused by external forced convection processes. These processes are parametrised through a finite Biot number, and hence through third-kind, or Robin, temperature conditions imposed on the lower and upper boundaries of the cylinder. Both the horizontal plane boundaries and the cylindrical sidewall are assumed to be impermeable; the sidewall is modelled as a thermally insulated boundary. The linear stability analysis is carried out by studying separable normal modes, and the principle of exchange of stabilities is proved. It is shown that the Biot number does not affect the ordering of the instability modes that, when the radius-to-height aspect ratio increases, are displayed in sequence at the onset of convection. On the other hand, the Biot number plays a central role in determining the transition aspect ratios from one mode to its follower. In the limit of a vanishingly small Biot number, just the first (non-axisymmetric) mode is displayed at the onset of convection, for every value of the aspect ratio. (C) 2013 American Institute of Physic

Probing e-e interactions in a periodic array of GaAs quantum wires

We present the results of non-linear tunnelling spectroscopy between an array of independent quantum wires and an adjacent two-dimensional electron gas (2DEG) in a double-quantum-well structure. The two layers are separately contacted using a surface-gate scheme, and the wires are all very regular, with dimensions chosen carefully so that there is minimal modulation of the 2DEG by the gates defining the wires. We have mapped the dispersion spectrum of the 1D wires down to the depletion of the last 1D subband by measuring the conductance \emph{G} as a function of the in-plane magnetic field \emph{B}, the interlayer bias $V_{\rm dc}$ and the wire gate voltage. There is a strong suppression of tunnelling at zero bias, with temperature and dc-bias dependences consistent with power laws, as expected for a Tomonaga-Luttinger Liquid caused by electron-electron interactions in the wires. In addition, the current peaks fit the free-electron model quite well, but with just one 1D subband there is extra structure that may indicate interactions.Comment: 3 pages, 3 figures; formatting correcte

Fluid Flows of Mixed Regimes in Porous Media

In porous media, there are three known regimes of fluid flows, namely, pre-Darcy, Darcy and post-Darcy. Because of their different natures, these are usually treated separately in literature. To study complex flows when all three regimes may be present in different portions of a same domain, we use a single equation of motion to unify them. Several scenarios and models are then considered for slightly compressible fluids. A nonlinear parabolic equation for the pressure is derived, which is degenerate when the pressure gradient is either small or large. We estimate the pressure and its gradient for all time in terms of initial and boundary data. We also obtain their particular bounds for large time which depend on the asymptotic behavior of the boundary data but not on the initial one. Moreover, the continuous dependence of the solutions on initial and boundary data, and the structural stability for the equation are established.Comment: 33 page