195 research outputs found
Penetrative Convection at High Rayleigh Numbers
We study penetrative convection of a fluid confined between two horizontal
plates, the temperatures of which are such that a temperature of maximum
density lies between them. The range of Rayleigh numbers studied is and the Prandtl numbers are and . An
evolution equation for the growth of the convecting region is obtained through
an integral energy balance. We identify a new non-dimensional parameter,
, which is the ratio of temperature difference between the stable and
unstable regions of the flow; larger values of denote increased
stability of the upper stable layer. We study the effects of on the
flow field using well-resolved lattice Boltzmann simulations, and show that the
characteristics of the flow depend sensitively upon it. For the range , we find that for a fixed the Nusselt number,
, increases with decreasing . We also investigate the effects of
on the vertical variation of convective heat flux and the
Brunt-V\"{a}is\"{a}l\"{a} frequency. Our results clearly indicate that in the
limit the problem reduces to that of the classical
Rayleigh-B\'enard convection.Comment: 12 pages, 19 figure
Nonlinear threshold behavior during the loss of Arctic sea ice
In light of the rapid recent retreat of Arctic sea ice, a number of studies have discussed the possibility of a critical threshold (or “tipping point”) beyond which the ice–albedo feedback causes the ice cover to melt away in an irreversible process. The focus has typically been centered on the annual minimum (September) ice cover, which is often seen as particularly susceptible to destabilization by the ice–albedo feedback. Here, we examine the central physical processes associated with the transition from ice-covered to ice-free Arctic Ocean conditions. We show that although the ice–albedo feedback promotes the existence of multiple ice-cover states, the stabilizing thermodynamic effects of sea ice mitigate this when the Arctic Ocean is ice covered during a sufficiently large fraction of the year. These results suggest that critical threshold behavior is unlikely during the approach from current perennial sea-ice conditions to seasonally ice-free conditions. In a further warmed climate, however, we find that a critical threshold associated with the sudden loss of the remaining wintertime-only sea ice cover may be likely
Can planetesimals form by collisional fusion?
As a test bed for the growth of protoplanetary bodies in a turbulent
circumstellar disk we examine the fate of a boulder using direct numerical
simulations of particle seeded gas flowing around it. We provide an accurate
description of the flow by imposing no-slip and non-penetrating boundary
conditions on the boulder surface using the immersed boundary method pioneered
by Peskin (2002). Advected by the turbulent disk flow, the dust grains collide
with the boulder and we compute the probability density function (PDF) of the
normal component of the collisional velocity. Through this examination of the
statistics of collisional velocities we test the recently developed concept of
collisional fusion which provides a physical basis for a range of collisional
velocities exhibiting perfect sticking. A boulder can then grow sufficiently
rapidly to settle into a Keplerian orbit on disk evolution time scales.Comment: Astrophysical Journal, in pres
Onsager reciprocity in premelting solids
The diffusive motion of foreign particles dispersed in a premelting solid is analyzed within the framework of irreversible thermodynamics. We determine the mass diffusion coefficient, thermal diffusion coefficient and Soret coefficient of the particles in the dilute limit, and find good agreement with experimental data. In contrast to liquid suspensions, the unique nature of premelting solids allows us to derive an expression for the Dufour coefficient and independently verify the Onsager reciprocal relation coupling diffusion to the flow of heat
Theory of ice premelting in porous media
Premelting describes the confluence of phenomena that are responsible for the
stable existence of the liquid phase of matter in the solid region of its bulk
phase diagram. Here we develop a theoretical description of the premelting of
water ice contained in a porous matrix, made of a material with a melting
temperature substantially larger than ice itself, to predict the amount of
liquid water in the matrix at temperatures below its bulk freezing point. Our
theory combines the interfacial premelting of ice in contact with the matrix,
grain boundary melting in the ice, and impurity and curvature induced
premelting, the latter occurring in regions which force the ice-liquid
interface into a high curvature configuration. These regions are typically
found at points where the matrix surface is concave, along contact lines of a
grain boundary with the matrix, and in liquid veins. Both interfacial
premelting and curvature induced premelting depend on the concentration of
impurities in the liquid, which, due to the small segregation coefficient of
impurities in ice are treated as homogeneously distributed in the premelted
liquid. Our principal result is an equation for the fraction of liquid in the
porous medium as a function of the undercooling, which embodies the combined
effects of interfacial premelting, curvature induced premelting, and
impurities. The result is analyzed in detail and applied to a range of
experimentally relevant settings.Comment: 14 pages, 10 figures, accepted for publication in Physical Review
A fundamental measure theory for the sticky hard sphere fluid
We construct a density functional theory (DFT) for the sticky hard sphere
(SHS) fluid which, like Rosenfeld's fundamental measure theory (FMT) for the
hard sphere fluid [Phys. Rev. Lett. {\bf 63}, 980 (1989)], is based on a set of
weighted densities and an exact result from scaled particle theory (SPT). It is
demonstrated that the excess free energy density of the inhomogeneous SHS fluid
is uniquely defined when (a) it is solely a function of the
weighted densities from Kierlik and Rosinberg's version of FMT [Phys. Rev. A
{\bf 42}, 3382 (1990)], (b) it satisfies the SPT differential equation, and (c)
it yields any given direct correlation function (DCF) from the class of
generalized Percus-Yevick closures introduced by Gazzillo and Giacometti [J.
Chem. Phys. {\bf 120}, 4742 (2004)]. The resulting DFT is shown to be in very
good agreement with simulation data. In particular, this FMT yields the correct
contact value of the density profiles with no adjustable parameters. Rather
than requiring higher order DCFs, such as perturbative DFTs, our SHS FMT
produces them. Interestingly, although equivalent to Kierlik and Rosinberg's
FMT in the case of hard spheres, the set of weighted densities used for
Rosenfeld's original FMT is insufficient for constructing a DFT which yields
the SHS DCF.Comment: 11 pages, 3 figure
- …