152 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
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
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
Morphological instability of a nonequilibrium icecolloid interface
We assess the morphological stability of a nonequilibrium icecolloidal suspension interface, and apply the theory to bentonite clay. An experimentally convenient scaling is employed which takes advantage of the vanishing segregation coefficient at low freezing velocities, and when anisotropic kinetic effects are included the interface is shown to be unstable to travelling waves. The potential for traveling wave modes reveals a possible mechanism for the polygonal and spiral ice lenses observed in frozen clays. A weakly nonlinear analysis yields a long-wave evolution equation for the interface shape containing a new parameter related to the highly nonlinear liquidus curve in colloidal systems. We discuss the implications of these results for the frost susceptibility of soils and the fabrication of microtailored porous materials
Streaks to Rings to Vortex Grids: Generic Patterns in Transient Convective Spin-Up
We observe the transient formation of a ringed pattern state during spin-up
of an evaporating fluid on a time scale of order a few Ekman spin-up times. The
ringed state is probed using infrared thermometry and particle image
velocimetry and it is demonstrated to be a consequence of the transient balance
between Coriolis and viscous forces which dominate inertia, each of which are
extracted from the measured velocity field. The breakdown of the ringed state
is quantified in terms of the antiphasing of these force components which
drives a Kelvin-Helmholtz instability and we show that the resulting vortex
grid spacing scales with the ring wavelength. This is the fundamental route to
quasi-two dimensional turbulent vortex flow and thus may have implications in
astrophysics and geophysics wherein rotating convection is ubiquitous. sics.Comment: 4 pages, 5 figure
- …