1,972 research outputs found
Is turbulent mixing a self convolution process ?
Experimental results for the evolution of the probability distribution
function (PDF) of a scalar mixed by a turbulence flow in a channel are
presented. The sequence of PDF from an initial skewed distribution to a sharp
Gaussian is found to be non universal. The route toward homogeneization depends
on the ratio between the cross sections of the dye injector and the channel. In
link with this observation, advantages, shortcomings and applicability of
models for the PDF evolution based on a self-convolution mechanisms are
discussed.Comment: 4 page
The Last Stages of Terrestrial Planet Formation: Dynamical Friction and the Late Veneer
The final stage of terrestrial planet formation consists of the cleanup of
residual planetesimals after the giant impact phase. Dynamically, a residual
planetesimal population is needed to damp the high eccentricities of the
terrestrial planets after the giant impact stage. Geochemically, highly
siderophile element (HSE) abundance patterns inferred for the terrestrial
planets and the Moon suggest that a total of about 0.01 M_Earth of chondritic
material was delivered as `late veneer' by planetesimals to the terrestrial
planets after the end of giant impacts. Here we combine these two independent
lines of evidence for a leftover population of planetesimals and show that: 1)
A residual planetesimal population containing 0.01 M_Earth is able to damp the
eccentricities of the terrestrial planets after giant impacts to their observed
values. 2) At the same time, this planetesimal population can account for the
observed relative amounts of late veneer added to the Earth, Moon and Mars
provided that the majority of the late veneer was delivered by small
planetesimals with radii <10m. These small planetesimal sizes are required to
ensure efficient damping of the planetesimal's velocity dispersion by mutual
collisions, which in turn ensures that the planets' accretion cross sections
are significantly enhanced by gravitational focusing above their geometric
values. Specifically we find, in the limit that the relative velocity between
the terrestrial planets and the planetesimals is significantly less than the
terrestrial planets' escape velocities, that gravitational focusing yields an
accretion ratio Earth/Mars~17, which agrees well with the accretion ratio
inferred from HSEs of 12-23. For the Earth-Moon system, we find an accretion
ratio of ~200, which is consistent with estimates of 150-700 derived from HSE
abundances that include the lunar crust as well as mantle component. (Abridged)Comment: accepted for publication in ApJ, 9 pages, 4 figures; minor
corrections, additional references adde
Constraints on the Growth and Spin of the Supermassive Black Hole in M32 From High Cadence Visible Light Observations
We present 1-second cadence observations of M32 (NGC221) with the CHIMERA
instrument at the Hale 200-inch telescope of the Palomar Observatory. Using
field stars as a baseline for relative photometry, we are able to construct a
light curve of the nucleus in the g-prime and r-prime band with 1sigma=36
milli-mag photometric stability. We derive a temporal power spectrum for the
nucleus and find no evidence for a time-variable signal above the noise as
would be expected if the nuclear black hole were accreting gas. Thus, we are
unable to constrain the spin of the black hole although future work will use
this powerful instrument to target more actively accreting black holes. Given
the black hole mass of (2.5+/-0.5)*10^6 Msun inferred from stellar kinematics,
the absence of a contribution from a nuclear time-variable signal places an
upper limit on the accretion rate which is 4.6*10^{-8} of the Eddington rate, a
factor of two more stringent than past upper limits from HST. The low mass of
the black hole despite the high stellar density suggests that the gas liberated
by stellar interactions was primarily at early cosmic times when the low-mass
black hole had a small Eddington luminosity. This is at least partly driven by
a top-heavy stellar initial mass function at early cosmic times which is an
efficient producer of stellar mass black holes. The implication is that
supermassive black holes likely arise from seeds formed through the coalescence
of 3-100 Msun mass black holes that then accrete gas produced through stellar
interaction processes.Comment: 8 pages, 3 figures, submitted to the Astrophysical Journal, comments
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Theory of pressure acoustics with boundary layers and streaming in curved elastic cavities
The acoustic fields and streaming in a confined fluid depend strongly on the
acoustic boundary layer forming near the wall. The width of this layer is
typically much smaller than the bulk length scale set by the geometry or the
acoustic wavelength, which makes direct numerical simulations challenging.
Based on this separation in length scales, we extend the classical theory of
pressure acoustics by deriving a boundary condition for the acoustic pressure
that takes boundary-layer effects fully into account. Using the same
length-scale separation for the steady second-order streaming, and combining it
with time-averaged short-range products of first-order fields, we replace the
usual limiting-velocity theory with an analytical slip-velocity condition on
the long-range streaming field at the wall. The derived boundary conditions are
valid for oscillating cavities of arbitrary shape and wall motion as long as
the wall curvature and displacement amplitude are both sufficiently small.
Finally, we validate our theory by comparison with direct numerical simulation
in two examples of two-dimensional water-filled cavities: The well-studied
rectangular cavity with prescribed wall actuation, and the more generic
elliptical cavity embedded in an externally actuated rectangular elastic glass
block.Comment: 18 pages, 5 figures, pdfLatex, RevTe
Near-equilibrium isotope fractionation during planetesimal evaporation
Silicon and Mg in differentiated rocky bodies exhibit heavy isotope
enrichments that have been attributed to evaporation of partially or entirely
molten planetesimals. We evaluate the mechanisms of planetesimal evaporation in
the early solar system and the conditions that controlled attendant isotope
fractionations. Energy balance at the surface of a body accreted within ~1 Myr
of CAI formation and heated from within by 26Al decay results in internal
temperatures exceeding the silicate solidus, producing a transient magma ocean
with a thin surface boundary layer of order < 1 meter that would be subject to
foundering. Bodies that are massive enough to form magma oceans by radioisotope
decay (ge 0.1%) can retain hot rock vapor even in the absence of ambient
nebular gas. We find that a steady-state rock vapor forms within minutes to
hours and results from a balance between rates of magma evaporation and
atmospheric escape. Vapor pressure buildup adjacent to the surfaces of the
evaporating magmas would have inevitably led to an approach to equilibrium
isotope partitioning between the vapor phase and the silicate melt. Numerical
simulations of this near-equilibrium evaporation process for a body with a
radius of ~ 700 km yield a steady-state far-field vapor pressure corresponding
to 95% saturation. Approaches to equilibrium isotope fractionation between
vapor and melt should have been the norm during planet formation due to the
formation of steady-state rock vapor atmospheres and/or the presence of
protostellar gas. We model the Si and Mg isotopic composition of bulk Earth and
show that the best fit is for a carbonaceous chondrite-like source material
with about 12% loss of Mg and 15% loss of Si resulting from near-equilibrium
evaporation into the solar protostellar disk of hydrogen gas on timescales of
10,000 to 100,000 years.Comment: 35 pages, 15 figure
Experimental and numerical investigations of flow structure and momentum transport in a turbulent buoyancy-driven flow inside a tilted tube.
Buoyancy-driven turbulent mixing of fluids of slightly different densities [At = Δρ/(2〈ρ〉) = 1.15×10−2] in a long circular tube tilted at an angle θ = 15° from the vertical is studied at the local scale, both experimentally from particle image velocimetry and laser induced fluorescence measurements in the vertical diametrical plane and numerically throughout the tube using direct numerical simulation. In a given cross section of the tube, the axial mean velocity and the mean concentration both vary linearly with the crosswise distance z from the tube axis in the central 70% of the diameter. A small crosswise velocity component is detected in the measurement plane and is found to result from a four-cell mean secondary flow associated with a nonzero streamwise component of the vorticity. In the central region of the tube cross section, the intensities of the three turbulent velocity fluctuations are found to be strongly different, that of the streamwise fluctuation being more than twice larger than that of the spanwise fluctuation which itself is about 50% larger than that of the crosswise fluctuation. This marked anisotropy indicates that the turbulent structure is close to that observed in homogeneous turbulent shear flows. Still in the central region, the turbulent shear stress dominates over the viscous stress and reaches a maximum on the tube axis. Its crosswise variation is approximately accounted for by a mixing length whose value is about one-tenth of the tube diameter. The momentum exchange in the core of the cross section takes place between its lower and higher density parts and there is no net momentum exchange between the core and the near-wall regions. A sizable part of this transfer is due both to the mean secondary flow and to the spanwise turbulent shear stress. Near-wall regions located beyond the location of the extrema of the axial velocity (|z|≳0.36 d) are dominated by viscous stresses which transfer momentum toward (from) the wall near the top (bottom) of the tube
Application of an Energy-Vorticity Turbulence Model to Fully rough Pipe flow
Based on a more direct analogy between turbulent and molecular transport, a foundation was recently presented for an energy-vorticity turbulence model. The new turbulent-energytransport equation contains two closure coefficients; a viscous-dissipation coefficient and a turbulent-transport coefficient. To help evaluate the closure coefficients and provide insight into the energy-vorticity turbulence variables, fully rough pipe flow is considered. For this fully developed flow, excellent agreement with experimental data for velocity profiles and friction factors is attained over a wide range of closure coefficients, provided that a given relation between the coefficients is maintained
Shear Effects in Non-Homogeneous Turbulence
Motivated by recent experimental and numerical results, a simple unifying
picture of intermittency in turbulent shear flows is suggested. Integral
Structure Functions (ISF), taking into account explicitly the shear intensity,
are introduced on phenomenological grounds. ISF can exhibit a universal scaling
behavior, independent of the shear intensity. This picture is in satisfactory
agreement with both experimental and numerical data. Possible extension to
convective turbulence and implication on closure conditions for Large-Eddy
Simulation of non-homogeneous flows are briefly discussed.Comment: 4 pages, 5 figure
Cavitation inception of a van der Waals fluid at a sack-wall obstacle
Cavitation in a liquid moving past a constraint is numerically investigated
by means of a free-energy lattice Boltzmann simulation based on the van der
Waals equation of state. The fluid is streamed past an obstacle and, depending
on the pressure drop between inlet and outlet, vapor formation underneath the
corner of the sack-wall is observed. The circumstances of cavitation formation
are investigated and it is found that the local bulk pressure and mean stress
are insufficient to explain the phenomenon. Results obtained in this study
strongly suggest that the viscous stress, interfacial contributions to the
local pressure, and the Laplace pressure are relevant to the opening of a vapor
cavity. This can be described by a generalization of Joseph's criterion that
includes these contributions. A macroscopic investigation measuring mass flow
rate behavior and discharge coefficient was also performed. As theoretically
predicted, mass flow rate increases linearly with the square root of the
pressure drop. However, when cavitation occurs, the mass flow growth rate is
reduced and eventually it collapses into a choked flow state. In the cavitating
regime, as theoretically predicted and experimentally verified, the discharge
coefficient grows with the Nurick cavitation number
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