381,001 research outputs found
Mach Stem Height and Growth Rate Predictions
A new, more accurate prediction of Mach stem height in steady flow is presented. In addition, starting with a regular reflection in the dual-solution domain, the growth rate of the Mach stem from the time it is first formed till it reaches its steady-state height is presented. Comparisons between theory, experiments, and computations are presented for the Mach stem height. The theory for the Mach stem growth rate in both two and three dimensions is compared to computational results. The Mach stem growth theory provides an explanation for why, once formed, a Mach stem is relatively persistent
Cosmic Mach Number as a Function of Overdensity and Galaxy Age
We carry out an extensive study of the cosmic Mach number (\mach) on scales
of R=5, 10 and 20h^-1Mpc using an LCDM hydrodynamical simulation. We
particularly put emphasis on the environmental dependence of \mach on
overdensity, galaxy mass, and galaxy age. We start by discussing the difference
in the resulting \mach according to different definitions of \mach and
different methods of calculation. The simulated Mach numbers are slightly lower
than the linear theory predictions even when a non-linear power spectrum was
used in the calculation, reflecting the non-linear evolution in the simulation.
We find that the observed \mach is higher than the simulated mean by more than
2-standard deviations, which suggests either that the Local Group is in a
relatively low-density region or that the true value of \Omega_m is ~ 0.2,
significantly lower than the simulated value of 0.37. We show from our
simulation that the Mach number is a weakly decreasing function of overdensity.
We also investigate the correlations between galaxy age, overdensity and \mach
for two different samples of galaxies --- DWARFs and GIANTs. Older systems
cluster in higher density regions with lower \mach, while younger ones tend to
reside in lower density regions with larger \mach, as expected from the
hierarchical structure formation scenario. However, for DWARFs, the correlation
is weakened by the fact that some of the oldest DWARFs are left over in
low-density regions during the structure formation history. For giant systems,
one expects blue-selected samples to have higher \mach than red-selected ones.
We briefly comment on the effect of the warm dark matter on the expected Mach
number.Comment: 43 pages, including 15 figures. Accepted version in ApJ. Included
correlation function of different samples of galaxies, and the cumulative
number fraction distribution as a fcn. of overdensity. Reorganized figures
and added some reference
Regularity of weak solutions to rate-independent systems in one-dimension
We show that under some appropriate assumptions, every weak solution (e.g.
energetic solution) to a given rate-independent system is of class SBV, or has fi�nite jumps, or is even piecewise C1. Our assumption is essentially imposed on the energy functional, but not convexity is required
Computational/experimental analysis of three low sonic boom configurations with design modifications
The Euler code, designated AIRPLANE, which uses an unstructured tetrahedral mesh was used to compute near-field sonic boom pressure signatures on three modern low sonic boom configurations: the Mach 2, Mach 3, and Haglund models. The TEAM code which uses a multi-zoned structured grid was used to calculate pressure signatures for the Mach 2 model. The computational pressure signatures for the Mach 2 and Mach 3 models are compared with recent experimental data. The computed pressure signatures were extracted at distances less than one body length below the configuration and extrapolated to the experimental distance. The Mach 2 model was found to have larger overpressures off-ground-track than on-ground-track in both computational and experimental results. The correlations with the experiment were acceptable where the signatures were not contaminated by instrumentation and model-support hardware. AIRPLANE was used to study selected modifications to improve the overpressures of the Mach 2 model
Low Mach number effect in simulation of high Mach number flow
In this note, we relate the two well-known difficulties of Godunov schemes:
the carbuncle phenomena in simulating high Mach number flow, and the inaccurate
pressure profile in simulating low Mach number flow. We introduced two simple
low-Mach-number modifications for the classical Roe flux to decrease the
difference between the acoustic and advection contributions of the numerical
dissipation. While the first modification increases the local numerical
dissipation, the second decreases it. The numerical tests on the double-Mach
reflection problem show that both modifications eliminate the kinked Mach stem
suffered by the original flux. These results suggest that, other than
insufficient numerical dissipation near the shock front, the carbuncle
phenomena is strongly relevant to the non-comparable acoustic and advection
contributions of the numerical dissipation produced by Godunov schemes due to
the low Mach number effect.Comment: 9 pages, 1 figur
Mach Number Dependence of Electron Heating in High Mach Number Quasiperpendicular Shocks
Efficiency of electron heating through microinstabilities generated in the
transition region of a quasi-perpendicular shock for wide ange of Mach numbers
is investigated by utilizing PIC (Particle-In-Cell) simulation and model
analyses. In the model analyses saturation levels of effective electron
temperature as a result of microinstabilities are estimated from an extended
quasilinear (trapping) analysis for relatively low (high) Mach number shocks.
Here, MTSI (modified two-stream instability) is assumed to become dominant in
low Mach number regime, while BI (Buneman instability) to become dominant in
high Mach number regime, respectively. It is revealed that Mach number
dependence of the effective electron temperature in the MTSI dominant case is
essentially different from that in the BI dominant case. The effective electron
temperature through the MTSI does not depend much on the Mach number, although
that through the BI increases with the Mach number as in the past studies. The
results are confirmed to be consistent with the PIC simulations both in
qualitative and quantitative levels. The model analyses predict that a critical
Mach number above which steep rise of electron heating rate occurs may arise at
the Mach number of a few tens.Comment: 9 pages, 5 figures, Phys. Plasmas in pres
Self-gravitating Newtonian disks revisited
Recent analytic results concerning stationary, self-gravitating fluids in
Newtonian theory are discussed. We give a theorem that forbids infinitely
extended fluids, depending on the assumed equation of state and the rotation
law. This part extends previous results that have been obtained for static
configurations. The second part discusses a Sobolev bound on the mass of the
fluid and a rigorous Jeans-type inequality that is valid in the stationary
case.Comment: A talk given at the Spanish Relativity Meeting in Portugal 2012. To
appear in Progress in Mathematical Relativity, Gravitation and Cosmology,
Proceedings of the Spanish Relativity Meeting ERE2012, University of Minho,
Guimaraes, Portugal, 3-7 September 2012, Springer Proceedings in Mathematics
& Statistics, Vol. 6
The compressible turbulent shear layer: an experimental study
The growth rate and turbulent structure of the compressible, plane shear layer are investigated experimentally in a novel facility. In this facility, it is possible to flow similar or dissimilar gases of different densities and to select different Mach numbers for each stream. Ten combinations of gases and Mach numbers are studied in which the free-stream Mach numbers range from 0.2 to 4. Schlieren photography of 20-ns exposure time reveals very low spreading rates and large-scale structures. The growth of the turbulent region is defined by means of Pitot-pressure profiles measured at several streamwise locations. A compressibility-effect parameter is defined that correlates and unifies the experimental results. It is the Mach number in a coordinate system convecting with the velocity of the dominant waves and structures of the shear layer, called here the convective Mach number. It happens to have nearly the same value for each stream. In the current experiments, it ranges from 0 to 1.9. The correlations of the growth rate with convective Mach number fall approximately onto one curve when the growth rate is normalized by its incompressible value at the same velocity and density ratios. The normalized growth rate, which is unity for incompressible flow, decreases rapidly with increasing convective Mach number, reaching an asymptotic value of about 0.2 for supersonic convective Mach numbers
Low sonic boom design and performance of a Mach 2.4/1.8 overland high speed civil transport
This paper describes the design features of a Douglas Mach 2.4/1.8 Low Sonic Boom High Speed Civil Transport (HSCT) configuration developed for NASA. The configuration is designed to fly over water at Mach 2.4 for highest productivity and economic worth, and fly over land at Mach 1.8 with reduced sonic boom loudness
Effect of Mach number on the structure of turbulent spots
Direct numerical simulations have been performed to study the dynamics of isolated turbulent spots in compressible isothermal-wall boundary layers. Results of a bypass transition scenario at Mach 2, 4 and 6 are presented. At all Mach numbers the evolved spots have a leading-edge overhang, followed by a turbulent core and a calmed region at the rear interface. The spots have an upstream-pointing arrowhead shape when visualized by near-wall slices, but a downstream-pointing arrowhead in slices away front the wall. The lateral spreading of the spot decreases substantially with the Mach number, consistent with a growth mechanism based on the instability of lateral shear layers. Evidence for a supersonic (Mach) mode substructure is found in the Mach 6 case, where coherent spanwise structures are observed under the spot overhang region
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