The structure of hypersonic shock waves using Navier-Stokes equations modified to include mass diffusion

Howard Brenner has recently proposed modifications to the Navier-Stokes equations that relate to a diffusion of fluid volume that would be significant for flows with high density gradients. In a previous paper (Greenshields & Reese, 2007), we found these modifications gave good predictions of the viscous structure of shock waves in argon in the range Mach 1.0-12.0 (while conventional Navier-Stokes equations are known to fail above about Mach 2). However, some areas of concern with this model were a somewhat arbitrary choice of modelling coefficient, and potentially unphysical and unstable solutions. In this paper, we therefore present slightly different modifications to include molecule mass diffusion fully in the Navier-Stokes equations. These modifications are shown to be stable and produce physical solutions to the shock problem of a quality broadly similar to those from the family of extended hydrodynamic models that includes the Burnett equations. The modifications primarily add a diffusion term to the mass conservation equation, so are at least as simple to solve as the Navier-Stokes equations; there are none of the numerical implementation problems of conventional extended hydrodynamics models, particularly in respect of boundary conditions. We recommend further investigation and testing on a number of different benchmark non-equilibrium flow cases.Comment: written for the 2nd European Conference on AeroSpace Sciences (EUCASS), Belgium, 200

Quasi-static granular flow of ice mélange

We use Landsat 8 imagery to generate ice mélange velocity fields at Greenland’s three most productive outlet glaciers: Jakobshavn Isbræ, Helheim Glacier, and Kangerdlugssuaq Glacier. Winter velocity fields are generally steady and highly uniform. Summer velocity fields, on the other hand, tend to be much more variable and can be uniform, compressional, or extensional. We rarely observe compressional flow at Jakobshavn Isbræ or extensional flow at Helheim Glacier, while both are observed at Kangerdlugssuaq Glacier. Transverse velocity profiles from all three locations are suggestive of viscoplastic flow, in which deformation occurs primarily in shear zones along the fjord walls. We analyze the transverse profiles in the context of quasi-static flow using continuum rheologies for granular materials and find that the force per unit width that ice mélange exerts on glacier termini increases exponentially with the ice mélange length-to-width ratio and the effective coefficient of friction. Our estimates of ice mélange resistance are consistent with other independent estimates and suggest that ice mélange may be capable of inhibiting iceberg calving events, especially during winter. Moreover, our results provide geophysical-scale support for constitutive relationships for granular materials and suggest a potential avenue for modeling ice mélange dynamics with continuum models.From acknowledgments: Funding for this project was provided by the U.S. National Science Foundation (DMR-1506446 and DMR-1506307). Digital elevation models were provided by the Polar Geospatial Center under the U.S. National Science Foundation (OPP-1043681, OPP-1559691, and OPP-1542736)Ye

The structure of shock waves as a test of Brenner's modifications to the Navier-Stokes equations

Brenner has recently proposed modifications to the Navier-Stokes equations that are based on theoretical arguments but supported only by experiments having a fairly limited range. These modifications relate to a diffusion of fluid volume that would be significant for flows with high density gradients. So the viscous structure of shock waves in gases should provide an excellent test case for this new model. In this paper we detail the shock structure problem and propose exponents for the gas viscosity-temperature relation based on empirical viscosity data that is independent of shock experiments. We then simulate shocks in the range Mach 1.0-12.0 using the Navier-Stokes equations, both with and without Brenner's modifications. Initial simulations showed Brenner's modifications display unphysical behaviour when the coefficient of volume diffusion exceeds the kinematic viscosity. Our subsequent analyses attribute this behaviour to both an instability to temporal disturbances and a spurious phase velocity-frequency relationship. On equating the volume diffusivity to the kinematic viscosity, however, we find the results with Brenner's modifications are significantly better than those of the standard Navier-Stokes equations, and broadly similar to those from the family of extended hydrodynamic models that includes the Burnett equations. Brenner's modifications add only two terms to the Navier-Stokes equations, and the numerical implementation is much simpler than conventional extended hydrodynamic models, particularly in respect of boundary conditions. We recommend further investigation and testing on a number of different benchmark non-equilibrium flow cases

Quasi-static granular flow of ice mélange

We use Landsat 8 imagery to generate ice mélange velocity fields at Greenland’s three most productive outlet glaciers: Jakobshavn Isbræ, Helheim Glacier, and Kangerdlugssuaq Glacier. Winter velocity fields are generally steady and highly uniform. Summer velocity fields, on the other hand, tend to be much more variable and can be uniform, compressional, or extensional. We rarely observe compressional flow at Jakobshavn Isbræ or extensional flow at Helheim Glacier, while both are observed at Kangerdlugssuaq Glacier. Transverse velocity profiles from all three locations are suggestive of viscoplastic flow, in which deformation occurs primarily in shear zones along the fjord walls. We analyze the transverse profiles in the context of quasi-static flow using continuum rheologies for granular materials and find that the force per unit width that ice mélange exerts on glacier termini increases exponentially with the ice mélange length-to-width ratio and the effective coefficient of friction. Our estimates of ice mélange resistance are consistent with other independent estimates and suggest that ice mélange may be capable of inhibiting iceberg calving events, especially during winter. Moreover, our results provide geophysical-scale support for constitutive relationships for granular materials and suggest a potential avenue for modeling ice mélange dynamics with continuum models.From acknowledgments: Funding for this project was provided by the U.S. National Science Foundation (DMR-1506446 and DMR-1506307). Digital elevation models were provided by the Polar Geospatial Center under the U.S. National Science Foundation (OPP-1043681, OPP-1559691, and OPP-1542736)Ye

A concurrent precursor inflow method for Large Eddy Simulations and applications to finite length wind farms

In order to enable simulations of developing wind turbine array boundary layers with highly realistic inflow conditions a concurrent precursor method for Large Eddy Simulations is proposed. In this method we consider two domains simultaneously, i.e. in one domain a turbulent Atmospheric Boundary Layer (ABL) without wind turbines is simulated in order to generate the turbulent inflow conditions for a second domain in which the wind turbines are placed. The benefit of this approach is that a) it avoids the need for large databases in which the turbulent inflow conditions are stored and the correspondingly slow I/O operations and b) we are sure that the simulations are not negatively affected by statically swept fixed inflow fields or synthetic fields lacking the proper ABL coherent structures. Sample applications are presented, in which, in agreement with field data a strong decrease of the power output of downstream wind-turbines with respect to the first row of wind-turbines is observed for perfectly aligned inflow.Comment: 13 pages, 5 figure

Evidence for Correlated Titanium and Deuterium Depletion in the Galactic ISM

Current measurements indicate that the deuterium abundance in diffuse interstellar gas varies spatially by a factor of ~4 among sightlines extending beyond the Local Bubble. One plausible explanation for the scatter is the variable depletion of D onto dust grains. To test this scenario, we have obtained high signal-to-noise, high resolution profiles of the refractory ion TiII along seven Galactic sightlines with D/H ranging from 0.65 to 2.1x10^-5. These measurements, acquired with the recently upgraded Keck/HIRES spectrometer, indicate a correlation between Ti/H and D/H at the >95% c.l. Therefore, our observations support the interpretation that D/H scatter is associated with differential depletion. We note, however, that Ti/H values taken from the literature do not uniformly show the correlation. Finally, we identify significant component-to-component variations in the depletion levels among individual sightlines and discuss complications arising from this behavior.Comment: 4 pages; Accepted to Astrophysical Journal Letter

Entanglement of two qubits in a relativistic orbit

The creation and destruction of entanglement between a pair of interacting two-level detectors accelerating about diametrically opposite points of a circular path is investigated. It is found that any non-zero acceleration has the effect of suppressing the vacuum entanglement and enhancing the acceleration radiation thereby reducing the entangling capacity of the detectors. Given that for large accelerations the acceleration radiation is the dominant effect, we investigate the evolution of a two detector system initially prepared in a Bell state using a perturbative mater equation and treating the vacuum fluctuations as an unobserved environment. A general function for the concurrence is obtained for stationary and symmetric worldlines in flatspace. The entanglement sudden death time is computed.Comment: v2: Some typo's fixed, figures compressed to smaller filesize and added some references

The Magellanic Bridge: The Nearest Purely Tidal Stellar Population

We report on observations of the stellar populations in twelve fields spanning the region between the Magellanic Clouds, made with the Mosaic-II camera on the 4-meter telescope at the Cerro-Tololo Inter-American Observatory. The two main goals of the observations are to characterize the young stellar population (which presumably formed in situ in the Bridge and therefore represents the nearest stellar population formed from tidal debris), and to search for an older stellar component (which would have been stripped from either Cloud as stars, by the same tidal forces which formed the gaseous Bridge). We determine the star-formation history of the young inter-Cloud population, which provides a constraint on the timing of the gravitational interaction which formed the Bridge. We do not detect an older stellar population belonging to the Bridge in any of our fields, implying that the material that was stripped from the Clouds to form the Magellanic Bridge was very nearly a pure gas.Comment: 19 pages, 9 figures. Accepted to Ap