Resonant drag instability of grains streaming in fluids

We show that grains streaming through a fluid are generically unstable if their velocity, projected along some direction, matches the phase velocity of a fluid wave (linear oscillation). This can occur whenever grains stream faster than any fluid wave. The wave itself can be quite general--sound waves, magnetosonic waves, epicyclic oscillations, and Brunt-V\"ais\"al\"a oscillations each generate instabilities, for example. We derive a simple expression for the growth rates of these "resonant drag instabilities" (RDI). This expression (i) illustrates why such instabilities are so virulent and generic, and (ii) allows for simple analytic computation of RDI growth rates and properties for different fluids. As examples, we introduce several new instabilities, which could see application across a variety of physical systems from atmospheres to protoplanetary disks, the interstellar medium, and galactic outflows. The matrix-based resonance formalism we introduce can also be applied more generally in other (nonfluid) contexts, providing a simple means for calculating and understanding the stability properties of interacting systems.Comment: 5 Pages. Published in ApJ

Physical models of streaming instabilities in protoplanetary discs

We develop simple, physically motivated models for drag-induced dust–gas streaming instabilities, which are thought to be crucial for clumping grains to form planetesimals in protoplanetary discs. The models explain, based on the physics of gaseous epicyclic motion and dust–gas drag forces, the most important features of the streaming instability and its simple generalization, the disc settling instability. Some of the key properties explained by our models include the sudden change in the growth rate of the streaming instability when the dust-to-gas mass ratio surpasses one, the slow growth rate of the streaming instability compared to the settling instability for smaller grains, and the main physical processes underlying the growth of the most unstable modes in different regimes. As well as providing helpful simplified pictures for understanding the operation of an interesting and fundamental astrophysical fluid instability, our models may prove useful for analysing simulations and developing non-linear theories of planetesimal growth in discs

The distribution of density in supersonic turbulence

We propose a model for the density statistics in supersonic turbulence, which play a crucial role in star-formation and the physics of the interstellar medium (ISM). Motivated by [Hopkins, MNRAS, 430, 1880 (2013)], the model considers the density to be arranged into a collection of strong shocks of width $\sim\! \mathcal{M}^{-2}$, where $\mathcal{M}$ is the turbulent Mach number. With two physically motivated parameters, the model predicts all density statistics for $\mathcal{M}>1$ turbulence: the density probability distribution and its intermittency (deviation from log-normality), the density variance-Mach number relation, power spectra, and structure functions. For the proposed model parameters, reasonable agreement is seen between model predictions and numerical simulations, albeit within the large uncertainties associated with current simulation results. More generally, the model could provide a useful framework for more detailed analysis of future simulations and observational data. Due to the simple physical motivations for the model in terms of shocks, it is straightforward to generalize to more complex physical processes, which will be helpful in future more detailed applications to the ISM. We see good qualitative agreement between such extensions and recent simulations of non-isothermal turbulence

Nonlinear Evolution of Instabilities Between Dust and Sound Waves

We study the non-linear evolution of the acoustic 'Resonant Drag Instability' (RDI) using numerical simulations. The acoustic RDI is excited in a dust-gas mixture when dust grains stream through gas, interacting with sound waves to cause a linear instability. We study this process in a periodic box by accelerating neutral dust with an external driving force. The instability grows as predicted by linear theory, eventually breaking into turbulence and saturating. As in linear theory, the non-linear behavior is characterized by three regimes - high, intermediate, and low wavenumbers - the boundary between which is determined by the dust-gas coupling strength and the dust-to-gas mass ratio. The high and intermediate wavenumber regimes behave similarly to one another, with large dust-to-gas ratio fluctuations while the gas remains largely incompressible. The saturated state is highly anisotropic: dust is concentrated in filaments, jets, or plumes along the direction of acceleration, with turbulent vortex-like structures rapidly forming and dissipating in the perpendicular directions. The low-wavenumber regime exhibits large fluctuations in gas and dust density, but the dust and gas remain more strongly coupled in coherent 'fronts' perpendicular to the acceleration. These behaviors are qualitatively different from those of dust 'passively' driven by external hydrodynamic turbulence, with no back-reaction force from dust onto gas. The virulent nature of these instabilities has interesting implications for dust-driven winds in a variety of astrophysical systems, including around cool-stars, in dusty torii around active-galactic-nuclei, and in and around giant molecular clouds.Comment: 11 pages, 9 figure

Assessing the importance of river bank erosion for fine sediment delivery to Bassenthwaite Lake

Available evidence from lake sediment core records and short-term sediment flux sampling programs has suggested increased fine sediment deposition and suspended sediment transfers to Bassenthwaite Lake, Cumbria, U.K over recent decades. This increase in sedimentation has been associated with a decline in water quality in the lake which is thought to have had serious consequences for the population of the vendace (Coregonu albula), which also declined markedly during the 1990ร and into the 21 St Century. Recent studies of sediment delivery risk in the catchment have suggested that there are potentially large sediment sources in the lowland river network, especially the River Derwent between Derwent Water and Bassenthwaite Lake. The aim of this research is to describe the characteristics of fluvial suspended sediment transfers to Bassenthwaite Lake through direct monitoring of the River Dement and Newlands Beck (at the head of Bassenthwaite Lake) in order to assess the potential contribution of river bank erosion on the lowland River Derwent to fine sediment delivery. Three suspended sediment monitoring stations at Portinscale and Low Stock Bndge on the River Derwent and at Newlands Beck Bridge are used to assess changes in sediment transport along these important river reaches. The potential contribution of river bank erosion to fluvial sediment delivery was assessed by river bank mapping and surveying of erosion features on the 5.7km reach of the River Derwent between Derwent Water and Bassenthwaite Lake, along with a detailed study of morphological change on three river banks near Low Stock Bridge using a terrestrial laser scanner. The main findings of this project suggest that the River Derwent dominates suspended sediment transfers to Bassenthwaite Lake. The fine sediment load transported on the Derwent is over five times greater than that of Newlands Beck and the mean suspended sediment concentration on the lower Derwent is 56% higher than that on Newlands Beck. Specific catchment sediment yields for the River Derwent and Newlands Beck, based on effective drainage area, are 50.871 km(^2) a(^-1) and 35.721 km2 a(^-1) respectively. A high proportion of all suspended sediment transfers in the lowland Bassenthwaite Lake catchment were observed to occur in high-magnitude, low-frequency flow events, with approximately two- thirds of total suspended sediment transport occurring in just over 10% of the time. There is also direct evidence for increased fine sediment supply on the lowland River Derwent, as an estimated 1,158 ta(^-1) increase in the overall sediment load was observed on the 3.7 km reach of the Derwent between Portinscale and Low stock Bridge. Hysteresis analysis and analysis of suspended sediment transfers during high flow events on the Derwent support this hypothesis. Overall, 21.1% of all river banks on the River Derwent were assessed as eroded, with 9.4% of banks undergoing active river bank erosion. Therefore, it is suggested that river bank erosion is a significant fine sediment source in the lowland Bassenthwaite catchment, and that it is responsible for a large proportion of sediment inputs on the lowland River Derwent (c. 18.9%), and ultimately to Bassenthwaite Lake

Knowledge of, and response to, upland flash flooding: a case study of flood risk management of the 2005 flash flood in upper Ryedale, North Yorkshire, U.K.

The dangerous hazard posed by flash flooding to upland communities is likely to increase due to climate change. The flood risk management policy approach has become predominant since the 1990s, with an emphasis on the public awareness of, and responses to, flood risks; however, the unpredictable nature of upland flash flooding means that responses to such hazards are uncertain. This thesis uses an integrated analysis of social and physical science datasets to study responses by local residents and the Environment Agency to flash flooding, using a case study of a major upland flood in North Yorkshire. Responses to flash flooding within upland communities were found to be mostly present as changes to individual behaviour and awareness. However, physical, damage reducing modifications were limited. Flash flood hazard perception was found to be linked to knowledge and experience of local flooding. Major flash flood events occurring in areas which have not experienced other recent floods are unlikely to increase perceptions or provoke responses. Although local awareness of changing weather patterns was found, supporting analyses of rainfall records, local flood risks were frequently framed in the context of river management, rather than climate change. The implementation of policy changes and responses to flash flooding by the Environment Agency will prove difficult at the local level, due to the nature of attitudes and perceptions encountered at the local level, including important differences in the perception of the flash flood hazard between local residents and representatives from nationwide organisations. Encouraging property-level modifications following flash floods, in accordance with national policies, is very difficult. In order to increase local perceptions of the flash flood hazard, the use of participatory work, focusing on long-term awareness raising and the sharing of locally held flood knowledge may be beneficial, alongside the support of existing resilience in upland communities

The effect of probe tilt angle on the quality of scanning tunneling microscope measurements

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2005.Includes bibliographical references (p. 39 ).The effect of probe tilt angle on the quality of Scanning Tunneling Microscopy (STM) measurements was explored. A small but consistent improvement in slope accuracy was documented lending some support to the effort to develop a new, five-axis STM capable of tilting in a controlled manner while scanning. The objective of such a machine would be to allow its probe to trace the sample's contour with greater accuracy than the currently available three-axis STM can. It is postulated that an STM with a probe that can change its roll and pitch in addition to its position along the traditional x, y, and z axes would be capable of reducing imaging errors produced as a result of geometric constraints, lateral electron discharge effects, and the tendency for the tip to bend during scanning due to electrostatic surface forces. In order to quantify the effects of incorporating probe tilt into the scanning process, a traditional, three-axis STM was manipulated in a way that allowed a standard sample grid to be imaged using a probe that was placed at seven different angles of tilt ranging from -13 to +13 degrees. Twenty-five different cavities in a standard STM scanning sample were scanned at these seven angles to determine notable trends and effects in the images produced.(cont.) It was determined that for each degree of angle change in the tilt of the probe, the slopes of the cavity walls imaged improved by an amount of slope equal to approximately 0.001 nm/nm, which corresponds to 0.0093% less imaging error. This seemingly trivial improvement in wall slope is significant in light of the fact that the change in slope per degree of probe tilt is on the same order of magnitude as the slopes of the cavity walls measured by the STM.by Jonathan B. Hopkins.S.B