Unsteady turbulent buoyant plumes

We model the unsteady evolution of turbulent buoyant plumes following temporal changes to the source conditions. The integral model is derived from radial integration of the governing equations expressing the conservation of mass, axial momentum and buoyancy. The non-uniform radial profiles of the axial velocity and density deficit in the plume are explicitly described by shape factors in the integral equations; the commonly-assumed top-hat profiles lead to shape factors equal to unity. The resultant model is hyperbolic when the momentum shape factor, determined from the radial profile of the mean axial velocity, differs from unity. The solutions of the model when source conditions are maintained at constant values retain the form of the well-established steady plume solutions. We demonstrate that the inclusion of a momentum shape factor that differs from unity leads to a well-posed integral model. Therefore, our model does not exhibit the mathematical pathologies that appear in previously proposed unsteady integral models of turbulent plumes. A stability threshold for the value of the shape factor is identified, resulting in a range of its values where the amplitude of small perturbations to the steady solutions decay with distance from the source. The hyperbolic character of the system allows the formation of discontinuities in the fields describing the plume properties during the unsteady evolution. We compute numerical solutions to illustrate the transient development following an abrupt change in the source conditions. The adjustment to the new source conditions occurs through the propagation of a pulse of fluid through the plume. The dynamics of this pulse are described by a similarity solution and, by constructing this new similarity solution, we identify three regimes in which the evolution of the transient pulse following adjustment of the source qualitatively differ.Comment: 41 pages, 16 figures, under consideration for publication in Journal of Fluid Mechanic

Are there reliable constitutive laws for dynamic friction?

Structural vibration controlled by interfacial friction is widespread, ranging from friction dampers in gas turbines to the motion of violin strings. To predict, control or prevent such vibration, a constitutive description of frictional interactions is inevitably required. A variety of friction models are discussed to assess their scope and validity, in the light of constraints provided by different experimental observations. Three contrasting case studies are used to illustrate how predicted behaviour can be extremely sensitive to the choice of frictional constitutive model, and to explore possible experimental paths to discriminate between and calibrate dynamic friction models over the full parameter range needed for real applications.A.M. and T.P., respectively, acknowledge support from the CUED EPSRC Doctoral Training award and the EPSRC programme grant ‘Engineering Nonlinearity’ (ref. EP/K003836/1).This is the final version of the article. It first appeared from the Royal Society via http://dx.doi.org/10.1098/rsta.2014.040

Uncertainty analysis of a model of wind-blown volcanic plumes

Mathematical models of natural processes can be used as inversion tools to predict unobserved properties from measured quantities. Uncertainty in observations and model formulation impact on the efficacy of inverse modelling. We present a general methodology, history matching, that can be used to investigate the effect of observational and model uncertainty on inverse modelling studies. We demonstrate history matching on an integral model of volcanic plumes that is used to estimate source conditions from observations of the rise height of plumes during the eruptions of Eyjafjallajökull, Iceland, in 2010 and Grímsvötn, Iceland, in 2011. Sources of uncertainty are identified and quantified, and propagated through the integral plume model. A preliminary sensitivity analysis is performed to identify the uncertain model parameters that strongly influence model predictions. Model predictions are assessed against observations through an implausibility measure that rules out model inputs that are considered implausible given the quantified uncertainty. We demonstrate that the source mass flux at the volcano can be estimated from plume height observations, but the magmatic temperature, exit velocity and exsolved gas mass fraction cannot be accurately determined. Uncertainty in plume height observations and entrainment coefficients results in a large range of plausible values of the source mass flux. Our analysis shows that better constraints on entrainment coefficients for volcanic plumes and more precise observations of plume height are required to obtain tightly constrained estimates of the source mass flux

Earthquake source parameters from GPS-measured static displacements with potential for real-time application

We describe a method for determining an optimal centroid–moment tensor solution of an earthquake from a set of static displacements measured using a network of Global Positioning System receivers. Using static displacements observed after the 4 April 2010, MW 7.2 El Mayor-Cucapah, Mexico, earthquake, we perform an iterative inversion to obtain the source mechanism and location, which minimize the least-squares difference between data and synthetics. The efficiency of our algorithm for forward modeling static displacements in a layered elastic medium allows the inversion to be performed in real-time on a single processor without the need for precomputed libraries of excitation kernels; we present simulated real-time results for the El Mayor-Cucapah earthquake. The only a priori information that our inversion scheme needs is a crustal model and approximate source location, so the method proposed here may represent an improvement on existing early warning approaches that rely on foreknowledge of fault locations and geometries

Comparative capitalism and the empirical taxonomy of context: enhancing the institutionalist blueprint

Purpose Critiques of international business (IB) have long pointed to the weaknesses in the understanding of context. This has ignited debate on the understanding of institutions and how they “matter” for IB. Yet how institutions matter ultimately depends on how IB applies institutional theory. It is argued that institutional-based research is dominated by a narrow set of approaches, largely overlooking institutional perspectives that account for institutional diversity. This paper aims to forward the argument that IB research should lend greater attention to comparing the topography of institutional configurations by bringing political economy “back in” to the IB domain. Design/methodology/approach Using principal components analysis and hierarchical cluster analysis, the authors provide IB with a taxonomy of capitalist institutional diversity which defines the landscape of political economies. Findings The authors show institutional diversity is characterised by a range of capitalist clusters and configuration arrangements, identifying four clusters with distinct modes of capitalism as well as specifying intra-cluster differences to propose nine varieties of capitalism. This paper allows IB scholars to lend closer attention to the institutional context within which firms operate. If the configurations of institutions “matter” for IB scholarship, then clearly, a quantitative blueprint to assess institutional diversity remains central to the momentum of such “institutional turn.” Originality/value This paper provides a comprehensive survey of institutional theory, serving as a valuable resource for the application of context within international business. Further, our taxonomy allows international business scholars to utilise a robust framework to examine the diverse institutional context within which firms operate, whilst extending to support the analysis of broader socioeconomic outcomes. This taxonomy therefore allows international business scholars to utilise a robust framework to examine the institutional context within which firms operate

Atmospheric processes affecting the separation of volcanic ash and SO2 in volcanic eruptions: inferences from the May 2011 Grímsvötn eruption

The separation of volcanic ash and sulfur dioxide (SO2) gas is sometimes observed during volcanic eruptions. The exact conditions under which separation occurs are not fully understood but the phenomenon is of importance because of the effects volcanic emissions have on aviation, on the environment, and on the earth’s radiation balance. The eruption of Grímsvötn, a subglacial volcano under the Vatnajökull glacier in Iceland during 21–28 May 2011 produced one of the most spectacular examples of ash and SO2 separation, which led to errors in the forecasting of ash in the atmosphere over northern Europe. Satellite data from several sources coupled with meteorological wind data and photographic evidence suggest that the eruption column was unable to sustain itself, resulting in a large deposition of ash, which left a low-level ash-rich atmospheric plume moving southwards and then eastwards towards the southern Scandinavian coast and a high-level predominantly SO2 plume travelling northwards and then spreading eastwards and westwards. Here we provide observational and modelling perspectives on the separation of ash and SO2 and present quantitative estimates of the masses of ash and SO2 that erupted, the directions of transport, and the likely impacts. We hypothesise that a partial column collapse or “sloughing” fed with ash from pyroclastic density currents (PDCs) occurred during the early stage of the eruption, leading to an ash-laden gravity intrusion that was swept southwards, separated from the main column. Our model suggests that water-mediated aggregation caused enhanced ash removal because of the plentiful supply of source water from melted glacial ice and from entrained atmospheric water. The analysis also suggests that ash and SO2 should be treated with separate source terms, leading to improvements in forecasting the movement of both types of emissions

Simulating shallow morphodynamic flows on evolving topographies

We derive general depth-integrated model equations for overland flows featuring the evolution of suspended sediment that may be eroded from or deposited onto the underlying topography ('morphodynamics'). The resulting equations include geometric corrections that account for large variations in slope angle. These are often non-negligible for Earth-surface flows and may consequently be important for simulating natural hazards. We also show how to adapt existing finite volume schemes for the classical shallow water equations, to simulate our new equations in a way that preserves uniform steady states and exactly conserves the combined mass of the flow and bed. Finally, to demonstrate our formulation, we present computations using simple example model closures, fed by point flux sources. On initially constant slopes, flows exhibit different behaviours depending on the grade. Shallow slopes lead to weakly morphodynamic spreading flows that agree well with analytical similarity solutions. On more severe slopes, rapid erosion occurs, leading to self-channelising flows and ultimately a 'super-erosive' state, in which sediment entrainment and gravitational acceleration perpetually reinforce each other.Comment: 28 pages, 8 figures, 1 tabl