The present study addresses the reaction zone structure and burning mechanism of unstable detonations. Experiments investigated mainly two-dimensional methane–oxygen cellular detonations in a thin channel geometry. The sufficiently high temporal resolution permitted the determination of the probability density function of the shock distribution, a power law with an exponent of $-3$, and the burning rate of unreacted pockets from their edges – through surface turbulent flames with a speed approximately 3–7 times larger than the laminar one at the local conditions. Numerical simulations were performed using a novel large-eddy simulation method where the reactions due to both autoignition and turbulent transport were treated exactly at the subgrid scale in a reaction–diffusion formulation. The model is an extension of Kerstein and Menon’s linear eddy model for large-eddy simulation to treat flows with shock waves and rapid gas-dynamic transients. The two-dimensional simulations recovered well the amplification of the laminar flame speed due to the turbulence generated mainly by the shear layers originating from the triple points and subsequent Richtmyer–Meshkov instability associated with the internal pressure waves. The simulations clarified how the level of turbulence generated controlled the burning rate of the pockets, the hydrodynamic thickness of the wave, the cellular structure and its distribution. Three-dimensional simulations were found to be in general good agreement with the two-dimensional ones, in that the subgrid-scale model captured the ensuing turbulent burning once the scales associated with the cellular dynamics, where turbulent kinetic energy is injected, are well resolved.

Star formation occurs in dark molecular regions where the number density of hydrogen nuclei nH exceeds 104 cm−3 and the fractional ionization is 10−7 or less. Dust grains with sizes ranging up to tenths of microns and perhaps down to tens of nanometers contain just less than 1% of the mass. Recombination on grains is important for the removal of gas-phase ions, which are produced by cosmic rays penetrating the dark regions. Collisions of neutrals with charged grains contribute significantly to the coupling of the magnetic field to the neutral gas. Consequently, the dynamics of the grains must be included in the magnetohydrodynamic models of large-scale collapse, the evolution of waves and the structures of shocks important in star formation.

By using 2D simulations, we examine the generation of dense cores and substructures by magnetosonic waves. We find that the excitation of slow-mode waves by fast-mode waves produces these high-density structures.

The importance of vorticity production in combustion systems has been highlighted previously by several authors (Markstein 1964; Picone et al. 1984). The consequent distortion and enlargement of flame surfaces can lead to substantial enhancement of the burning rate which may be beneficial or disastrous depending on the physical context. We describe the results of numerical simulations of an experimental configuration similar to that described by Scarinci & Thomas (1992), who examined the effect of initially planar pressure signals on two-dimensional flame balls. The flame ball is here set-up from ignition using a code, based on the second-order Godunov scheme described by Falle (1991). A simple Arrhenius reaction scheme is adopted in modelling a unimolecular decomposition. As in previous papers (Batley et al. 1993 a, b) the thermal conductivity is assumed to vary linearly with temperature, and the Lewis and Prandtl numbers are taken as unity. A short time after ignition, when the flame ball has reached a radius of approximately 2 cm, a very short-lengthscale pressure step disturbance is introduced, propagating towards the combustion region. As the signal crosses the flame, the interaction of the sharp, misaligned pressure and density gradients, creates a strong vorticity field. The resulting roll-up of the flame eventually divides it into two smaller rotating reacting regions. In order to gauge the effect of the chemical reaction and in particular the viscous diffusion on the evolution of the vorticity field, the results are compared with analogous solutions of the Euler equations.

Damped Lyman-$\alpha$ (DLA) and sub-DLA quasar absorption lines provide powerful probes of the evolution of metals, gas, and stars in galaxies. One major obstacle in trying to understand the evolution of DLAs and sub-DLAs has been the small number of metallicity measurements at $z<1.5$, an epoch spanning $\sim 70$% of the cosmic history. In recent surveys with the Hubble Space Telescope and Multiple Mirror Telescope, we have doubled the DLA Zn sample at $z<1.5$. Combining our results with those at higher redshifts from the literature, we find that the global mean metallicity of DLAs does not rise to the Solar value at low redshifts. These surprising results appear to contradict the near-Solar mean metallicity observed for nearby ($z \approx 0$) galaxies and the predictions of cosmic chemical evolution models based on the global star formation history. Finally, we discuss direct constraints on the star formation rates (SFRs) in the absorber galaxies from our deep Fabry-Perot Ly-$\alpha$ imaging study and other emission-line studies in the literature. A large fraction of the observed heavy-element quasar absorbers at $0<z<3.4$ appear to have SFRs substantially below the global mean SFR, consistent with the low metallicities observed in the spectroscopic studies.

The paper considers the derivation and properties of the Fanno model for nearly unidirectional turbulent flow of gas in a tube. The model is relevant to many industrial processes. Approximate solutions are derived and numerically validated for evolving flows of initially small amplitude, and these solutions reveal the prevalence of localized large-time behaviour, which is in contrast to inviscid acoustic theory. The properties of large-amplitude travelling waves are summarized, which are also surprising when compared to those of inviscid theory.

In recent years, numerical solutions of the equations of compressible magnetohydrodynamic (MHD) flows have been found to contain intermediate shocks for certain kinds of problems. Since these results would seem to be in conflict with the classical theory of MHD shocks, they have stimulated attempts to reexamine various aspects of this theory, in particular the role of dissipation. In this paper, we study the general relationship between the evolutionary conditions for discontinuous solutions of the dissipation-free system and the existence and uniqueness of steady dissipative shock structures for systems of quasilinear conservation laws with a concave entropy function. Our results confirm the classical theory. We also show that the appearance of intermediate shocks in numerical simulations can be understood in terms of the properties of the equations of planar MHD, for which some of these shocks turn out to be evolutionary. Finally, we discuss ways in which numerical schemes can be modified in order to avoid the appearance of intermediate shocks in simulations with such symmetry.

In this paper we perform high-resolution one-dimensional time-dependent numerical simulations of detonations for which the underlying steady planar waves are of the pathological type. Pathological detonations are possible when there are endothermic or dissipative effects in the system. We consider a system with two consecutive irreversible reactions A→B→C, with an Arrhenius form of the reaction rates and the second reaction endothermic. The self-sustaining steady planar detonation then travels at the minimum speed, which is faster than the Chapman–Jouguet speed, and has an internal frozen sonic point at which the thermicity vanishes. The flow downstream of this sonic point is supersonic if the detonation is unsupported or subsonic if the detonation is supported, the two cases having very different detonation wave structures. We compare and contrast the long-time nonlinear behaviour of the unsupported and supported pathological detonations. We show that the stability of the supported and unsupported steady waves can be quite different, even near the stability boundary. Indeed, the unsupported detonation can easily fail while the supported wave propagates as a pulsating detonation. We also consider overdriven detonations for the system. We show that, in agreement with a linear stability analysis, the stability of the steady wave is very sensitive to the degree of overdrive near the pathological detonation speed, and that increasing the overdrive can destabilize the wave, in contrast to systems where the self-sustaining wave is the Chapman–Jouguet detonation.

Unsteady flow in collapsible tubes has been widely studied for a number of different physiological applications; the principal motivation for the work of this paper is the study of blood flow in the jugular vein of an upright, long-necked subject (a giraffe). The one-dimensional equations governing gravity- or pressure-driven flow in collapsible tubes have been solved in the past using finite-difference (MacCormack) methods. Such schemes, however, produce numerical artifacts near discontinuities such as elastic jumps. This paper describes a numerical scheme developed to solve the one-dimensional equations using a more accurate upwind finite volume (Godunov) scheme that has been used successfully in gas dynamics and shallow water wave problems. The adapatation of the Godunov method to the present application is non-trivial due to the highly nonlinear nature of the pressure–area relation for collapsible tubes.

The code is tested by comparing both unsteady and converged solutions with analytical solutions where available. Further tests include comparison with solutions obtained from MacCormack methods which illustrate the accuracy of the present method.

Finally the possibility of roll waves occurring in collapsible tubes is also considered, both as a test case for the scheme and as an interesting phenomenon in its own right, arising out of the similarity of the collapsible tube equations to those governing shallow water flow.

In this paper we present a theoretical model of the Cygnus Loop which, with only a small number of free parameters, accounts for most of the gross features of the observations. We believe that none of the models described in the literature can explain the observations in such a simple way.