The purely conductive state in configurations such as the Rayleigh–Bénard one is linearly stable for yield stress fluids at all Rayleigh numbers, $Ra$. However, on changing to localized heater configurations the static background state exists only if the yield stress is sufficiently large. Otherwise, thermal plumes may be induced in a stationary viscoplastic fluid layer, as illustrated in the recent experimental study of Davaille et al. (J. Non-Newtonian Fluid Mech., vol. 193, 2013, 144–153). Here, we study an analogous problem both analytically and computationally, from the perspective of an ideal yield stress fluid (Bingham fluid) that is initially stationary in a locally heated rectangular tank. We show that for a non-zero yield stress the onset of flow waits for a start time $t_{s}$ that increases with the dimensionless ratio of yield stress to buoyancy stress, denoted $B$. We provide a precise mathematical definition of $t_{s}$ and approximately evaluate this for different values of $B$, using both computational and semianalytical methods. For sufficiently large $B\geqslant B_{cr}$, the fluid is unable to yield. For the flow studied, $B_{cr}\approx 0.00307$. The critical value $B_{cr}$ and the start time $t_{s}$, for $B<B_{cr}$, are wholly independent of $Ra$ and $Pr$. For $B<B_{cr}$, yielding starts at $t=t_{s}$. The flow develops into either a weakly or a strongly convective flow. In the former case the passage to a steady state is relatively smooth and monotone, resulting eventually in a steady convective plume above the heater, rising and impinging on the upper wall, then recirculating steadily around the tank. With strongly convecting flows, for progressively larger $Ra$ we observe an increasing number of distinct plume heads and a tendency for plumes to develop as short-lived pulses. Over a certain range of $(Ra,B)$ the flow becomes temporarily frozen between two consecutive pulses. Such characteristics are distinctly reminiscent of the experimental work of Davaille et al. (J. Non-Newtonian Fluid Mech., vol. 193, 2013, 144–153). The yield stress plays a multifaceted role here as it affects plume temperature, size and velocity through different mechanisms. On the one hand, increasing $B$ tends to increase the maximum temperature of the plume heads. On the other hand, for larger $B\rightarrow B_{cr}$, the plume never starts.

We explore the transport of heavy particles through an upward displacement-ventilated space. The space incorporates a localised source of buoyancy which generates a turbulent buoyant plume. The plume fluid is contaminated with a small concentration of particles, which are subject to gravitational settling. A constant flow of uncontaminated fluid is supplied at a low level into the space, while an equal amount of fluid is vented from the space at a high level. At steady state, a two-layer density stratification develops associated with the source of buoyancy. New laboratory experiments are conducted to explore how particles are transported by this flow. The experiments identify that the upper layer may either become well-mixed in particles or it may develop a vertical stratification in particle concentration, with the particle concentration decreasing with height. We develop a quantitative model which identifies that such stratification develops for larger particle setting speeds, or smaller ventilation rates. In accord with our experiments, the model predicts that the number of particles extracted from the space through the high-level vent is controlled by the magnitude of the particle stratification in the upper layer, and this in turn depends on the particle settling speed relative to the ventilation speed and also the cross-sectional area and height of the space. We compare the predictions of the model with measurements of the flux of particles vented from the space for a range of operating conditions. We explore the relevance of the model for the removal of airborne contaminants by displacement ventilation in hospital rooms, and we discuss how contamination is propagated in the room as a result of lateral mixing of pathogens in the upper layer.

The fractography and conditions of propagation of joints that cut Devonian siltstones in the Appalachian Plateau, New York, and Eocene chalks from the Beer Sheva Syncline, Israel, are investigated. The joints cutting the siltstones are marked by S-type and C-type plumes, and the joints cutting the Lower Eocene and Middle Eocene chalks are marked by coarse and delicate plumes, respectively. The four plume types propagated under sub-critical (slow propagation) conditions. On the semi-quantitative fracture velocity (v) versus the tensile stress intensity (KI) curves, the S and C plume types fall in the KI=0.073–0.79 MPa m1/2 and v=2×10−4–10−2 m/s and KI=0.073–0.79 MPa m1/2 and v=10−6–10−4 m/s ranges respectively. The coarse and delicate plumes fall in the KI=0.03–0.17 MPa m1/2 and v=10−6–4×10−5 m/s and KI=0.03–0.17 MPa m1/2 and v=10−4–5×10−3 m/s ranges, respectively. Generally, slow plumes are relatively short, show periodicity, and typically exhibit superposition of arrest marks. On the other hand, faster plumes are longer and continuous, occur particularly in thinner layers, and show no superposition of arrest marks. There is a clear distinction between two en échelon segmentation end-members in the joint fringe, the ‘discontinuous breakdown type’ and the ‘continuous breakdown type’. There are also ‘transitional’ variations between the end-members. Only curved ‘discontinuous breakdown type’ boundaries of en échelon fringes can be equated with mirror boundaries.

We report on a series of experiments in which a Hele-Shaw cell containing aqueous solutions of NH4Cl was translated at prescribed rates through a steady temperature gradient. The salt formed the primary solid phase of a mushy layer as the solution solidified, with the salt-depleted residual fluid driving buoyancy-driven convection and the development of chimneys in the mushy layer. Depending on the operating conditions, several morphological transitions occurred. A regime diagram is presented quantifying these transitions as a function of freezing rate and the initial concentration of the solution. In general, for a given concentration, increasing the freezing rate caused the steady-state system to change from a convecting mushy layer with chimneys to a non-convecting mushy layer below a relatively quiescent liquid, and then to a much thinner mushy layer separated from the liquid by a region of active secondary nucleation. At higher initial concentrations the second of these states did not occur. At lower concentrations, but still above the eutectic, the mushy layer disappeared. A simple mathematical model of the system is developed which compares well with the experimental measurements of the intermediate, non-convecting state and serves as a benchmark against which to understand some of the effects of convection. Movies are available with the online version of the paper.

Three small picritic dykes, intruded at a late stage in the evolution of the Rum basic–ultra-basic complex, Inner Hebrides, shed new light on the nature of the magmas responsible for the main complex. The magmas are of transitional (mildly alkalic) type, generated by relatively small-fraction (6–7%) melting of a depleted mantle source. Melting is tentatively deduced to have commenced at ±100 km, straddling the garnet–spinel transition. Of the three samples, one (M9) is remarkable for the preservation of very primitive characteristics, with olivines of Fo93 containing highly aluminous spinels; these appear unique within the British Tertiary Volcanic Province. Sr, Nd and Pb isotopes indicate only minor ([les ]4%) contamination with Precambrian crustal lithologies, reflecting the rapidity of ascent of the magma batches. The Rum picrites have 187Os/188Os ratios and trace element characteristics comparable to those of recent picrites from Iceland, suggesting minimal temporal change of the depleted parts of the Iceland plume over 60 Ma. Movements of the Long Loch Fault may have been instrumental in causing decompression melting of the spreading Iceland plume-head and facilitating ascent of the melts to near-surface levels.