The ubiquity of dykes in the Earth's crust is evidence that the transport of magma by fluid‐induced fracture of the lithosphere is an important phenomenon. Magma fracture transports melt vertically from regions of production in the mantle to surface eruptions or near‐surface magma chambers and then laterally from the magma chambers in dykes and sills. In order to investigate the mechanics of magma fracture, the driving and resisting pressures in a propagating dyke are estimated and the dominant physical balances between these pressures are described. It is shown that the transport of magma in feeder dykes is characterized by a local balance between buoyancy forces and viscous pressure drop, that elastic forces play a secondary role except near the dyke tip and that the influence of the fracture resistance of crustal rocks on dyke propagation is negligible. The local nature of the force balance implies that the local density difference controls the height of magma ascent rather than the total hydrostatic head and hence that magma is emplaced at its level of neutral buoyancy (LNB) in the crust. There is a small overshoot beyond this level which is calculated to be typically a few kilometres. Magma accumulating at the LNB will be intruded in lateral dykes and sills which are directed along the LNB by buoyancy forces since the magma is in gravitational equilibrium at this level. Laboratory analogue experiments demonstrate the physical principle of buoyancy‐controlled propagation to and along the LNB. The equations governing the dynamics of magma fracture are solved for the cases of lithospheric ascent and of lateral intrusion. Volatiles are predicted to be exsolved from the melt at the tips of extending fractures due to the generation of low pressures by viscous flow into the tip. Chilling of magma at the edges of a dyke inhibits cross‐stream propagation and concentrates the downstream flow into a wider dyke. The family of theoretical solutions in different geometries provides simple models which describe the relation between the elastic and fluid‐mechanical phenomena and from which the lengths, widths and rates of propagation can be calculated. The predicted dimensions are in broad agreement with geological observations.

The turbulent fountain that results from the injection of a dense fluid upwards into a large tank of stably stratified fluid of lower density is studied experimentally and theoretically. For both axisymmetric and line fountains, we have used a combination of dimensional arguments and laboratory experiments to determine the initial height above the source at which the flow first comes to rest. Depending on the strength of the stratification and the fluxes of momentum and buoyancy at the source, the subsequent down flow may either spread along the base of the tank or intrude at an intermediate height in the environment. We determine both the height of intermediate intrusion and the critical condition for spreading along the base. We also relate numerical solutions of the entrainment equations to our experimental observations, and obtain effective entrainment coefficients for both axisymmetric and line fountains. Finally, we discuss the quantitative application of our results to the replenishment of magma chambers and to the heating or cooling of a room.

A theoretical model of axisymmetric turbulent fountains in both homogeneous and stratified fluids is developed. The model quantifies the entrainment of ambient fluid into the initial fountain upflow, and the entrainment of fluid from both the upflow and environment into the subsequently formed downflow. Four different variations of the model are considered, comprising the two most reasonable formulations of the body forces acting on the ‘double’ structure and two formulations of the rate of entrainment between the flows. The four model variations are tested by comparing the predictions from each of them with experimental measurements of fountains in homogeneous and stratified fluids.

. Our modeling indicates that the former was possible for long eruption durations (months), whereas the latter was possible for short eruption durations (<2 weeks). As the latter hypothesis is more consistent with the existing field evidence for thermal erosion at Kambalda, we believe it is the preferred interpretation.

We examine the dissolution of a vertical solid surface in the case where the heat and mass transfer is driven by turbulent compositional convection. A theoretical model of the turbulent dissolution of a vertical wall is developed, which builds on the scaling analysis presented by Kerr (J. Fluid Mech., vol. 280, 1994, pp. 287–302) for the turbulent dissolution of a horizontal floor or roof. The model has no free parameters and no dependence on height. The analysis is tested by comparing it with laboratory measurements of the ablation of a vertical ice wall in contact with salty water. The model is found to accurately predict the dissolution velocity for water temperatures up to approximately 5–$6\,^{\circ }\text{C}$, where there is a transition from turbulent dissolution to turbulent melting. We quantify the turbulent convective dissolution of vertical ice bodies in the polar oceans, and compare our results with some field observations.