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.

Fluid‐mechanical models of crack propagation and their application to magma transport in dykes

The subject of this monograph is the fluid dynamics of liquid turbomachines, particularly pumps. Rather than attempt a general treatise on turbomachines, we shall focus attention on those special problems and design issues associated with the flow of liquid through a rotating machine. There are two characteristics of a liquid that lead to these special problems, and cause a significantly different set of concerns than would occur in, say, a gas turbine. These are the potential for cavitation and the high density of liquids that enhances the possibility of damaging unsteady flows and forces.

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Hydrodynamics of Pumps

A two-control-volume model is employed for honeycomb-stator/smooth-rotor seals, with a conventional control-volume used for the throughflow and a capacitance-accumulator model for the honeycomb cells. The control volume for the honeycomb cells is shown to cause a dramatic reduction in the effective acoustic velocity of the main flow, dropping the lowest acoustic frequency into the frequency range of interest for rotordynamics. In these circumstances, the impedance functions for the seals cannot be modeled with conventional (frequency-independent) stiffness, damping, and mass coefficients. More general transform functions are required to account for the reaction forces, and the transfer functions calculated here are a lead-lag term for the direct force function and a lag term for the cross-coupled function. Experimental measurements verify the magnitude and phase trends of the proposed transfer functions. These first-order functions are simple, compared to transfer functions for magnetic bearings or foundations. For synchronous response due to imbalance, they can be approximated by running-speed-dependent stiffness and damping coefficients in conventional rotordynamics codes. Correct predictions for stability and transient response will require more general algorithms, presumably using a state-space format.

The Acoustic Influence of Cell Depth on the Rotordynamic Characteristics of Smooth-Rotor/Honeycomb-Stator Annular Gas Seals

Transport of magma and hydrothermal solutions by laminar and turbulent fluid fracture

A theoretical basis for static and dynamic operation of tilting pad journal bearings (TPJBs)
has evolved over the last 50 years. Originally demonstrated by Lund using the pad assembly
method and a classic Reynolds equation solution, the current state of the art includes full
thermoelastohydrodynamic solutions of the generalized Reynolds equation that include fluid
convective inertia effects, pad motions; and thermal and mechanical deformations of the
pads and shaft. The development of TPJB theory is reviewed, emphasizing dynamic modeling. The paper begins with the early analyses of fixed geometry bearings and continues to
modern analyses that include pad motion and stiffness and damping effects. The development
of thermohydrodynamic, thermoelastohydrodynamic, and bulk-flow analyses is reviewed. The
theories of TPJB dynamics, including synchronous and nonsynchronous models, are reviewed.
A discussion of temporal inertia effects in tilting pad bearing is considered. Future
trends are discussed, and a path for experimental verification is proposed.

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G. G. Hirs

Papers

A Bulk-Flow Theory for Turbulence in Lubricant Films