Ross W. Griffiths

Stirring and structure in mantle starting plumes

Simple arguments show that ascending thermal plumes will entrain their surroundings as the result of coupling between conduction of heat and laminar stirring driven by the plume motion. In the initial stages of ascent of a plume fed by a continuous buoyancy flux (a starting plume) the plume consists of a large buoyant head followed by a narrow vertical conduit. Laboratory experiments reported here show that the spherical head entrains ambient material as it rises, while the axial conduit carries hot source material to the stagnation point at the cap of the plume, from where it spreads laterally into thin laminae. We develop an analysis of the effects of entrainment on the structure and dynamics of starting plumes. The analysis predicts that under conditions appropriate to the earths mantle large volumes of cooler lower mantle will be stirred into the head of a plume by the time it reaches the top of the mantle if it originates at the core-mantle boundary. The result is a major cooling and enlargement of the head. Source material ascending in the trailing conduit will undergo little contamination or cooling until the conduit is deflected from the vertical by large scale shear associated with plate motion. This plume structure explains the close association of high-temperature melts (komafiites or picrites) with more voluminous, lower temperature basalts in Archaean greenstones and modem continental flood basalt provinces: the picrites can be produced by melting in the hot axial conduit and the basalts from the cooler bulk of the head. More generally, we put forward stirring in plumes as one plausible mechanism contributing to compositional heterogeneity in hotspot melts. The predicted diameter of plume heads originating at the core-mantle boundary is - 1000 km and this is expected to enlarge to -2000 km when the plume collapses beneath the lithosphere. This result is in excellent agreement with the observed extent of volcanism and uplift associated with continental flood volcanism. It also provides support for the hypothesis that at least some plumes originate at the core-mantle boundary.

Mantle Plumes and Continental Tectonics

Mantle plumes and plate tectonics, the result of two distinct modes of convection within the Earth, operate largely independently. Although plumes are secondary in terms of heat transport, they have probably played an important role in continental geology. A new plume starts with a large spherical head that can cause uplift and flood basalt volcanism, and may be responsible for regional-scale metamorphism or crustal melting and varying amounts of crustal extension. Plume heads are followed by narrow tails that give rise to the familiar hot-spot tracks. The cumulative effect of processes associated with tail volcanism may also significantly affect continental crust.

Interaction of mantle plume heads with the Earth's surface and onset of small‐scale convection

We investigate the behavior of a spherical blob of buoyant fluid as gravity forces it toward either a rigid horizontal boundary or a free surface. The diapir fluid is assumed much less viscous than the ambient fluid. This fundamental problem is the simplest unsteady model relevant to the ascent of hot plumes of buoyant material toward Earths surface or the base of the lithosphere and closely models the heads of starting plumes. As the diapir approaches the boundary, it collapses in the vertical and spreads horizontally while a layer of the surrounding mantle is slowly squeezed out from betweeen the diapir and the surface. Experimental results for the thinning and lateral spreading of the bouyant fluid, and for the thinning of the squeeze layer, are given for both the case of a rigid, nonslip boundary and that of a free surface. These are compared with similarity scaling laws based on a balance between the bouyancy of the diapir and viscous stresses in the diapirs surroundings. We also observe that the squeeze layer can become gravitationally unstable, leading to a bifurcation from convection on the scale of the original plume to convection on scales much smaller than the diapir. The vertical exchange on smaller horizontal scales enables the plume to more rapidly approach the boundary. At the time instability occurs the diapir has spread to roughly twice its initial diameter. Application of these results, and previous results from surface uplift, to the plumes responsible for continental flood basalts is subject to knowledge of the local value of upper mantle viscosity. If this is taken to be 3×1020 Pa s, most uplift takes place ovcer approximately 5 m.y. Eruption of voluminous basalts will not take place until at least 5–10 m.y. after the surface has reached its maximum elevation. If small-scale instabilities do develop within mantle plume heads, they may be an essential mechanism allowing the top of the plume to ascend to the shallow depths required for extensive melting. It may also explain the observation of Hooper (1990) that volcanism in the Deccan and Columbian Plateau begins before the onset of crustal extension.

Laboratory models of the thermal evolution of the mantle during rollback subduction

The subduction of oceanic lithosphere plays a key role in plate tectonics, the thermal evolution of the mantle and recycling processes between Earths interior and surface. Information on mantle flow, thermal conditions and chemical transport in subduction zones come from the geochemistry of arc volcanoes, seismic images and geodynamic models. The majority of this work considers subduction as a two-dimensional process, assuming limited variability in the direction parallel to the trench. In contrast, observationally based models increasingly appeal to three-dimensional flow associated with trench migration and the sinking of oceanic plates with a translational component of motion (rollback). Here we report results from laboratory experiments that reveal fundamental differences in three-dimensional mantle circulation and temperature structure in response to subduction with and without a rollback component. Without rollback motion, flow in the mantle wedge is sluggish, there is no mass flux around the plate and plate edges heat up faster than plate centres. In contrast, during rollback subduction flow is driven around and beneath the sinking plate, velocities increase within the mantle wedge and are focused towards the centre of the plate, and the surface of the plate heats more along the centreline.

Solidification and Morphology of Submarine Lavas: A Dependence on Extrusion Rate

The results of recent laboratory experiments with wax extruded beneath relatively cold water may be extrapolated to predict the surface morphology of submarine lavas as a function of the extrusion rate and melt viscosity. The experiments with solidifying wax indicated that the surface morphology was controlled by a single parameter, the ratio of the time taken for the surface to solidify, and a time scale for lateral flow. For submarine basalts a solution of the cooling problem (which is dominated by conduction in the lava but convective heat transfer in the water) and estimates of lava viscosities place this parameter within the empirically determined “pillowing” regime over a wide range of extrusion rates. This result is consistent with the observation that pillow basalts are the most common products of submarine eruptions. Smoother surfaces corresponding to the various types of submarine sheet flows are predicted for sufficiently rapid extrusions of basaltic magma. Still higher eruption rates in regions of low topographic relief may produce submarine lava lakes. Minimum emplacement times can be calculated for submarine volcanic constructs of a single lava flow type.

A laboratory investigation of effects of trench migration on the descent of subducted slabs

A laboratory investigation of viscous slabs subducted from a migrating trench reveals a range of possible behaviours. The slab dip in a uniform mantle is found to be steady or oscillatory, depending on the rates of descent and trench migration. In addition, density and viscosity interfaces are used to model the increased resistance to sinking of stiff slabs through the seismic discontinuity at a depth of about 660 km in Earths mantle. If the slab is denser than the lower layer and its dip in the upper layer is steady, it can continue to descend through the lower layer in a tabular form and in either a steady or oscillatory manner, or it can be laid horizontally on the interface for a distance before descending in a chain of diapirs resulting from gravitational instability at the interface. If the slab dip in the upper layer is unstable, the slab sinks into the lower layer in a chain of large diapirs at a spacing determined by the frequency of oscillations set by instability of the slab within the upper layer. The style of penetration depends on the trench migration speed and the ratio of sinking velocities in the two layers. Estimates for mantle slabs indicate that they may range across the major regime transitions. The experimental system provides a gross simplification of mantle conditions but the results are a testimony to the possibility of a range of complex behaviour of subducted lithosphere. They also indicate that the relationship between the structural features in the lower mantle revealed by seismic imaging and present-day tectonic processes at the surface may not be obvious. Tomographic images of western Pacific subduction zones and data for the migration rates of associated trenches suggest a dependence of slab behaviour on migration rate similar to that seen in the experiments.

Radial spreading of viscous-gravity currents with solidifying crust

We have investigated the effect of a solidifying crust on the dynamics and surface morphology of radial viscous-gravity currents. Liquid polyethylene glycol was admitted into the base of a tank filled with cold sucrose solution maintained at a temperature below the wax freezing point. As the radial current advanced away from the inlet, its surface solidified and deformed through a combination of folding and fracturing. For the warmest experiments, during which solidification did not occur, the radius of the current increased in proportion to the square root of time, as demonstrated both experimentally and theoretically for isothermal viscous fluids by Huppert (1982). When cooling was sufficiently rapid, solid crust formed and caused the spreading rate to decrease. A cooling model combining conduction in the wax with convection in the sucrose solution predicts the distance from the source at which the solid crust first appeared Progressively colder experiments revealed a sequence of surface morphologies which resembled features observed on cooling lava flows and lava lakes. Flows in which crust formed very slowly developed marginal levees which contained and channelled the main portion of the current. Colder flows with more rapid crust growth formed regularly spaced surface folds, multi-armed rift structures complete with shear offsets, and bulbous lobate forms similar to pillow lavas seen under the ocean. The same transitions between modes of surface deformation were also generated by keeping the ambient water temperature constant and decreasing the extrusion rate. This demonstration that surfaces can exhibit a well-defined sequence of morphologies which depend on the underlying flow conditions offers the prospect of more successful interpretation of natural lava flows.

The stability of vortices in a rotating, stratified fluid

Axisymmetric flows with a two-layer density stratification are produced by releasing either a constant flux of fluid from a point source or a constant volume of fluid into a rotating environment with a different density. In both experiments the density interface intersects one horizontal boundary, forming a front. Transition to non-axisym-metric flow is observed and can be described by two parameters: θ, the square of the ratio of the internal Rossby radius of deformation to the horizontal length scale of the flow, and δ, the fraction of the total fluid depth occupied by the layer inside the front. For θ [Lt ] 1 and δ > 10 −1 unstable disturbances obtain most of their energy from the potential energy of the flow, whilst for δ −1 extraction of kinetic energy from the basic shear becomes the dominant driving mechanism. When the front intersects the free surface, n = 2 is the minimum azimuthal wavenumber for an unstable disturbance. At large amplitude of the growing waves, baroclinic and barotropic processes combine to form n vortex dipole structures which entrain buoyant fluid from the original vortex and propagate radially over the free surface. Vortices are also produced by the continuous release of fluid from a confined source at its own density level in a region of constant density gradient. As in the two-layer case the axisymmetric vortex grows to a critical size and then becomes unstable to a disturbance with wavenumber n = 2, producing, at large amplitude, two vortex pairs.

Ageostrophic instability of ocean currents

We investigate the stability of gravity currents, in a rotating system, that are infinitely long and uniform in the direction of flow and for which the current depth vanishes on both sides of the flow. Thus, owing to the role of the Earths rotation in restraining horizontal motions, the currents are bounded on both sides by free streamlines, or sharp density fronts. A model is used in which only one layer of fluid is dynamically important, with a second layer being infinitely deep and passive. The analysis includes the influence of vanishing layer depth and large inertial effects near the edges of the current, and shows that such currents are always unstable to linearized perturbations (except possibly in very special cases), even when there is no extremum (or gradient) in the potential vorticity profile. Hence the established Rayleigh condition for instability in quasi-geostrophic models, where inertial effects are assumed to be vanishingly small relative to Coriolis effects, does not apply. The instability does not depend upon the vorticity profile but instead relies upon a coupling of the two free streamlines. The waves permit the release of both kinetic and potential energy from the mean flow. They can have rapid growth rates, the e -folding time for waves on a current with zero potential vorticity, for example, being close to one-half of a rotation period. Though they are not discussed here, there are other unstable solutions to this same model when the potential vorticity varies monotonically across the stream, verifying that flows involving a sharp density front are much more likely to be unstable than flows with a small ratio of inertial to Coriolis forces. Experiments with a current of buoyant fluid at the free surface of a lower layer are described, and the observations are compared with the computed mode of maximum growth rate for a flow with a uniform potential vorticity. The current is observed to be always unstable, but, contrary to the predicted behaviour of the one-layer coupled mode, the dominant length scale of growing disturbances is independent of current width. On the other hand, the structure of the observed disturbances does vary: when the current is sufficiently narrow compared with the Rossby deformation radius (and the lower layer is deep) disturbances have the structure predicted by our one-layer model. The flow then breaks up into a chain of anticyclonic eddies. When the current is wide, unstable waves appear to grow independently on each edge of the current and, at large amplitude, form both anticyclonic and cyclonic eddies in the two-layer fluid. This behaviour is attributed to another unstable mode.

THE STABILITY OF BUOYANCY-DRIVEN COASTAL CURRENTS

Griffiths, R.W. and Linden, P.F., 1981. The stability of buoyancy-driven coastal currents. Dyn. Atmos. Oceans, 5: 281--306. Buoyancy-driven boundary currents were generated in the laboratory by releasing buoyant fluid from a source adjacent to a vertical boundary in a rotating container. The boundary removed the Coriolis force parallel to it, allowing the buoyant fluid to spread in a current along the boundary. Use of a cylindrical boundary and a line source that released fluid uniformly around the circumference enabled an axisymmetric (zonal) current to be produced. With the continuous release of fluid from the source, the current grew in width and depth until it became unstable to non-axisymmetric disturbances. The wavelength and phase velocities of the disturbances were consistent with a model of baroclinic instability of two-layer flow when frictional dissipation due to Ekman layers is included. However, when the current only occupied a small fraction of the total depth, barotropic processes were also thought to be important, with the growing waves gaining energy from the horizontal shear. In other experiments, gravity currents were produced by a point source adjacent to either a zonal (circular) or a meridional (radial) vertical boundary. The currents were also observed to become unstable to the same upstream breaking waves as those on the continuous zonal current. Finally, some comparisons are made with oceanic coastal currents.