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Dive into the research topics where John A. Whitehead is active.

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Featured researches published by John A. Whitehead.


Journal of Fluid Mechanics | 1969

Finite bandwidth, finite amplitude convection

Alan C. Newell; John A. Whitehead

The main purpose of this work is to show how a continuous finite bandwidth of modes can be readily incorporated into the description of post-critical Rayleigh-Benard convection by the use of slowly varying (in space and time) amplitudes. Previous attempts have used a multimodal discrete analysis. We show that in addition to obtaining results consistent with the discrete mode approach, there is a larger class of stable and realizable solutions. The main feature of these solutions is that the amplitude and wave-number of the motion is that of the most unstable mode almost everywhere, but, depending on external and initial conditions, the roll couplets in different parts of space may be 180° out of phase. The resulting discontinuities are smoothed by hyperbolic tangent functions. In addition, it is clear that the mechanism for propagating spatial nonuniformities is diffusive in character.


Science | 1992

Mantle Plumes and Entrainment: Isotopic Evidence

Stanley R. Hart; Erik H. Hauri; L. A. Oschmann; John A. Whitehead

Many oceanic island basalts show sublinear subparallel arrays in Sr-Nd-Pb isotopic space. The depleted upper mantle is rarely a mixing end-member of these arrays, as would be expected if mantle plumes originated at a 670-kilometer boundary layer and entrained upper mantle during ascent. Instead, the arrays are fan-shaped and appear to converge on a volume in isotopic space characterized by low 87Sr/86Sr and high 143Nd/144Nd, 206Pb/204Pb, and 3He/4He ratios. This new isotopic component may be the lower mantle, entrained into plumes originating from the core-mantle boundary layer.


Journal of Geophysical Research | 1994

Fluid dynamic and geochemical aspects of entrainment in mantle plumes

Erik H. Hauri; John A. Whitehead; Stanley R. Hart

A similarity solution has been developed for vertical, steady-state mantle plume conduits by considering the boundary layer flow emanating from a point source of heat in an axisymmetric geometry. This model includes the effects of temperature and shear stress on viscosity, and incorporates depth-dependent viscosity and thermal expansivity. Plumes with variable viscosity have upward velocities of 0.30–100 m/yr and radii of 30–250 km, depending on temperature, rheology and buoyancy flux. These results demonstrate the small lateral scale of plume features relative to the resolution of most large-scale convection models and seismological studies. All of the plumes studied showed significant entrainment of ambient mantie surrounding the plume conduit, driven by the radial conduction of heat from the plume. This heat raises the buoyancy and lowers the viscosity of the ambient mantel, thereby entraining it into the conduit flow. For buoyancy fluxes of 0.1–10 Mg/s, similar to the range estimated for plumes in the Earths mantle, we calculate a range of entrainment of >90% to <5% ambient mantle, correlating negatively with buoyancy flux. Examination of the streamlines of mantle material which is entrained into thermal plumes indicates that most of the entrained fraction originates from approximately the lower half of the layer traversed by the plume, and shows minor entrainment of upper level material. This is especially true for non-Newtonian and depth dependent rheologies, and for depth-dependent thermal expansivity. Upwelling of depleted upper mantle, viscously coupled to the plume flow, is proposed as a mechanism for generating post-shield stage alkalic basalts erupted on oceanic island chains and their associated flexural arches. The existing Sr-Nd-Pb isotope data for oceanic basalts indicate the presence of a component which is common to hotspot basalts worldwide, and which is distinct from the upper mantle source of mid-ocean ridge basalts. This component (termed “FOZO” by Hart et al. (1992)) has moderately depleted Sr and Nd signatures, radiogenic Pb isotopes, and elevated 3He/4He ratios. The high He isotope ratios of FOZO suggest an origin for this component in the lower mantle, and would appear to provide independent evidence to support the fluid dynamic observations for significant entrainment of lower mantle in plumes and exclusion of upper mantle. If the composition of FOZO is representative of the isotopic composition of the lower mantle, then it would appear that this reservoir has been differentiated relative to estimates for the bulk silicate earth (BSE). This may be due either to melting and differentiation at higher levels in the mantle, or to fractionation of high pressure phases from a terrestrial magma ocean.


Journal of Geophysical Research | 1995

Experiments on flow focusing in soluble porous media, with applications to melt extraction from the mantle

Peter B. Kelemen; John A. Whitehead; Einat Aharonov; Kelsey A. Jordahl

We demonstrate finite structures formed as a consequence of the “reactive infiltration instability” (Chadam et al., 1986) in a series of laboratory and numerical experiments with growth of solution channels parallel to the fluid flow direction. Regions with initially high porosity have high ratios of fluid volume to soluble solid surface area and exhibit more rapid fluid flow at constant pressure, so that dissolution reactions in these regions produce a relatively rapid increase in porosity. As channels grow, large ones entrain flow laterally inward and extend rapidly. As a result, small channels are starved and disappear. The growth of large channels is an exponential function of time, as predicted by linear stability analysis for growth of infinitesimal perturbations in porosity. Our experiments demonstrate channel growth in the presence of an initial solution front and without an initial solution front where there is a gradient in the solubility of the solid matrix. In the gradient case, diffuse flow is unstable everywhere, channels can form and grow at any point, and channels may extend over the length scale of the gradient. As a consequence of the gradient results, we suggest that the reactive infiltration instability is important in the Earths mantle, where partial melts in the mantle ascend adiabatically. Mantle peridotite becomes increasingly soluble as the melts decompress. Dissolution reactions between melts and peridotite will produce an increase in liquid mass and lead to formation of porous channels composed of dunite (>95% olivine). Replacive dunite is commonly observed in the mantle section of ophiolites. Focused flow of poly baric partial melts of ascending peridotite within dunite channels may explain the observed chemical disequilibrium between shallow, oceanic mantle peridotites and mid-oceanic ridge basalts (MORB). This hypothesis represents an important alternative to MORB extraction in fractures, since fractures may not form in weak, viscously deforming asthenospheric mantle. We also briefly consider the effects of crystallization, rather than dissolution reactions, on the morphology of porous flow via a second set of experiments where fluid becomes supersaturated in a solid phase. Formation of short-lived conduits parallel to the flow direction occurs rapidly, and then each conduit is eventually choked by interior crystallization; fluid flow then passes through the most permeable portion of the walls to form a new conduit. On long time scales and length scales, transient formation and destruction of conduits will result in random and diffuse flow. Where liquid cools as it rises through mantle tectosphere on a conductive geotherm, it will become saturated in pyroxene as well as olivine and decrease in mass. This process may produce a series of walled conduits, as in our experiments. Development of a low-porosity cap overlying high porosity conduits may create hydrostatic overpressure sufficient to cause fracture and magma transport to the surface in dikes.


Journal of Geophysical Research | 1995

Channeling instability of upwelling melt in the mantle

Einat Aharonov; John A. Whitehead; Peter B. Kelemen; Marc Spiegelman

We present results of a theoretical study aimed at understanding melt extraction from the upper mantle. Specifically, we address mechanisms for focusing of porous flow of melt into conduits beneath mid-ocean ridges in order to explain the observation that most oceanic residual peridotites are not in equilibrium with mid-ocean ridge basalt. The existence of such conduits might also explain geological features, termed replacive dunites, that are observed in exposed mantle sections. We show here, by linear analysis, that flow in a chemically reactive porous media is unstable in the presence of a solubility gradient, such as induced by adiabatic ascent of melt underneath mid-ocean ridges. The initially homogeneous flow becomes focused in time to produce elongated high-porosity fingers that act as conduits for transport of fast flowing melt. This instability arises due to a positive feedback mechanism in which a region of slightly higher than average porosity causes increased influx of unsaturated flow, leading to increased dissolution which further reduces the porosity. Even in the presence of matrix compaction and chemical diffusion the instability is demonstrated to be robust. Our analysis also indicates the existence of growing, traveling waves which transport and amplify porosity and concentration perturbations.


Journal of Fluid Mechanics | 1971

Instabilities of convection rolls in a high Prandtl number fluid

F. H. Busse; John A. Whitehead

An experiment on the stability of convection rolls with varying wave-number is described in extension of the earlier work by Chen & Whitehead (1968). The results agree with the theoretical predictions by Busse (1967 a ) and show two distinct types of instability in the form of non-oscillatory disturbances. The ‘zigzag instability’ corresponds to a bending of the original rolls; in the ‘cross-roll instability’ rolls emerge at right angles to the original rolls. At Rayleigh numbers above 23,000 rolls are unstable for all wave-numbers and are replaced by a three-dimensional form of stationary convection for which the name ‘bimodal convection’ is proposed.


Geophysical and Astrophysical Fluid Dynamics | 1974

Rotating hydraulics of strait and sill flows

John A. Whitehead; A. Leetmaa; R. A. Knox

Theoretical and laboratory models of certain types of strait and sill flows are discussed. Specifically, we consider a two‐layer rotating fluid; the upper layer is at rest and the lower layer flows from one large basin to another via a connecting channel. The flow is assumed to be principally in a down‐channel direction. The cross‐channel balance is therefore geostrophic and the Bernoulli and potential vorticity equations are simplified. We further invoke the usual non‐rotating hydraulic principle of maximum transport in flow over a weir—here the end of the channel—and thereby calculate relations between transport, rotation rate, and upstream interface height. One of these relations is tested experimentally with favorable results. A nonsteady decaying flow in the same system is analyzed similarly and also compares well with experiment, as does a flow in both layers driven by an initial density imbalance. Some connections with oceanic strait and sill flows are discussed.


Journal of Fluid Mechanics | 1974

Oscillatory and collective instabilities in large Prandtl number convection

F. H. Busse; John A. Whitehead

An experimental study of transitions from steady bimodal convection to timedependent forms of convection is described. Using controlled initial conditions for the onset of bimodal convection two mechanisms of instability can be separated from the effects of random noise. The oscillatory instability of bimodaI cells introduces standing waves closely resembling those occurring in low Prandtl number convection. The collective instability introduces spoke-pattern convection which is characteristic for turbulent large Prandtl number convection. Both instabilities originate primarily from the momentum advection terms in the equations of motion, as is evident from the strong Prandtl number dependence of the critical Rayleigh number R, for the onset of oscillations. The results are discussed in relation to previous experiments and recent theoretical work.


Journal of Fluid Mechanics | 1982

The intrusion of a density current along the coast of a rotating fluid

Melvin E. Stern; John A. Whitehead; Bach-Lien Hua

When light rotating fluid spreads over heavier fluid in the vicinity of a vertical wall (coast) a boundary jet of width Λ forms, the leading edge or nose of which propagates with speed ĉ along the coast. A certain fraction 8 of the boundary transport is not carried by the nose but is deflected backwards (detrained) and left behind the propagating nose. Theoretical and experimental results for Λ,ĉ, and δ are given for a quasi-equilibrium (constant-ĉ) regime. Over longer time intervals the laboratory observations suggest that the nose slows down and stagnates, whereupon the trailing flow separates from the coast and an intermittent boundary current forms. These processes may be relevant to the mixing of oceanic coastal currents and the maintenance of the mean current.


Journal of Physical Oceanography | 2004

A dense current flowing down a sloping bottom in a rotating fluid

Claudia Cenedese; John A. Whitehead; T. A. Ascarelli; M. Ohiwa

A density-driven current was generated in the laboratory by releasing dense fluid over a sloping bottom in a rotating freshwater system. The behavior of the dense fluid descending the slope has been investigated by systematically varying four parameters: the rotation rate, the bottom slope, the flow rate of the dense fluid, and the density of the dense fluid. Over a wide range of parameter values, the following three flow types were found: a laminar regime in which the dense current had a constant thickness behind the head, a wave regime in which wavelike disturbances appeared on the interface between the dense and fresh fluids, and an eddy regime in which periodic formation of cyclonic eddies in the fresh overlying ambient fluid was observed. All of the experiments revealed that increasing the slope angle and the density of the bottom fluid allowed the flow to evolve from the laminar to the wave regime. Furthermore, increasing rotation rate induced the formation of eddies. A theoretical solution for the downslope velocity field has been found using a steady-state model. Comparison between the theoretical and experimental downslope velocities gave good agreement. The wave regime was observed to occur for values of the Froude number greater than 1. The laminar regime was found for values of the Froude number less than 1. The amount of mixing between the dense and the ambient fluids was measured. Mixing increased significantly when passing from the laminar to the wave regime, that is, with increasing Froude number. Good agreement between the amount of mixing observed in the ocean and in the laboratory experiments is encouraging and makes the waves observed in the present experiments a possible candidate for the mixing observed during oceanic dense current overflows.

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Claudia Cenedese

Woods Hole Oceanographic Institution

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Stanley R. Hart

Woods Hole Oceanographic Institution

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Aline Cotel

University of Michigan

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Mark D. Behn

Woods Hole Oceanographic Institution

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Karl R. Helfrich

Woods Hole Oceanographic Institution

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Lawrence J. Pratt

Woods Hole Oceanographic Institution

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John Marshall

Massachusetts Institute of Technology

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John Salzig

Woods Hole Oceanographic Institution

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