Paper: J.A. Whitehead and D.S. Luther, Dynamics of laboratory diapir and plume models,
JGR 80, 705–717, 1975.
á What was the inspiration for this paper?
o Plate tectonics was relatively new, behavior of the Hawaiian hot spot was intriguing
o Diastrophic processes could potentially disturb continents
o Whitehead actually did a lot of work with plate tectonics and mantle convection
o Interested in determining what caused spacing and shape of jets
á Initial Instability
o Experiment set up with then layer of less dense fluid on top of more dense fluid, then inverted to create density inversion.
o They described the initial instability created by the inversion using wavenumber.
¤ Wavenumber is a function of different viscosities and thickness
o The experiment was set up with fixed, solid boundaries and only viscosities of the different fluids were changed.
o Interface deforms due to Rayleigh-Taylor instability
¤ An initial disturbance changes potential energy, establishes pressure gradient leading to feedback
¤ Deformation puts the system in a lower energy state
¤ Boundary conditions determine fastest growing wavenumber (Equations 6 and 7)
á Objectives of math presented in paper
o Introduce the preferred wavenumber (Figures 4 and 5)
o Provide motivation using physical balances
o Showing that the wavenumber is smaller for Fig. 1 than Fig. 2
o Mathematical motivation provided in the Appendices
á What was the purpose of the additional experiments (ie. Continuous flow)?
o The experiments shown in Figs. 1 and 2 speak to initiation and spacing of diapirs, but want to talk about whatÕs happening with the blob at the top.
¤ Model from Equation 10 is insufficient to describe this
¤ Go to different system where the layer is not considered
o Supply fluid at particular flux, observe the form
o Discover agreement between simple theory (p.711) and previous experiments
á Other considerations
o What would happen if you had gas rising through the fluid?
¤ Density difference driving motion
o What would happen if you cut off flow as soon as the head formed?
¤ Hypothetically the structure and shape could change
á Overall Goal of Paper
o Describe the shapes formed in Figs. 1 and 2
o Use Figs. 7 and 8 to understand fluid dynamics
o Focus not just on salt domes like everyone else
á Last part of the paper
o Discussion of mantle plumes, granite batholiths, generally potential applications
o Pretty hypothetical discussion of mantle plumes due to lack of constrained variables
¤ Difficulty determining viscosity of lower mantle
¤ Isostatic rebound gives constraints on viscosity of upper mantle
¤ Possibly long-term normal modes of large earthquakes
¤ Chemistry?