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Displaying 12 authors out of 12
C. JAUPART (Inst. de Physique du Globe de Paris, France)
Introduction of energy equation. Boussinesq approximation.
Plumes and thermals. Use these to derive scaling relations for velocity as a function of power input and to discuss dynamical regimes (laminar vs. turbulent). Use plumes to illustrate Prandtl number, diffusion of heat and momentum and boundary layer structure. (Application of simple convection code)
Rayleigh-Bénard convection (no internal heating). Heuristic argument to introduce Rayleigh number. Dimensional analysis. Rayleigh number, Prandtl number, Reynolds number for convective flow.
Examples of convective systems: mantle, magma reservoirs. Marginal stability: Influence of boundary conditions (Free boundaries, rigid boundaries, fixed temperature, fixed heat flux).
Equation for the horizontally averaged temperature and the convective heat flux Thermal structure of fluid layer: boundary layers and well-mixed interior.
Free boundaries versus rigid boundaries. Large Prandtl number fluids. Convective loop model. Scaling relations for velocity and heat flux (no internal heating).
Scaling for internally heated fluids. Thermal structure of fluid layer
Temperature-dependent viscosity. Scaling for velocity and heat flux.
Non-Newtonian rheology. Non-Newtonian with temperature-dependent rheology. Scaling for velocity, heat flux, stress and strain-rate.
Two-layer mantle: convection regimes, thermal structure.
Evolution of initially stratified fluid
C. JAUPART, P. MOLNAR (Inst. de Physique du Globe de Paris, France, University of Colorado at Boulder, USA)
Chemical differences. Buoyancy number: Marginal stability, dependence on Rayleigh number and Buoyancy number.
C. JAUPART, S. ZHONG (Inst. de Physique du Globe de Paris, France, Univ. of Colorado at Boulder, USA)
Convection driven by density anomalies in the Earth s mantle. Dynamic topography.
Practicals and exercises: problem sets + a few computer runs.
Practicals and exercises: problem sets + a few computer runs.
G. HOUSEMAN (University of Leeds, UK)
Stress and strain, and basic isostasy (statics).
Derivation of thin viscous sheet equations
Diagnostics of thin sheet deformation: matching gradients in strain-rates to gradients in GPE, and faulting response. Case studies: Tibet, Aegean and Indian Ocean.
Scaling of areal extent of deformation to dimensions of boundaries and to n (England, Houseman, and Sonder, 1985), plus dependence on Ar. Exercises on simple boundary-driven deformation problems using basic solutions. Dependence on the Argand number, Ar, and the exponent n.
Derivation of basic equation for growth rate. Example of instability
Growth rate as a function of wavenumber, dependence on boundary conditions, eigenfunctions
Rayleigh-Taylor instability, effects of non-Newtonian viscosity. Derivation of the dependence of growth rate on n.
Examples using sybil to examine the time dependence of growth: exponential for n = 1, and super-exponential with n > 1 Scaling of growth rate to n.
Basil/sybil exercise with a sinking sphere or cylinder
G. HOUSEMAN, P. MOLNAR (Univ. of Leeds, UK, Univ. of Colorado at Boulder, USA)
Scaling of stress differences to elevations (in isostasy), and simple problems illustrating force per unit length
J. NIEMALA (ICTP, Trieste)
Turbulence, planform of convection, boundary layer and plumes at high Rayleigh number
Turbulence, planform of convection, boundary layer and plumes at high Rayleigh number
M. MANGA (Univ. of California, Berkeley, USA)
Stokes equation, equation of continuity, and constitutive laws (both Newtonian, and non-Newtonian with underlying physics).
Derivation of the basic heat transfer equation and heating or cooling by diffusion
Examples of a cooling lithosphere: both cooling plate and cooling half-space, comparison of different boundary conditions (fixed temperature and fixed heat flux).
Solidification Scaling of time and depth in thermal diffusion
Mixing and Volcanos
M. MANGA, P. MOLNAR (Univ. of California, USA , Univ. of Colorado at Boulder, USA)
What are scaling laws, why are they important in geodynamics, and what problems in geophysics make them attractive.
P. MOLNAR (Univ. of Colorado at Boulder, USA)
Simple problems of isostasy
Derivation of GPE. 2D stress balance for different crustal structure/boundary conditions
ICTP COLLOQUIUM: Mantle dynamics and the rise and fall of mountain belts
Stokes flow and dynamic topography Stokes problem of a sinking sphere
Deflection of the surface above a sinking sphere and associated gravity anomalies and geoid. [Morgan, 1965]
Molnar and England’s S in thrust faulting
P. MOLNAR, G. HOUSEMAN (Univ. of Colorado at Boulder, USA Univ. of Leeds, UK)
Some simple problems to relate stress and strain and illustrate constitutive laws, such as enhanced localization with non-Newtonian viscosity, with channel flow as an example. Exercises illustrating channel flow: Couette flow: problems, non-Newtonian material, exponential viscosity
R. KATZ (Univ. of Oxford, UK)
MAGMATIC SYSTEMS: MECHANICS. Derivation of conservation of mass & momentum equations. Scaling and the compaction length. Magma wave solutions.
Latent heat of crystallization and melting. Stefan number. Diffusive cooling: pure substance. Mushy layers: observations (lava lakes). Mushy layers: models.
Convection and crystallization in magma reservoirs: thermal and compositional.
Thermodynamics & chemistry.
Equilibrium & disequilibrium formulations. Melting column solutions.
Instabilities & the tectonic context. Mechanical and reactive melting instabilities. Magma-genesis and focussing at mid-ocean ridges
S. ZHONG (Univ. of Colorado at Boulder, USA)
Dissipation equation. New derivation of Nusselt number vs. Rayleigh number relationship
Characteristics of plumes in Rayleigh-Bénard convection at high Ra
Small-scale convection beneath oceanic and continental lithosphere
DEEP CONVECTION: Pressure-dependence of density: non-Boussinesq flow. Dissipation number, temperature scale height Isentropes and adiabats. Energy balance and scaling of dissipation with Rayleigh number.

Organizers

Directors: A. Aoudia, P. Molnar, G. Houseman, C. Jaupart, M. Manga