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Advanced School on Scaling Laws in Geophysics: Mechanical and Thermal Processes in Geodynamics | (smr 2240)
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  • Tuesday, 24 May 2011
    • 09:00 - 10:00 Derivation of GPE. 2D stress balance for different crustal structure/boundary conditions
      • 09:00 Derivation of GPE. 2D stress balance for different crustal structure/boundary conditions 1h0'
        Speaker: P. Molnar (Univ. of Colorado at Boulder, USA)
        Material: lecture notes
    • 10:00 - 10:30 Coffee break
      • 10:00 Coffee break 30'
    • 10:30 - 12:00 Derivation of thin viscous sheet equations
      • 10:30 Derivation of thin viscous sheet equations 1h30'
        Speaker: G. Houseman (Univ. of Leeds, UK)
        Material: lecture notes
    • 12:00 - 12:30 Scaling of stress differences to elevations (in isostasy), and simple problems illustrating force per unit length
      • 12:00 Scaling of stress differences to elevations (in isostasy), and simple problems illustrating force per unit length 30'
        Speaker: G. Houseman, P. Molnar (Univ. of Leeds, UK, Univ. of Colorado at Boulder, USA)
        Material: lecture notes
    • 12:30 - 14:00 Lunch Break
      Location: Adriatico Guest House Cafeteria
      • 12:30 Lunch Break 1h30'
    • 14:00 - 16:00 Diagnostics of thin sheet deformation: matching gradients in strain-rates to gradients in GPE, and faulting response. Case studies: Tibet, Aegean and Indian Ocean.
      • 14:00 Diagnostics of thin sheet deformation: matching gradients in strain-rates to gradients in GPE, and faulting response. Case studies: Tibet, Aegean and Indian Ocean. 2h0'
        Speaker: G. Houseman (Univ. of Leeds, UK)
        Material: lecture notes
    • 16:00 - 16:30 Coffee Break
      Location: Adriatico Guest House (Terrace)
      • 16:00 Coffee Break 30'
    • 16:30 - 17:30 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.
      • 16:30 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. 1h0'
        Speaker: G. Houseman (Univ. of Leeds, UK)
        Material: Exercise
  • Wednesday, 25 May 2011
    • 09:00 - 10:30 Derivation of basic equation for growth rate. Example of instability
      • 09:00 Derivation of basic equation for growth rate. Example of instability 1h30'
        Speaker: G. Houseman (Univ. of Leeds, UK)
        Material: lecture notes
    • 10:30 - 11:00 Coffee Break
      Location: Adriatico Guest House (Terrace)
      • 10:30 Coffee Break 30'
    • 11:00 - 12:00 Growth rate as a function of wavenumber, dependence on boundary conditions, eigenfunctions
      • 11:00 Growth rate as a function of wavenumber, dependence on boundary conditions, eigenfunctions 1h0'
        Speaker: G. Houseman (Univ. of Leeds, UK)
    • 12:00 - 12:30 Examples using Houseman s code sybil to examine exponential form of blobs and thinning using runs already carried out. Derive the growth rate for a simple case. (For instance, 2 half-spaces with constant, different density, and exponentially decreasing viscosity), Scaling of growth rate to various parameters (density, g, thickness, and viscosity).
      • 12:00 Examples using Houseman s code sybil to examine exponential form of blobs and thinning using runs already carried out. Derive the growth rate for a simple case. (For instance, 2 half-spaces with constant, different density, and exponentially decreasing viscosity), Scaling of growth rate to various parameters (density, g, thickness, and viscosity). 30'
    • 12:30 - 14:00 Lunch Break
      Location: Adriatico Guest House Cafeteria
      • 12:30 Lunch Break 1h30'
    • 14:00 - 14:30 Rayleigh-Taylor instability, effects of non-Newtonian viscosity. Derivation of the dependence of growth rate on n.
      • 14:00 Rayleigh-Taylor instability, effects of non-Newtonian viscosity. Derivation of the dependence of growth rate on n. 30'
        Speaker: G. Houseman (Univ. of Leeds, UK)
        Material: Exercise
    • 14:30 - 15:30 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.
      • 14:30 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. 1h0'
        Speaker: G. Houseman (Univ. of Leeds, UK)
    • 15:30 - 16:00 Coffee Break
      Location: Adriatico Guest House (Terrace)
      • 15:30 Coffee Break 30'
    • 16:30 - 17:30 ICTP COLLOQUIUM: Mantle dynamics and the rise and fall of mountain belts
      Location: Leonardo da Vinci Building Main Lecture Hall
      • 16:30 ICTP COLLOQUIUM: Mantle dynamics and the rise and fall of mountain belts 1h0'
        Speaker: P. Molnar (Univ. of Colorado at Boulder, USA)
  • Thursday, 26 May 2011
    • 09:00 - 10:00 Stokes flow and dynamic topography Stokes problem of a sinking sphere
      • 09:00 Stokes flow and dynamic topography Stokes problem of a sinking sphere 1h0'
        Speaker: P. Molnar (Univ. of Colorado at Boulder, USA)
        Material: lecture notes
    • 10:00 - 10:30 Coffee Break
      Location: Adriatico Guest House (Terrace)
      • 10:00 Coffee Break 30'
    • 10:30 - 11:30 Deflection of the surface above a sinking sphere and associated gravity anomalies and geoid. [Morgan, 1965]
      • 10:30 Deflection of the surface above a sinking sphere and associated gravity anomalies and geoid. [Morgan, 1965] 1h0'
        Speaker: P. Molnar (Univ. of Colorado at Boulder, USA)
        Material: lecture notes
    • 11:30 - 12:30 Basil/sybil exercise with a sinking sphere or cylinder
      • 11:30 Basil/sybil exercise with a sinking sphere or cylinder 1h0'
        Speaker: G. Houseman (Univ. of Leeds, UK)
        Material: Exercise
    • 12:30 - 14:00 Lunch Break
      Location: Adriatico Guest House Cafeteria
      • 12:30 Lunch Break 1h30'
    • 14:00 - 15:00 Derivation of the basic heat transfer equation and heating or cooling by diffusion
      • 14:00 Derivation of the basic heat transfer equation and heating or cooling by diffusion 1h0'
        Speaker: M. Manga (Univ. of California, Berkeley, USA)
        Material: lecture notes
    • 15:00 - 15:30 Coffee Break
      Location: Adriatico Guest House (Terrace)
      • 15:00 Coffee Break 30'
    • 15:30 - 16:30 Examples of a cooling lithosphere: both cooling plate and cooling half-space, comparison of different boundary conditions (fixed temperature and fixed heat flux).
      • 15:30 Examples of a cooling lithosphere: both cooling plate and cooling half-space, comparison of different boundary conditions (fixed temperature and fixed heat flux). 1h0'
        Speaker: M. Manga (Univ. of California, Berkeley, USA)
        Material: lecture notes
    • 16:30 - 17:00 Solidification Scaling of time and depth in thermal diffusion
      • 16:30 Solidification Scaling of time and depth in thermal diffusion 30'
        Speaker: M. Manga (Univ. of California, Berkeley, USA)
    • 17:00 - 17:30 Molnar and England’s S in thrust faulting
      • 17:00 Molnar and England’s S in thrust faulting 30'
        Speaker: P. Molnar (Univ. of Colorado at Boulder, USA)
        Material: lecture notes
  • Friday, 27 May 2011
    • 09:00 - 10:00 Turbulence, planform of convection, boundary layer and plumes at high Rayleigh number
      • 09:00 Turbulence, planform of convection, boundary layer and plumes at high Rayleigh number 1h0'
        Speaker: J. Niemala (ICTP, Trieste)
    • 10:00 - 10:30 Coffee Break
      Location: Adriatico Guest House (Terrace)
      • 10:00 Coffee Break 30'
    • 10:30 - 12:30 Turbulence, planform of convection, boundary layer and plumes at high Rayleigh number
      • 10:30 Turbulence, planform of convection, boundary layer and plumes at high Rayleigh number 2h0'
        Speaker: J. Niemala (ICTP, Trieste)
    • 12:30 - 14:00 Lunch Break
      Location: Adriatico Guest House Cafeteria
      • 12:30 Lunch Break 1h30'
    • 14:00 - 16:00 Mixing and Volcanos
      • 14:00 Mixing and Volcanos 2h0'
        Speaker: M. Manga (Univ. of California, Berkeley, USA)
        Material: lecture notes
    • 16:00 - 16:30 Coffee Break
      Location: Adriatico Guest House (Terrace)
      • 16:00 Coffee Break 30'
    • 16:30 - 18:30 Visit to Laboratory
      • 16:30 Visit to Laboratory 2h0'
  • Monday, 30 May 2011
    • 09:00 - 10:30 Introduction of energy equation. Boussinesq approximation.
      • 09:00 Introduction of energy equation. Boussinesq approximation. 1h30'
        Speaker: C. Jaupart (Inst. de Physique du Globe de Paris, France)
        Material: lecture notes
    • 10:30 - 11:00 Coffee Break
      Location: Adriatico Guest House (Terrace)
      • 10:30 Coffee Break 30'
    • 11:00 - 12:30 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)
      • 11:00 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) 1h30'
        Speaker: C. Jaupart (Inst. de Physique du Globe de Paris, France)
        Material: lecture notes
    • 12:30 - 14:00 Lunch Break
      Location: Adriatico Guest House (Terrace)
      • 12:30 Lunch Break 1h30'
    • 14:00 - 15:30 Rayleigh-Bénard convection (no internal heating). Heuristic argument to introduce Rayleigh number. Dimensional analysis. Rayleigh number, Prandtl number, Reynolds number for convective flow.
      • 14:00 Rayleigh-Bénard convection (no internal heating). Heuristic argument to introduce Rayleigh number. Dimensional analysis. Rayleigh number, Prandtl number, Reynolds number for convective flow. 1h30'
        Speaker: C. Jaupart (Inst. de Physique du Globe de Paris, France)
        Material: lecture notes
    • 15:30 - 16:00 Coffee Break
      Location: Adriatico Guest House (Terrace)
      • 15:30 Coffee Break 30'
    • 16:00 - 17:30 Examples of convective systems: mantle, magma reservoirs. Marginal stability: Influence of boundary conditions (Free boundaries, rigid boundaries, fixed temperature, fixed heat flux).
      • 16:00 Examples of convective systems: mantle, magma reservoirs. Marginal stability: Influence of boundary conditions (Free boundaries, rigid boundaries, fixed temperature, fixed heat flux). 1h30'
        Speaker: C. Jaupart (Inst. de Physique du Globe de Paris, France)
  • Tuesday, 31 May 2011
    • 09:00 - 10:00 MAGMATIC SYSTEMS: MECHANICS. Derivation of conservation of mass & momentum equations. Scaling and the compaction length. Magma wave solutions.
      • 09:00 MAGMATIC SYSTEMS: MECHANICS. Derivation of conservation of mass & momentum equations. Scaling and the compaction length. Magma wave solutions. 1h0'
        Speaker: R. Katz (Univ. of Oxford, UK)
        Material: lecture notes
    • 10:00 - 10:30 Coffee Break
      Location: Adriatico Guest House (Lower Level 1)
      • 10:00 Coffee Break 30'
    • 10:30 - 12:00 Latent heat of crystallization and melting. Stefan number. Diffusive cooling: pure substance. Mushy layers: observations (lava lakes). Mushy layers: models.
      • 10:30 Latent heat of crystallization and melting. Stefan number. Diffusive cooling: pure substance. Mushy layers: observations (lava lakes). Mushy layers: models. 1h30'
        Speaker: R. Katz (Univ. of Oxford, UK)
        Material: lecture notes
    • 12:00 - 12:30 Convection and crystallization in magma reservoirs: thermal and compositional.
      • 12:00 Convection and crystallization in magma reservoirs: thermal and compositional. 30'
        Speaker: R. Katz (Univ. of Oxford, UK)
        Material: lecture notes
    • 12:30 - 14:00 Lunch Break
      Location: Adriatico Guest House Cafeteria
      • 12:30 Lunch Break 1h30'
    • 14:00 - 15:30 Equation for the horizontally averaged temperature and the convective heat flux Thermal structure of fluid layer: boundary layers and well-mixed interior.
      • 14:00 Equation for the horizontally averaged temperature and the convective heat flux Thermal structure of fluid layer: boundary layers and well-mixed interior. 1h30'
        Speaker: C. Jaupart (Inst. de Physique du Globe de Paris, France)
        Material: lecture notes
    • 15:30 - 16:00 Coffee Break
      Location: Adriatico Guest House (Lower Level 1)
      • 15:30 Coffee Break 30'
    • 16:00 - 17:00 Free boundaries versus rigid boundaries. Large Prandtl number fluids. Convective loop model. Scaling relations for velocity and heat flux (no internal heating).
      • 16:00 Free boundaries versus rigid boundaries. Large Prandtl number fluids. Convective loop model. Scaling relations for velocity and heat flux (no internal heating). 1h0'
        Speaker: C. Jaupart (Inst. de Physique du Globe de Paris, France)
        Material: lecture notes
    • 17:00 - 17:30 Convection driven by density anomalies in the Earth s mantle. Dynamic topography.
      • 17:00 Convection driven by density anomalies in the Earth s mantle. Dynamic topography. 30'
        Speaker: C. Jaupart, S. Zhong (Inst. de Physique du Globe de Paris, France, Univ. of Colorado at Boulder, USA)
        Material: lecture notes
  • Wednesday, 1 June 2011
    • 09:00 - 10:00 Thermodynamics & chemistry.
      • 09:00 Thermodynamics & chemistry. 1h0'
        Speaker: R. Katz (Univ. of Oxford, UK)
        Material: lecture notes
    • 10:00 - 10:30 Coffee Break
      Location: Adriatico Guest House (Lower Level 1)
      • 10:00 Coffee Break 30'
    • 10:30 - 12:00 Equilibrium & disequilibrium formulations. Melting column solutions.
      • 10:30 Equilibrium & disequilibrium formulations. Melting column solutions. 1h30'
        Speaker: R. Katz (Univ. of Oxford, UK)
        Material: lecture notes
    • 12:00 - 12:30 Instabilities & the tectonic context. Mechanical and reactive melting instabilities. Magma-genesis and focussing at mid-ocean ridges
      • 12:00 Instabilities & the tectonic context. Mechanical and reactive melting instabilities. Magma-genesis and focussing at mid-ocean ridges 30'
        Speaker: R. Katz (Univ. of Oxford, UK)
        Material: Exercise
    • 12:30 - 14:00 Lunch Break
      Location: Adriatico Guest House Cafeteria
      • 12:30 Lunch Break 1h30'
    • 14:00 - 15:00 Scaling for internally heated fluids. Thermal structure of fluid layer
      • 14:00 Scaling for internally heated fluids. Thermal structure of fluid layer 1h0'
        Speaker: C. Jaupart (Inst. de Physique du Globe de Paris, France)
        Material: lecture notes
    • 15:00 - 15:30 Coffee Break
      Location: Adriatico Guest House (Lower Level 1)
      • 15:00 Coffee Break 30'
    • 15:30 - 16:30 Dissipation equation. New derivation of Nusselt number vs. Rayleigh number relationship
      • 15:30 Dissipation equation. New derivation of Nusselt number vs. Rayleigh number relationship 1h0'
        Speaker: S. Zhong (Univ. of Colorado at Boulder, USA)
        Material: lecture notes
    • 16:30 - 17:00 Characteristics of plumes in Rayleigh-Bénard convection at high Ra
      • 16:30 Characteristics of plumes in Rayleigh-Bénard convection at high Ra 30'
        Speaker: S. Zhong (Univ. of Colorado at Boulder, USA)
        Material: lecture notes
  • Thursday, 2 June 2011
    • 09:00 - 10:00 Temperature-dependent viscosity. Scaling for velocity and heat flux.
      • 09:00 Temperature-dependent viscosity. Scaling for velocity and heat flux. 1h0'
        Speaker: C. Jaupart (Inst. de Physique du Globe de Paris, France)
        Material: lecture notes
    • 10:00 - 10:30 Coffee Break
      Location: Adriatico Guest House (Terrace)
      • 10:00 Coffee Break 30'
    • 10:30 - 12:00 Non-Newtonian rheology. Non-Newtonian with temperature-dependent rheology. Scaling for velocity, heat flux, stress and strain-rate.
      • 10:30 Non-Newtonian rheology. Non-Newtonian with temperature-dependent rheology. Scaling for velocity, heat flux, stress and strain-rate. 1h30'
        Speaker: C. Jaupart (Inst. de Physique du Globe de Paris, France)
        Material: lecture notes
    • 12:00 - 12:30 Small-scale convection beneath oceanic and continental lithosphere
      • 12:00 Small-scale convection beneath oceanic and continental lithosphere 30'
        Speaker: S. Zhong (Univ. of Colorado at Boulder, USA)
        Material: lecture notes
    • 12:30 - 14:00 Lunch Break
      Location: Adriatico Guest House (Terrace)
      • 12:30 Lunch Break 1h30'
    • 14:00 - 15:30 Practicals and exercises: problem sets + a few computer runs.
      Location: Adriatico Guest House Informatics Lab.
      • 14:00 Practicals and exercises: problem sets + a few computer runs. 1h30'
        Speaker: C. Jaupart, S. Zhong (Inst. de Physique du Globe de Paris, France, Univ. of Colorado at Boulder, USA)
    • 15:30 - 16:00 Coffee Break
      Location: Adriatico Guest House (Terrace)
      • 15:30 Coffee Break 30'
    • 16:00 - 17:30 Practicals and exercises: problem sets + a few computer runs.
      Location: Adriatico Guest House Informatics Lab.
      • 16:00 Practicals and exercises: problem sets + a few computer runs. 1h30'
        Speaker: C. Jaupart, S. Zhong (Inst. de Physique du Globe de Paris, France, Univ. of Colorado at Boulder, USA)
  • Friday, 3 June 2011
    • 09:00 - 10:30 Chemical differences. Buoyancy number: Marginal stability, dependence on Rayleigh number and Buoyancy number.
      • 09:00 Chemical differences. Buoyancy number: Marginal stability, dependence on Rayleigh number and Buoyancy number. 1h30'
        Speaker: C. Jaupart, P. Molnar (Inst. de Physique du Globe de Paris, France, University of Colorado at Boulder, USA)
        Material: lecture notes
    • 10:30 - 11:00 Coffee Break
      Location: Adriatico Guest House (Terrace)
      • 10:30 Coffee Break 30'
    • 11:00 - 12:00 Two-layer mantle: convection regimes, thermal structure.
      • 11:00 Two-layer mantle: convection regimes, thermal structure. 1h0'
        Speaker: C. Jaupart (Inst. de Physique du Globe de Paris, France)
        Material: lecture notes
    • 12:00 - 12:30 Evolution of initially stratified fluid
      • 12:00 Evolution of initially stratified fluid 30'
        Speaker: C. Jaupart (Inst. de Physique du Globe de Paris, France)
        Material: lecture notes
    • 12:30 - 14:00 Lunch Break
      Location: Adriatico Guest House Cafeteria
      • 12:30 Lunch Break 1h30'
    • 14:00 - 15:00 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.
      • 14:00 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. 1h0'
        Speaker: S. Zhong (Univ. of Colorado at Boulder, USA)
        Material: lecture notes
    • 15:00 - 15:30 Coffee break
      Location: Adriatico Guest House (Terrace)
      • 15:00 Coffee break 30'
    • 15:30 - 17:00 OPEN DISCUSSION AND CONCLUSION
      • 15:30 OPEN DISCUSSION AND CONCLUSION 1h30'
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