Syllabus
* Laws of conservation
Basic equations - conservation of mass, momentum and energy, rheological relationship, equation of state, boundary conditions.
* Thermal convection in the Earth's mantle
Boussinesq approximation. Dimensionless quantities; Prandtl, Rayleigh and dissipation numbers. Boundary conditions. Static solution. Decomposition of a solenoidal field. 2-D modelling - stream function.
* Basic characteristics of thermal convection
Linearized theory - onset of convection. Dependence of the style of the convection on the Rayleigh number. Influence of inner heating, compressibility, pressure- and temperature-dependent rheology and phase transitions.
* Rheology and dynamics of subducted lithosphere
Seismic imaging of subducted lithosphere in the mantle. Rheology of subducted slabs. Phase transitions. Numerical modelling of subduction.
Annotation
Fundamental equations describing the thermal convection in the Earth. Newtonian fluid.
Thermal convection as a non-linear dynamical system.