========================================================================
Intensive Lecture Course
Nov 28 (Tue) - Nov 30 (Thr)
"FLUID DYNAMICS OF EARTH AND PLANETARY INTERIORS"
Ulrich Christensen
Max-Planck Institute for Solar System Research
Katlenburg-Lindau, Germany
Email: christensen@mps.mpg.de
This series of lectures will give an overview on various fluid
dynamical processes operating in the interior of the Earth and of
other planets. After a qualitative overview on our knowledge of the
internal structure and dynamics of planets, the basic concepts for the
underlying fluid-dynamical and magnetohydrodynamical processes will be
introduced in a quantitative way. More complex processes are
illustrated using the results of numerical simulations. Slow
convection in the very viscous silicate mantle is the cause for most
endogenic geological processes. Mantle plumes are a particular form of
convection leading to surface volcanism. The complex rheology of rocks
plays an essential role for mantle convection. Rotational forces are
important for convection in gas planets and in the fluid metal cores
of solid planets. They lead to the formation of the zonal jet flow
that dominates the surface motions at Jupiter and
Saturn. Electromagnetic forces balance the Coriolis force in
convection-driven planetary dynamos. Their understanding has advanced
very strongly in the past 10 years and today's models can match many
properties of the geomagnetic field.
Lecture 1 JOURNEY TO THE CENTER OF THE EARTH
A qualitative overview on the internal structure of the Earth's mantle
and core, the available sources for information, and on important
dynamical processes operating in the Earth's interior will be given.
Lecture 2 INTERIOR OF OTHER PLANETS
Our knowledge on the interior of other planets will be
reviewed. Earth-like planets, icy moons and gas planets of the outer
solar system are considered and the indicators for internal processes
are discussed.
Lecture 3 FUNDAMENTALS OF THERMAL CONVECTION: LINEAR STABILITY
The Boussinesq equations for Rayleigh Benard convection will be
introduced and the critical conditions for the onset of convection are
derived.
Lecture 4 FUNDAMENTALS OF THERMAL CONVECTION: FINITE AMPLITUDE
Scaling laws for characteristic velocity, heat transport and boundary
layer thicknesses in isoviscous convection at high Prandtl number are
derived and applied to creeping convection in the Earth's mantle.
Lecture 5 CONVECTION IN THE EARTH'S MANTLE: COMPLEX RHEOLOGY
The complications of strongly temperature-dependent and non-Newtonian
rheology for mantle convection are discussed. They lead to the
formation of surface plates and plume-like rising flow. The influence
of phase transitions on mantle convection will be described.
Lecture 6 CONVECTION IN ROTATING FLUIDS: FUNDAMENTALS
The fundamentals of convection in a rotating system, with strong
Coriolis forces affecting the flow, will be introduced. Their effect
on the onset of convection is studied.
Lecture 7 CONVECTION IN ROTATING SPHERICAL SHELLS
Convection in deep rotating spherical shells is relevant in the
Earth's fluid core and in the gas enveloppes of the planets in the
outer solar system. Their specific form and the excitation of
axisymmetric zonal jet flow will be discussed.
Lecture 8 FUNDAMENTALS OF MAGNETOHYDRODYNAMICS (MHD)
The fundamental equations for the flow of an electrically conducting
fluid in a magnetic field and some basic concepts for such flows will
be described. They can be applied to infer the pattern of flow in the
Earth's core from geomagnetic data.
Lecture 9 MAGNETOCONVECTION AND MHD FLOW IN SPHERICAL SHELLS
Convection in the presence of a magnetic field in a rotating system
will be treated, where the electromagnetic forces can counteract the
strong constraints of the Coriolis forces on the flow. Special
conditions apply for the motion of axial cylinders in a rotating
spherical shell.
Lecture 10 SELF-SUSTAINED DYNAMOS
The problem of self-sustained magnetic field generation in a
convecting and rotating spherical shell is treated. The basic ideas
for the mechanism of field generation are introduced and illustrated
with the help of numerical dynamo simulations.