Earth’s Fluid Dynamics

Perhaps the most salient fact about the earth is that it is a fluid. Only its thin outer skin (the lithosphere) and its small inner core (radius ~25% of the earth) are solid. The outer core (from ~0.25 Re to ~0.5 Re) is very fluid. Its turbulent convection generates the earth’s magnetic field. The earth’s mantle (~0.5 Re to ~Re) is fluid enough to be vigorously
convecting. Loads greater than a few hundred kilometers in diameter float on the mantle. Water and petroleum liquids move through the crust (the outermost lithosphere). The ~5 km deep oceans and ~ 7 km thick atmosphere are so fluid that viscosity can be ignored, but the rotation of the earth provides stiffness and structure to the flow.

The earth is thus a fluid that hosts other fluids, and the tools of fluid dynamics access almost the entirety of earth science, from turbulent convection in the core, to convection in the mantle, to hydrology, petroleum geology, oceanography, atmospheric circulation, and the plasma dynamics of the ionosphere. For students in the Earth Sciences fluid dynamics offers powerful insights into how the Earth works. For students who know fluid dynamics, the Earth offers spectacular applications and an opportunity to learn about our planet in an unusually fundamental way.

The lecture notes are hand written and may be difficult to read.  The first set of notes reviews the methods of fluid dynamics as presented in the first few chapters of P.K. Kundu and I.M. Cohen’s book Fluld Mechanics (3rd edition,EINYler, 2004. 7511 p.).  The methods developed are then applied to understand the origins of the Earth’s magnetic field,  the rheology and dynamics of the Earth’s mantle, and finally to hydrology.  Only topics in solid earth dynamics are covered.  The many fascinating applications to oceanography and atmospheric sciences may be added later.

Fluid Dynamic Principles

  • Lectures 1 and 2: The fundamental nature of a fluid at rest.  Internal energy, the scale height of the atmosphere,  perfect differentials and thermodynamics, perfect gas relationships, and the adiabatic temperature gradient of the atmosphere are topics addressed.
  • Lecture 3:  Vectors and tensors (any quantity that rotates like a vector), eigen vectors and values, principle coordinates- the tools needed to describe deformation.
  • Lecture 4:  Kinematics- capturing the trajectories of motion in Eulerian or Lagrangian reference frames.
  • Lecture 5:  Application of kinematic principles to strain rate and vorticies.
  • Lecture 6: Conservation Laws of mass, momentum, and energy.
  • Lecture 7:  The many forms of the Navier Stokes equation.
  • Lecture 8&9:  Rotation, and how it adds stiffness to inviscid fluids.

 The Earth’s Magnetic Field (the outer core) (Literature: Elsasser I, II, 1956, Eddy Cosmic Rays,  Feynman Lightening)

  • Lecture 10s: Solar and Planetary magnetic fields (short version).
  • Lecture 10:  Planetary and solar magnetic fields- observations, then explanations.  The dynamics of the Earth’s dipole and non-dipole fields.  Westward drift of the magnetic isopores.  Irregular reversals of the Earth’s dipole contrasted to regular reversals of the sun’s dipole.
  • Lecture 11:  Maxwell’s equations and the Elsasser dynamo.  Generating the Earth’s magnetic field would require 11 million times the total present human power consumption.
  • Lecture 12: The Elsasser Dynamo- how rotational energy is converted into magnetic energy.  Why surfaces matter in meteorology and the magnetic dynamos of the sun and earth.  Why the westward drift of the magnetic isopores is expected.
  • Lecture 12a: Cowlings theorem.
  • Lecture 13:  The earth’s magnetosphere; its shield to cosmic rays.  The aurora borealis.
  • Lecture 13a:  The solar wind and atmospheric chemistry.
  • Lecture 14: Electrical phenomenon in thunderstorms (after Feynman).  The 100 volt per meter electrical gradient in the atmosphere and why the electrical current through the atmosphere peaks every day at 7:00 pm London time.

The Earth’s Mantle

  • Lecture 15: Fourier transform techniques.
  • Lecture 16:  Spherical glacial isostatic adjustment equations and their solution.
  • Lecture 17:  Explanation and application of the GIA equations.
  • Lecture 18:  Detailed modeling.
  • Lecture 19:  The forces the drive plate tectonics.
  • Lecture 20: Crustal flexture and gravity after Watts.

Porous Media Fluid Flow and Ground Water Hydrology