Topic 24

The (Nonlinear) Dynamic Earth - Examples of Chaos Around Us

The world around us has a myriad of examples of nonlinear dynamical systems. Some have subtle feedback and appear 'linear' to first approximation. Others look completely chaotic.

Fluid Turbulance

Fluid motion is a ctritical element in the life of the Earth. We see it in atmospheric circulation, ocean circulation, groundwater percolation in theEarth's crust, and motion of liquid iron in theEarth's outer core (this generate the magneticfield).

Fluid motion may appear simpe and linear when velocities are low, but as speed increases nolinear interactions lead to turbulance (chaos).

This turbulant aspect of atmospheric circulation is what leads to unpredictability of the Earth's weather and climate.

Breakage Mechanics

Materials that are brittle, will eventually break if enough force is applied. That breakage creates new sized particles that follow a fractal distribution.

When materials break, they may first fracture but stay linked together. Faults at the Earth's surface are created in this way. Earthquakes which occur on faults have fractal spatial and temporal (?) distributions.

Reversal of the Earth's Magnetic Field

The Earth's magnetic field is generated by turbulant fuluid convection of iron in theouter cores. The physics of the electromagnetic method of regenerating field is nonlinear. We see the chaotic element of that nonlinearity when the field spontaneously reverses its polarity every few hundred thoussand years.

Population and Ecologic Variability

Simple models of predator/prey relationships behave in a chaotic manner. If there is enough food, a balance may occur between thepopulations of predators and their prey. If the predators feed too fast, the prey population may decrease rapidly leading to variations in both predator and prey populations. In the worst case scenario, theprey go extinct and then so do the predators if they can't find something else to eat.

Biologic Processes

Many processes in biological organisms are nonlinear or even, on occasion, chaotic. Examples include: neuron transmission of electrical impulses, heart rate, chemical production rates in glands.

On a larger scale, growth of organisms may follow fractal patterns. Also patterns of species variation in an ecosystem may do the same.