Mantle Dynamics EMSC 2022 - Quiz#
In this task, you will need to find out some extra information that is not spelled out in the lecture notes. A complete answer to any question needs to cite where the information was found. Be critical of what you find - is the source reputable, and do other sources agree ? If not, maybe you need to look elsewhere.
Q: Viscosity (2)
What is meant by the viscosity of a fluid (1).
What are the units of (dynamic) viscosity (1) ?
Note: There are two different definitions of viscosity: dynamic viscosity which usually has the symbol \(\eta\) or sometimes \(\mu\) and kinematic viscosity which is usually \(\nu\) and is defined as \(\eta/\rho\).
Q: Rayleigh number (4)
Estimate the Rayleigh number of the Earth’s mantle (2).
Use the following values:
Gravity, \(g \approx 10 \mathrm{m/s}^2\) through the mantle
Density, \(\rho \approx 3000 \mathrm{kg/m}^3\)
Thermal Expansivity, \(\alpha \approx 10^{-5} \mathrm{K}^{-1}\)
Temperature drop, \(\Delta T \approx 2000 \mathrm{K}\)
Thickness of the mantle, \(d \approx 3000 \mathrm{km}\)
Thermal diffusivity, \(\kappa \approx 10^{-7} \mathrm{m}^2 / \mathrm{s}\)
Viscosity, \(\eta \approx 10^{22} \textrm{viscosity units (!)}\)
How does this compare to the critical Rayleigh number and what does that tell us about mantle convection (2) ?
Q: Dimensionless Rayleigh number (2)
Show that the units of Rayleigh number disappear.
Hint: first convert the units of viscosity into units of \(m\), \(kg\), \(s\), using the idea that pressure is force per unit area
Q: Heat Engine (2)
What is meant by the term “Heat Engine” (1) ?
Why is it important to the understanding of geology that the Earth’s mantle is a heat engine (1) ?