Mantle Dynamics EMSC 2022 - Quiz (Advanced / Optional)#
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: H1 - Heat flow / Velocity and Rayleigh number (10)
Complete the following table which has data obtained from numerical simulations of convection (these are actually the examples given lecture notes)
\(\mathrm{Ra}\) |
\(\mathrm{Nu}\) |
\(\log_{10}(\mathrm{Nu})\) |
\(V_\mathrm{rms}\) |
\(\log_{10}(V_\mathrm{rms})\) |
|---|---|---|---|---|
\(10^0\) |
1.00 |
0.00 |
— |
|
\(10^1\) |
1.00 |
0.00 |
— |
|
\(10^2\) |
1.00 |
0.00 |
— |
|
\(657\) |
1.00 |
0.00 |
— |
|
\(10^3\) |
1.46 |
4.88 |
||
\(10^4\) |
4.85 |
45.39 |
||
\(10^5\) |
10.30 |
212.81 |
||
\(10^6\) |
20.09 |
931.11 |
||
\(10^7\) |
40.46 |
4,027.17 |
Assuming that the heat flow (Nusselt number) and average (root mean square) velocity are related to Rayleigh number in the following way:
Find the values of \(\alpha\) and \(\beta\) (e.g. by plotting a graph of \(\log_{10}(\mathrm{Nu})\) against \(\log_{10}(\mathrm{Ra})\)) or by fitting a curve as we did in the lab.