Whether from posed questions, other blog posts and cinematic detours, the core of Earth is every now and then sparking some interest. In a similar way “Inception” or “Shutter Island” spark interest: it sounds cool, you want to get what is going on, but although you tried several times, you still don’t get it.
Today I will report on the answer to a question originally posed by Lily, that was asked by Dr. I during a non-descript EGU 2022 event to a non-specified expert in core dynamics, Dr. S:
Which viscosity do you use in models of the core?
Admit it, you wanted a straight answer, right? Well…I have news for you: apparently there isn’t one. Go figure. Who knew that questions related to something as easily accessible as the core of Earth would not have easy answers?
The question was posed, and in response Dr. S, between the amused and the sarcastic, repeated back:
I could see Dr. I thinking: “Well, blimey, I just wanted a number here!!”
Dr. S continues: “We do not use viscosity per-se in geodynamo models”.
Mmmmhhh…the plot thickens. Dr. S goes on: “We use non-dimensional numbers in our models, like Rayleigh number and Prandtl number”.
Ok, I know these. But Dr. S introduces a new one: “Viscosity is usually characterised by the Ekman number, the ratio of rotational timescales over the viscous timescales”.
“Well…” I saw Dr. I thinking, “is that not the same as using dimensional quantities? What’s the catch?”
Dr. S explains: “The Ekman number for the core is about 10^(-15), and we cannot do that for computational limitations.”
Ok, hold on! The rotational timescales is a day, so that the viscous timescales is…calculate…calculate…calculate…3000 billion years!? Ok…this smells like a huge computational complication. What can we do then?
Dr. S already answers before the question is posed: “Best we can do is 10^(-7). This means that either your core rotates too slowly, or is way too viscous compared to the true thing. Typically we want to keep the length of a day correct.” (finally something that makes sense!) “Which then means your core is filled with a fluid that is about 10^8 times more viscous than molten iron. Pretty much the viscosity of liquid asphalt.”
That doesn’t sound like you are doing the right thing then!
Dr. S tries to quell our scepticism: “But somehow it works! These models can simulate an Earth-like geomagnetic field and reversals. Some have suggested that this is because geodynamo models are already in the right asymptotic regimes of fast rotation and low viscosity.”
So, there you go, Lily: best answer we got that night, before another round of beer prompted a change of topic, was that geodynamo models are run with viscosities that are a factor of 10^8 higher than that of the true core. That is the best we can do today and, although it does not sound like it, it is already a good enough value that the science we can get out of these models is useful to us.
And believe me: this was the short answer. Very little dirty laundry being exposed here. Now you know how this movie ends. If you want to rewatch it paying attention to the more subtle details, I will guide you along answering your most burning questions.
The Sassy Scientist
PS: Has Cobb being dreaming the whole time? Is Teddy really insane? I can’t go on without knowing!!