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AMA! Ph.D. in geophysical fluid mechanics and stratified flows
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So are you treating the Earth's crust as a shallow fluid layer? Or the mantle underneath? I would think the mantle is too thick for shallow water equations.
Usually for the troposphere or even the atmosphere and the ocean this can be a good model. As you said, I doubt if it can be used to represent lava flows under the earth - something a geologist would know and I am not one. 😀