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Updates doc equations #901

Merged
merged 9 commits into from
Apr 1, 2019
Merged

Updates doc equations #901

merged 9 commits into from
Apr 1, 2019

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navidcy
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@navidcy navidcy commented Mar 12, 2019

This PR changes vector notations in docs from the cumbersome and wrongly rendered arrow, e.g., in
Screen Shot 2019-03-12 at 2 30 45 PM
to bold notation, e.g.,
Screen Shot 2019-03-12 at 2 30 22 PM

Also, the PR fixes a few typos, e.g., definition of Φ was never rendered and equations were not punctuated.

NOTE 1

I believe there is an inconsistency between the "Vector invariant equations" and the "Governing equations". While the w-momentum equation is recovered from the vector invariant equation, the geopotential term in the horizontal momentum equations in the vector-invariant equations` reads as, e.g.,

ρ/ρ_0 ∂_x Φ

instead of

∂_x Φ

as the Governing equations say. I didn't know which of the two is correct so I left them as is.

NOTE 2

The notation δ_k in ALE algorithm is never defined.

@adcroft
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adcroft commented Mar 18, 2019

Indeed, grad Phi should be multiplied by rho/rho_0.

@navidcy
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navidcy commented Mar 18, 2019

@adcroft have a look now.

  1. What is the definition of \delta_k in ALE?

  2. I'm a bit confused with the horizontal gradient of the geopotential Φ. If Φ=gz, then in the continuous version of the equations (before averaging over layer thicknesses) isn't the term ∂_x Φ = ∂_y Φ = 0? Why does it then appear in governing.rst?

@adcroft adcroft merged commit d93b047 into mom-ocean:dev/gfdl Apr 1, 2019
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2 participants