Fixes to Omega v1 Governing Equations#326
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xylar merged 4 commits intoE3SM-Project:developfrom Feb 23, 2026
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@sbrus89, this doesn't include the other fixes to the HPGF we have discussed. That would follow up on these fixes. |
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@xylar , thanks a lot. I was also planning to fix the same places for \rho_0 and \tau. I will review soon. |
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Approved based on visual inspection (the compiled version is available here: https://users.nccs.gov/~hgkang/omega/omega_xylar/design/OmegaV1GoverningEqns.html).
Thanks, @xylar! The document has improved significantly. I think this PR and #326 can be merged into develop first and open another PR later if additional updates are needed.
Surface flux terms, body forces and pressure terms were all getting multiplied by $\rho_0$, leading to incorrect dimensions and inconsistency with the rest of the derivation.
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This pull request updates the documentation in
OmegaV1GoverningEqns.mdto improve the consistency, clarity, and correctness of the mathematical notation used in the derivation of the governing equations. The changes primarily remove unnecessary factors of\rho_0from several equations, clarify the definition and notation for surface forces, and correct integration limits and variable usage for consistency.Mathematical and Notational Corrections:
Removed unnecessary factors of
\rho_0from the pseudo-height mass, tracer, and momentum conservation equations, as well as from their layer-averaged and Reynolds-averaged forms, to ensure dimensionally consistent and simplified expressions. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]Clarified the definition of the surface force (traction vector) as
\tau = \sigma \cdot {\bf n}and distinguished the horizontal component\tau_\perpin the momentum equation, improving the physical interpretation and accuracy of boundary force terms. [1] [2]Consistency and Integration Limit Corrections:
Corrected integration limits and variable usage in the layer and Reynolds-averaged tracer equations to ensure consistency with the rest of the document and the intended physical meaning.
Updated several equations to use consistent notation for averages, fluctuations, and layer integrals, improving readability and reducing the risk of confusion. [1] [2] [3] [4] [5] [6]
Checklist