Omega V1 Governing Equations Design Document#223

Merged

mark-petersen merged 65 commits intoE3SM-Project:developfrom

mark-petersen:omega/design-doc-v1-eqns

Aug 13, 2025

Commits on Aug 6, 2025

update variables in V0 to match
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Add Omega V1 governing equations
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change rho to v specific volume
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updates from comments by Steve, Luke, Xylar
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Add paragraph on acoustic wave suppression, nabla_z --> nabla_r

xylar
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add geopotential to momentum eqn throughout, PR comments
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Integrate rho u, results in hu momentum eqn
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Revert "Integrate rho u, results in hu momentum eqn"
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Simplified Mom Int with constant in layer
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change back to layered version, with all terms
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spec vol to alpha, h in vert mom adv, nabla_z
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Add Xylars notes unchanged
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Change from dz to dp in tracer & mass eqn
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Introduce pseudo-height

xylar
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Add layered momentum and velocity equations

xylar
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move previous sections to OLD at end
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Revise based on PR comments
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2D \nabla to \nabla_z
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add control-volume equations
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add H-V separation, hydrostatic approx
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Add psuedo-vel, layered mass & tracer eqns
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Connect previous and new sections
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delete old sections
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add motivation for z-tilde offset
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Change p and tau back to z integral, due to missing rho
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add rho0 normalization to momentum equation terms
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Connect previous and new sections, small corrections
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deal with pressure and stress in 3D
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add 2D material derivative, alpha
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add vector identity for zeta grad K
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First commit with Favre averaging introduced

vanroekel
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Clarify change of notation

xylar
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Extensive revisions to "Horizontal & Vertical Separation"

xylar
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Revisions to notation and clarification in "Hydrostatic Approximation"

xylar
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First revisions of "Layered Tracer & Mass"

xylar
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Better handling of layer-interface gradient terms

xylar
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Adds new approach for tracer equation

vanroekel
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adds more detail on favre vs. reynolds

vanroekel
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Better handling of layer-interface gradient terms

xylar
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Expand derivation in the slope term section

xylar
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Fix Leibnitz

xylar
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Define pseudo-height earlier and use for vert flux

xylar
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Finishes tracer rewrite

vanroekel
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Finishes v1 rewrite of the tracer section

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start of layered momentum

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rough draft through momentum section

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cleans up extra ending sections

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updates to assumptions section

vanroekel
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cleans up design doc up to tracer equ in section 9

katsmith133
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cleans up design doc from tracers through mom in section 9

katsmith133
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updates through discrete equations

vanroekel
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first draft of everything but the variable table

vanroekel
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Adds text on vertical discrete derivatives

vanroekel
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Addresses most review comments

vanroekel
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updates nu and kappa horizontal

vanroekel
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Update the vertical tracer diffusion section of OmegaV1GoverningEqns.md

hyungyukang
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refines vertical tracer diffusion section

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Updates variable table

vanroekel
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update W_tr descriptions

vanroekel
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cleans up design doc from tracers through mom in section 9

katsmith133
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adds image for relating pseudo-velocities

katsmith133
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updates conf.py for figure numbering

vanroekel
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addresses many review comments

vanroekel
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updates tilde w figure

katsmith133
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Commits on Aug 13, 2025

Change sign on pressure gradient terms
mark-petersen
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