Modify velocity, kinetic energy, and curl terms to match dycore paper

[dennisYatunin]

Purpose

This PR modifies the reconstructions of cell face velocity, cell center kinetic energy, and the curl terms in the velocity tendencies to exactly match the dycore paper.

Content

• Change curlₕ in the vorticity components ᶠωʰ, ᶠωʲʰ, and ᶜω³ to wcurlₕ
  • This should give us discrete conservation of vorticity, which we didn't have before
• Change ᶠu³ from ᶠ⌈ᶜg³ʰ ᶜuₕ⌋ + ᶠg³³ ᶠu₃ to ᶠ⌈ᶜg³ʰ ᶜuₕ⌋ + ᶠ⌈ᶜg³³⌋ ᶠu₃
  • To preserve discrete conservation of kinetic energy, change ᶜ⟨ᶠg³³ ᶠu₃ ᶠu₃⟩ in the kinetic energy to ᶜg³³ ᶜ⟨ᶠu₃ ᶠu₃⟩
  • To preserve the consistency of diagnostic EDMF, change ᶠg³³ ᶠu₃ ᶠu₃ in the SGS kinetic energy to ᶜg³³ ᶠu₃ ᶠu₃
• Add ᶠu = ᶠ⌈ᶜuʰ⌋ + ᶠu³ to the list of precomputed quantities, along with ᶠu⁰ and ᶠuʲs for prognostic EDMF
  • We were previously assuming that ᶠu = ᶠ⟨ᶜuʰ⟩ + ᶠu³, but this was not clarified anywhere
  • To preserve discrete conservation of kinetic energy, change ᶜ⌈ᶠωʰ × ᶠuᵛ⌋ in the tendency of ᶜuₕ to ᶜ⟨ᶠωʰ × ᶠuᵛ⟩, and change ᶠωʰ × ᶠ⟨ᶜuʰ⟩ in the tendency of ᶠu₃ to ᶠωʰ × ᶠuʰ
  • Change ᶠωʲʰ × ᶠ⟨ᶜuʲʰ⟩ in the tendency of ᶠu₃ʲ to ᶠωʲʰ × ᶠuʲʰ
  • Use ᶠu in compute_gm_mixing_length! instead of recomputing it
  • Use ᶠu⁰ in set_prognostic_edmf_precomputed_quantities_closures! instead of recomputing it
• Split set_velocity_quantities! into two lazy functions center_velocity(ᶜuₕ, ᶠu₃) and face_velocity(ᶜρ, ᶜu, ᶠu₃), where the latter is a function of the grid-scale density ᶜρ
  • Modify set_diagnostic_edmf_precomputed_quantities_env_closures! to use center_velocity and face_velocity instead of redefining them, and clarify where we are ignoring the effects of topography
• Simplify vector conversions in compute_kinetic! (for grid-mean and prognostic EDMF) and kinetic_energy (for diagnostic EDMF)
  • Fix the topography-related term in the SGS kinetic energy, which was previously wrong for diagnostic EDMF
• Fix the metric terms in set_velocity_at_surface!

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• I have read and checked the items on the review checklist.

[szy21]

The ci is failing - maybe a typo somewhere? And we probably need to change the set_velocity_quantities! functions in prognostic edmf too?

[dennisYatunin]

As explained in #4015, this reconstruction is unstable for our model configurations because of some complicated math reason. It has been superseded by the reconstruction in #4028, which is equivalent to the first bullet point of this PR's description.