The vertical component of the momentum equation on the meridional plane

The axial component of eq:aniso:scalar:nse. Take the momentum equation at i = 2 from hsol.2.2.2.1, rewrite the convective sum with sum_convective_two_meridional and the Laplacian sum with sum_spatialSecondPartial_two_meridional, and rearrange. This is the simplest of the three: no centrifugal term and no 1/r² term.

theorem CIV.scalar_nse_z (u : CKN.Foundation.Parabolic.ParabolicPoint → CKN.Foundation.Parabolic.Vec3) (p : CKN.Foundation.Parabolic.ParabolicPoint → ℝ) (f : CKN.Foundation.Parabolic.ParabolicPoint → CKN.Foundation.Parabolic.Vec3) (hsol : IsClassicalSolutionOn u p f unitCylinder) (haxi : IsAxisymmetricOn u unitCylinder) (z : CKN.Foundation.Parabolic.ParabolicPoint) (hz : z ∈ unitCylinder) (hplane : z.1 1 = 0) (hr : z.1 0 ≠ 0) : CKN.timePartial (fun (w : CKN.Foundation.Parabolic.ParabolicPoint) => u w 2) z + u z 0 * CKN.spatialPartial (fun (w : CKN.Foundation.Parabolic.ParabolicPoint) => u w 2) 0 z + u z 2 * CKN.spatialPartial (fun (w : CKN.Foundation.Parabolic.ParabolicPoint) => u w 2) 2 z = CKN.spatialSecondPartial (fun (w : CKN.Foundation.Parabolic.ParabolicPoint) => u w 2) 0 0 z + CKN.spatialPartial (fun (w : CKN.Foundation.Parabolic.ParabolicPoint) => u w 2) 0 z / z.1 0 + CKN.spatialSecondPartial (fun (w : CKN.Foundation.Parabolic.ParabolicPoint) => u w 2) 2 2 z - CKN.spatialPartial p 2 z + f z 2