diffZF

differentiates a variable of (x,y,z) by projecting onto the F-modes, differentiating, and transforming back to (x,y,z)

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Declaration

 uz = diffZF(u)

Parameters

• u variable with dimensions \((x,y,z)\)

Returns

• uz differentiated variable with dimensions \((x,y,z)\)

Discussion

Each subclass implements this operation differently, depending on the vertical modes being used.

For hydrostatic vertical modes with a rigid-lid and zero buoyancy anomaly,

\[\partial_z u = -\frac{1}{g} N^2(z) \mathcal{G}^{-1} \left[ \mathcal{F} \left[ u \right] \right]\]

where we’ve used the same notation as defined for the discrete transformations.