WAp

Reconstructs \(w\) from \(A_+\).

Developer documentation: this item describes internal implementation details.

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Discussion

Reconstructs \(w\) from \(A_+\).

These reconstruction coefficients map \(A_+\) onto the \(w\) state variable. In the historical notation of Early et al. (2021), they are the row 4, column 1 entries of \(S\) for the primary internal-gravity-wave and geostrophic solutions in equation C4.

For \(k^2+l^2>0, j>0\) this is written as,

\[\textrm{WAp} \equiv - i K h\]

in the manuscript. In code this is computed with,

WAp = -sqrt(-1)*Kh.*self.h;

There are no \(k^2+l^2>0, j=0\) wave solutions for a rigid lid,

WAp(:,:,1) = 0;

The inertial solutions occupy the \(k^2+l^2=0\) portion of the matrix,

WAp(1,1,:) = 0;