NAp

Reconstructs density displacement from \(A_+\).

Developer documentation: this item describes internal implementation details.

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Discussion

Reconstructs density displacement from \(A_+\).

These reconstruction coefficients map \(A_+\) onto the density-displacement state variable. In the historical notation of Early et al. (2021), they are the row 3, 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,

\[\textrm{NAp} \equiv -\frac{k h}{\omega}\]

in the manuscript. In code this is computed with,

NAp = -Kh.*self.h./omega;

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

NAp(:,:,1) = 0;

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

NAp(1,1,:) = 0;