UA0

Reconstructs \(u\) from \(A_0\).

Developer documentation: this item describes internal implementation details.

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Description

Complex valued property with dimensions \((j,kl)\) and units of \(\mathrm{s^{-1}}\).

Discussion

Reconstructs \(u\) from \(A_0\).

These reconstruction coefficients map \(A_0\) onto the \(u\) state variable. In the historical notation of Early et al. (2021), they are the row 1, column 3 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,

\[\textrm{UA0} \equiv - i \frac{g}{f_0} l\]

in the manuscript. In code this is computed with,

UA0 = -sqrt(-1)*(g_/f)*L;

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

UA0(:,:,1) = 0;

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

UA0(1,1,:) = 0;