AmN

matrix component that multiplies \(\tilde{\eta}\) to compute \(A_m\).

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Description

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

Discussion

These are the row 1, column 3 components of the inverse wave-vortex (S)orting matrix, referred to as \(S^{-1}\) matrix in Early, et al. (2021). The primary internal gravity wave and geostrophic solutions that exist for \(k^2+l^2>0, j>0\) are summarized in equation C5.

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

\[\textrm{ApN} \equiv - \frac{g K}{2 \omega}\]

in the manuscript. In code this is computed with,

Kh = sqrt(K.*K + L.*L);
ApN = -g*Kh./(2*omega);

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

ApN(:,:,1) = 0;

The inertial solutions at \(k^2+l^2=0\) do not contribute to \(\eta\), so that component remains zero.