A0N

matrix component that multiplies \(\tilde{\eta}\) to compute \(A_0\).

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Description

Real valued property with dimensions \((j,kl)\) and no units.

Discussion

These are the row 3, 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 \(k^2+l^2>0, j>0\) (from either equation B14 or C5) this is written as,

\[\textrm{A0N} \equiv \frac{f_0^2}{\omega^2}\]

in the manuscript. In code this is computed with,

fOmega = f./omega;
A0N = fOmega.^2;

With a rigid lid the solution at \(k>0, l>0, j=0\) is from equation B11,

\[\textrm{A0N} \equiv 0\]

which in code is,

A0N(:,:,1) = 0;

The \(k=l=0, j>=0\) solution is a mean density anomaly,

A0N(1,1,:) = 1;