A0U

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

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Description

Complex valued property with dimensions \((j,kl)\) and units of \(s\).

Discussion

These are the row 3, column 1 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,

\[\textrm{A0U} \equiv i \frac{l h f_0}{\omega^2}\]

in the manuscript. In code this is computed with,

fOmega = f./omega;
A0U = sqrt(-1)*self.h.*(fOmega./omega) .* L;

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

\[\textrm{A0U} \equiv i \frac{f l}{g K^2}\]

which in code is,

A0U(:,:,1) = sqrt(-1)*(f/g_)*L(:,:,1)./K2(:,:,1);

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

A0U(1,1,:) = 0;