WAm

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

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Description

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

Discussion

These are the row 4, column 2 components of the wave-vortex (S)orting matrix, referred to as the \(S\) 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 C4.

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

\[\textrm{WAm} \equiv - i K h\]

in the manuscript. In code this is computed with,

WAm = -sqrt(-1)*Kh.*self.h;

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

WAm(:,:,1) = 0;

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

WAm(1,1,:) = 0;