A0V

Projects \(v\) onto \(A_0\).

Developer documentation: this item describes internal implementation details.

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Description

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

Discussion

Projects \(v\) onto \(A_0\).

These projection coefficients map the \(v\) state variable onto \(A_0\). In the historical notation of Early et al. (2021), they are the row 3, column 2 entries of \(S^{-1}\) for the primary internal-gravity-wave and geostrophic solutions in equation C5.

For \(k^2+l^2>0, j>0\) (from either equation B14 or C5) this is written as,

\[\textrm{A0V} \equiv - i \frac{k h f_0}{\omega^2}\]

in the manuscript. In code this is computed with,

fOmega = f./omega;
A0V = -sqrt(-1)*self.h.*(fOmega./omega) .* K;

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

\[\textrm{A0V} \equiv -i \frac{f k}{g K^2}\]

which in code is,

A0V(:,:,1) = -sqrt(-1)*(f/g_)*K(:,:,1)./K2(:,:,1);

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

A0V(1,1,:) = 0;