Ap
Positive-frequency wave–vortex coefficient array.
Description
Complex valued property with dimensions \((j,kl)\) and units of \(\mathrm{m\,s^{-1}}\).
Discussion
Positive-frequency wave–vortex coefficient array.
Ap stores the positive-frequency coefficients \(A_+^{k\ell j}\) for internal gravity waves and the positive-frequency member of the paired inertial representation. The coefficients have units of velocity and use the transform’s spectral layout.
These coefficients multiply the positive-frequency wave solutions described by Early, Lelong, and Sundermeyer (2021) and the current available-potential-vorticity formulation. The internal-gravity-wave and inertial-oscillation solutions appear as equations (3.18) and (3.15), respectively, in the 2021 paper.
For a three-dimensional wave-bearing transform, the flow constituents occupy Ap schematically as follows:
| Vertical mode | \(K_h=0\) | \(K_h>0\) |
|---|---|---|
| \(j=0\) | inertial oscillation | — |
| \(j>0\) | inertial oscillation | internal gravity wave, \(+\omega\) |
The inertial entries in Ap are the primary members of conjugate pairs whose partners are stored in Am. At nonzero horizontal wavenumber, Ap contains the positive-frequency member of each internal-gravity-wave pair. The transform’s inertialComponent.maskAp and waveComponent.maskAp properties are the executable definitions of these regions; the table suppresses geometry-specific conjugate storage, excluded Nyquist modes, and antialiasing details.
The stored phase is referenced to t0. Linear evolution does not overwrite Ap; use Apt for the coefficients evaluated at the current t. The wave and inertial primary-flow-component masks identify the active locations. Coefficients outside those masks must remain zero.
Together Ap and Am obey the transform’s Hermitian and inertial conjugacy relationships so the reconstructed physical fields are real. Quasigeostrophic transforms have no active Ap content.