Am
Negative-frequency wave–vortex coefficient array.
Description
Complex valued property with dimensions \((j,kl)\) and units of \(\mathrm{m\,s^{-1}}\).
Discussion
Negative-frequency wave–vortex coefficient array.
Am stores the negative-frequency coefficients \(A_-^{k\ell j}\) for internal gravity waves and inertial oscillations. The coefficients have units of velocity and use the transform’s spectral layout.
These coefficients multiply the negative-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 Am 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 Am are the conjugate partners of the primary inertial coefficients in Ap. At nonzero horizontal wavenumber, Am contains the negative-frequency member of each internal-gravity-wave pair. The transform’s inertialComponent.maskAm and waveComponent.maskAm 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 Am; use Amt 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 Am and Ap obey the transform’s Hermitian and inertial conjugacy relationships so the reconstructed physical fields are real. In particular, the inertial coefficients satisfy Am = conj(Ap) on their masks. Quasigeostrophic transforms have no active Am content.