InternalModesBasis

Store solved vertical modes together with their component roles.

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Declaration

classdef InternalModesBasis < CAAnnotatedClass

Overview

InternalModesBasis is the canonical container for a solved vertical mode basis. It records the sampled inverse modes \(F_j(z)\) and \(G_j(z)\), the equivalent depths \(h_j\), the quadrature grid, and whether each component has a Sturm-Liouville forward projection.

Geostrophic bases at \(\omega=0\) have canonical F and G projections,

\[\mathcal{F}_g^j[u] = \gamma_j^{-1}\int_{-D}^{0} u F_g^j\,dz, \qquad \mathcal{G}_g^j[\eta] = \frac{1}{g}\int_{-D}^{0} N^2 \eta G_g^j\,dz.\]

Nonzero-\(\kappa\) IGW bases have a canonical G projection,

\[\mathcal{G}_\kappa^j[\eta] = \frac{1}{g}\int_{-D}^{0} \left(N^2-f_0^2\right)\eta G_\kappa^j\,dz,\]

but no independent canonical wave-F projection.

basis = InternalModesBasis.fromSolverAtFrequency(im,0,nModes=32);
transform = basis.nativeTransform(component="G");

Topics

• Create vertical bases
  • InternalModesBasis Create a persisted vertical basis from canonical state.
  • fromSolvedModes Create a basis from already-solved mode arrays.
  • fromSolverAtFrequency Solve modes at fixed frequency and return an annotated basis.
  • fromSolverAtWavenumber Solve modes at fixed horizontal wavenumber.
• Inspect basis properties
  • D Water-column depth \(D=z_{\max}-z_{\min}\).
  • F Sampled F inverse modes with rows matching z.
  • G Sampled G inverse modes with rows matching z.
  • N2 Buoyancy frequency squared sampled at z.
  • componentRoleF Component role label for the F component.
  • componentRoleG Component role label for the G component.
  • f0 Coriolis parameter used by the mode solve.
  • forwardProjectionAvailableF Boolean flag indicating whether canonical F projection exists.
  • forwardProjectionAvailableG Boolean flag indicating whether canonical G projection exists.
  • g Gravitational acceleration used by the mode solve.
  • h Equivalent depths associated with the stored mode columns.
  • kappa Horizontal wavenumber associated with the solve.
  • omega Frequency associated with the solve.
  • orthogonalityWeightF Orthogonality weight label for F projections.
  • orthogonalityWeightG Orthogonality weight label for G projections.
  • problemType Text label identifying the vertical eigenvalue problem.
  • sourceDescription Text label identifying the source solver or factory path.
  • z Depth grid where the inverse modes are sampled.
• Build vertical transforms
  • fixedGridTransform Build a transform on another transform’s vertical grid.
  • modelTransform Build a prefix-retained transform for model vertical grids.
  • nativeTransform Build a transform on the basis’ native vertical grid.
  • observationProjection Build a vertical projection for an arbitrary observation grid.
• Analyze vertical spectra
  • spectralWeights Return Parseval weights for modal spectra.
• Other
  • classRequiredPropertyNames

Developer Topics

These items document internal implementation details and are not part of the primary public API.

• Developer topics
  • modeF F-mode index coordinate used by annotated NetCDF persistence.
  • modeG G-mode index coordinate used by annotated NetCDF persistence.
  • zIndex Row coordinate used by annotated NetCDF persistence.

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