InternalModesWKB

Compute WKB mode approximations from a spectrally resolved stratification.

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Declaration

classdef InternalModesWKB < InternalModesSpectral

Overview

InternalModesWKB uses the spectral initialization machinery of InternalModesSpectral to build smooth representations of \(\rho(z)\) and \(N^2(z)\), then applies the WKB asymptotic formulas for the fixed-\(\omega\) eigenvalue problem.

This class is most useful for asymptotic comparison, for exploring turning-point structure, and for the analytical Airy-style approximations discussed around Sections 2.3, 4.3, and 4.4 of Early, Lelong, and Smith (2020).

im = InternalModesWKB(rho=rho, zIn=zIn, zOut=zOut, latitude=latitude);
[F, G, h, k] = im.modesAtFrequency(5*im.f0);

Topics

• Create and initialize modes
  • InternalModesWKB Initialize the WKB approximation solver.
• Inspect analytical solutions
  • ModesAtFrequencyAiry Return the turning-point-aware Airy approximation for fixed \(\omega\).
  • N2_zLobatto Return the spectral Lobatto samples of \(N^2(z)\).
  • zLobatto Return the spectral Lobatto grid in physical depth coordinates.

Developer Topics

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

• Developer topics
  • Diff1_zCheb Return the spectral first-derivative operator in Chebyshev space.
  • ModesAtFrequencyApproximatedAiry Return the simplified WKB Airy approximation for fixed \(\omega\).
  • SurfaceModesAtWavenumberAlt Return the alternate WKB approximation for the surface SQG mode.

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