InternalModesWKBSpectral

Solve the vertical EVP on a WKB stretched coordinate with Chebyshev collocation.

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Declaration

classdef InternalModesWKBSpectral < InternalModesSpectral

Overview

InternalModesWKBSpectral implements the WKB-coordinate spectral method described in Section 4.3 of Early, Lelong, and Smith (2020). It introduces the stretched coordinate

\[s(z) = \int_z^D N(z') \, dz',\]

and solves the transformed fixed-\(K\) and fixed-\(\omega\) eigenproblems in \(s\), with

\[F_j = h_j N \, \partial_s G_j.\]

Compared with InternalModesSpectral, this class concentrates grid resolution where stratification is strong while preserving the public constructor contract used by downstream packages.

im = InternalModesWKBSpectral(rho=rho, zIn=zIn, zOut=zOut, latitude=latitude, nEVP=257);
[F, G, h, omega] = im.modesAtWavenumber(2*pi/1000);

Topics

• Create and initialize modes
  • InternalModesWKBSpectral Initialize the WKB-coordinate spectral solver.

Developer Topics

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

• Developer topics
  • Nz_function Derivative of \(N(z)\) used when assembling the stretched-coordinate EVP.
  • Nz_xLobatto \(\partial_z N\) sampled on the Lobatto grid in the WKB coordinate.

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