InternalModesDensitySpectral

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

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Declaration

classdef InternalModesDensitySpectral < InternalModesSpectral

Overview

InternalModesDensitySpectral implements the density-coordinate formulation discussed in Section 4.2 of Early, Lelong, and Smith (2020). It uses the stretched coordinate

\[s(z) = -\frac{g}{\rho_0}\rho(z) + g,\]

so that

\[F_j = h_j N^2 \partial_s G_j.\]

This coordinate concentrates points where the density varies most rapidly and therefore requires a monotonic background density profile.

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

Topics

• Create and initialize modes
  • InternalModesDensitySpectral Initialize the density-coordinate spectral solver.

Developer Topics

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

• Developer topics
  • N2z_xLobatto \(\partial_z N^2\) sampled on the Lobatto grid in the density coordinate.

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