InternalModesConstantStratification

Solve the vertical mode problem for constant buoyancy frequency.

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Declaration

classdef InternalModesConstantStratification < InternalModesBase

Overview

InternalModesConstantStratification provides the closed-form solutions used throughout the package for validation and smoke testing. In this model,

\[N^2(z) = N_0^2\]

and the background density is the linear profile

\[\bar{\rho}(z) = \rho_0 - \frac{N_0^2 \rho_0}{g} z.\]

The fixed-\(K\) and fixed-\(\omega\) solutions reduce to trigonometric or hyperbolic functions with analytically known equivalent depths, making this class the main reference implementation for checking the numerical solvers.

im = InternalModesConstantStratification(N0=5.2e-3, zIn=[-5000 0], zOut=zOut, latitude=33);
[F, G, h, omega] = im.modesAtWavenumber(2*pi/1000);

Topics

• Create and initialize modes
  • InternalModesConstantStratification Initialize the constant-stratification analytical solver.
• Inspect grids and stratification
  • N0 Constant buoyancy frequency \(N_0\) in radians per second.
• Compute modes
  • bottomModesAtWavenumber Return the analytical bottom SQG mode for constant stratification.
  • surfaceModesAtWavenumber Return the analytical surface SQG mode for constant stratification.
• Inspect analytical solutions
  • BaroclinicModesWithEigenvalue Evaluate the analytical baroclinic mode shapes for given eigenvalues.
  • BarotropicModeAtFrequency Return the analytical barotropic mode branch for fixed \(\omega\).
  • BarotropicModeAtWavenumber Return the analytical barotropic mode branch for fixed \(K\).
  • BuoyancyFrequencyFromConstantStratification Estimate N0 and rho0 from a constant-stratification profile.
  • IsStratificationConstant Test whether a supplied profile is close to constant stratification.

Developer Topics

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

• Developer topics
  • BaroclinicModeNormalization Return the requested analytical normalization factor for baroclinic modes.
  • BarotropicMode Evaluate a chosen analytical barotropic branch.
  • BarotropicModeNormalization Return the requested analytical normalization factor for the barotropic branch.

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