WVTransformHydrostatic

A class for disentangling hydrostatic waves and vortices in variable stratification

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Declaration

classdef WVTransformHydrostatic < WVTransform

Overview

To initialization an instance of the WVTransformHydrostatic class you must specific the domain size, the number of grid points and either the density profile or the stratification profile.

  N0 = 3*2*pi/3600;
  L_gm = 1300;
  N2 = @(z) N0*N0*exp(2*z/L_gm);
  wvt = WVTransformHydrostatic([100e3, 100e3, 4000],[64, 64, 65], N2=N2,latitude=30);

Topics

• Initialization
  • WVTransformHydrostatic create a wave-vortex transform for variable stratification
• Primary flow components
  • geostrophicComponent returns the geostrophic flow component
  • waveComponent returns the internal gravity wave flow component
  • inertialComponent returns the inertial oscillation flow component
  • mdaComponent returns the mean density anomaly component
• Stratification
  • rho_nm \(\rho_\textrm{nm}(z)\), no-motion density
  • N2 \(N^2(z)\), squared buoyancy frequency of the no-motion density, \(N^2\equiv - \frac{g}{\rho_0} \frac{\partial \rho_\textrm{nm}}{\partial z}\)
  • dLnN2 \(\frac{\partial \ln N^2}{\partial z}\), vertical variation of the log of the squared buoyancy frequency
  • verticalModes instance of the InternalModes class
  • effectiveVerticalGridResolution returns the effective vertical grid resolution in meters
  • Vertical modes
    • FMatrix transformation matrix \(F_g\)
    • FinvMatrix transformation matrix \(F_g^{-1}\)
    • GMatrix transformation matrix \(G_g\)
    • GinvMatrix transformation matrix \(G_g^{-1}\)
  • Validation
    • isDensityInValidRange checks if the density field is a valid adiabatic re-arrangement of the base state
• Initial conditions
  • Waves
    • addGMSpectrum add waves following a Garrett-Munk spectrum
    • addWaveModes add amplitudes of the given wave modes
    • addWavesWithFrequencySpectrum add waves with a specified frequency spectrum
    • initWavesWithFrequencySpectrum initialize with waves of a specified frequency spectrum
    • initWithAlternativeSpectrum initialize with an alternative formulation of the GM spectrum in the wavenumber domain.
    • initWithGMSpectrum initialize the wave field following a Garrett-Munk spectrum
    • initWithWaveModes initialize with the given wave modes
    • removeAllWaves removes all wave from the model, including inertial oscillations
    • setWaveModes set amplitudes of the given wave modes
  • Geostrophic Motions
    • initWithGeostrophicStreamfunction initialize with a geostrophic streamfunction
    • setGeostrophicStreamfunction set a geostrophic streamfunction
    • addGeostrophicStreamfunction add a geostrophic streamfunction to existing geostrophic motions
    • setGeostrophicModes set amplitudes of the given geostrophic modes
    • addGeostrophicModes add amplitudes of the given geostrophic modes
    • removeAllGeostrophicMotions remove all geostrophic motions
  • Inertial Oscillations
    • addInertialMotions add inertial motions to existing inertial motions
    • initWithInertialMotions initialize with inertial motions
    • removeAllInertialMotions remove all inertial motions
    • setInertialMotions set inertial motions
  • Mean density anomaly
    • addMeanDensityAnomaly add inertial motions to existing inertial motions
    • initWithMeanDensityAnomaly initialize with inertial motions
    • removeAllMeanDensityAnomaly remove all mean density anomalies
    • setMeanDensityAnomaly set inertial motions
• Energetics of flow components
  • geostrophicEnergy total energy, geostrophic
  • waveEnergy total energy, waves
  • inertialEnergy total energy, inertial oscillations
  • mdaEnergy total energy, mean density anomaly
• Operations
  • Differentiation
    • diffZF differentiates a variable of (x,y,z) by projecting onto the F-modes, differentiating, and transforming back to (x,y,z)
    • diffZG differentiates a variable of (x,y,z) by projecting onto the G-modes, differentiating, and transforming back to (x,y,z)
• Energetics
  • geostrophicKineticEnergy kinetic energy of the geostrophic flow
  • geostrophicPotentialEnergy potential energy of the geostrophic flow
• Other
  • N2Function
  • dLnN2Function
  • maxFg
  • maxFw
  • rhoFunction function handles
  • throwErrorIfDensityViolation checks if the proposed coefficients are a valid adiabatic re-arrangement of the base state

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