WVTransformBoussinesq

3D hydrostatic Boussinesq model with arbitrary stratification solved

---

Overview

in wave-vortex space

Couple of different initialization paths: 1) You want to run this as a prognostic model and therefore want the chebyshev points automatically found for you Init([Lx Ly Lz], [Nx Ny Nz], latitude, rho)

2) You want to run this as a diagnostic model and therefore want to specify the depths and modes yourself Init([Lx Ly Lz], [Nx Ny Nz], latitude, rho, ‘zgrid’, z)

Topics

• 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
• 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)
• 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
• Energetics of flow components
  • geostrophicEnergy total energy, geostrophic
  • waveEnergy total energy, waves
  • inertialEnergy total energy, inertial oscillations
  • mdaEnergy total energy, mean density anomaly
• Energetics
  • geostrophicKineticEnergy kinetic energy of the geostrophic flow
  • geostrophicPotentialEnergy potential energy of the geostrophic flow
• Other
  • N2Function
  • WVTransformBoussinesq First we need to initialize the WVStratifiedFlow.
  • buildInterpolationProjectionOperators
  • buildInterpolationProjectionOperatorsForGrid
  • buildVerticalModeProjectionOperators
  • dLnN2Function
  • maxFg
  • maxFw
  • nK2unique number of unique squared-wavenumbers
  • rhoFunction function handles
  • throwErrorIfDensityViolation checks if the proposed coefficients are a valid adiabatic re-arrangement of the base state
  • transformToSpatialDomainWithFInterp
  • transformToSpatialDomainWithFg arguments
  • transformToSpatialDomainWithFw
  • transformToSpatialDomainWithGInterp
  • transformToSpatialDomainWithGg arguments
  • transformToSpatialDomainWithGw

---