WVTransform

Represents the state of the ocean in terms of energetically orthogonal wave and geostrophic (vortex) solutions

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Declaration

classdef WVTransform < handle

Overview

The WVTransform subclasses encapsulate data representing the state of the ocean at a given instant in time. What makes the WVTransform subclasses special is that the state of the ocean is represented as energetically independent waves and geostrophic motions (vortices). These classes can be queried for any ocean state variable including \(u\), \(v\), \(w\), \(\rho\), \(p\), but also Ertel PV, relative vorticity, or custom defined state variables.

The WVTransform is an abstract class and as such you must instatiate one of the concrete subclasses,

• WVTransformConstantStratification
• WVTransformHydrostatic
• WVTransformSingleMode

Topics

• Initialization
  • waveVortexTransformFromFile Initialize a WVTransform instance from an existing file
  • waveVortexTransformWithDoubleResolution create a new WVTransform with double resolution
• Domain attributes
  • Omega frequency of oscillation of the linear waves
  • f Coriolis parameter
  • g gravity of Earth
  • inertialPeriod inertial period
  • isBarotropic Boolean indicating whether there is a single (equivalent barotropic) mode
  • latitude central latitude of the simulation
  • rho0 density of \(\rho_\textrm{nm}\) at the surface (z=0)
  • t time coordinate
  • t0 reference time of Ap, Am, A0
  • Grid
    • shouldAntialias whether antialiasing is enabled
    • Spectral
      • J j-coordinate matrix
      • K k-coordinate matrix
      • Kh horizontal wavenumber, \(Kh=\sqrt(K^2+L^2)\)
      • L l-coordinate matrix
      • Nj points in the j-coordinate, length(z)
      • Nkl points in the kl-coordinate, length(k)
      • j vertical mode number
      • k wavenumber coordinate in the x-direction
      • kRadial isotropic wavenumber dimension
      • kljGrid returns the K, L, J coordinate matrices
      • l wavenumber coordinate in the y-direction
      • spectralMatrixSize returns the size of any spectral matrix, e.g., Ap, Am, A0
    • Spatial
      • x x coordinate
      • y y coordinate
      • z z coordinate
      • Lx domain size in the x-direction
      • Ly domain size in the y-direction
      • Lz domain size in the z-direction
      • Nx points in the x-coordinate, length(x)
      • Ny points in the y-coordinate, length(y)
      • Nz points in the z-coordinate, length(z)
      • X x-coordinate matrix
      • Y y-coordinate matrix
      • Z z-coordinate matrix
      • spatialMatrixSize returns the size of all real-valued field variables
      • xyzGrid returns the X, Y, Z coordinate matrices
• Wave-vortex coefficients
  • at time \(t\)
    • A0t geostrophic coefficients at time t
    • Amt negative wave coefficients at time t
    • Apt positive wave coefficients at time t
• Initial Conditions
  • addRandomFlow add randomized flow to the existing state
  • addUVEta add \((u,v,\eta)\) to the existing values
  • initFromNetCDFFile initialize the flow from a NetCDF file
  • initWithRandomFlow initialize with a random flow state
  • initWithUVEta initialize with fluid variables \((u,v,\eta)\)
  • initWithUVRho initialize with fluid variables \((u,v,\rho)\)
  • Waves
    • removeAll removes all energy from the model
• Energetics
  • summarizeEnergyContent displays a summary of the energy content of the fluid
  • summarizeModeEnergy List the most energetic modes
  • Multiplicative factors
    • A0_TE_factor multiplicative factor that multiplies \(A_0^2\) to compute total energy.
    • Apm_TE_factor multiplicative factor that multiplies \(A_\pm^2\) to compute total energy.
• Wave-vortex sorting matrix
  • inverse components (\(S^{-1}\))
    • A0N matrix component that multiplies \(\tilde{\eta}\) to compute \(A_0\).
    • A0U matrix component that multiplies \(\tilde{u}\) to compute \(A_0\).
    • A0V matrix component that multiplies \(\tilde{v}\) to compute \(A_0\).
    • AmN matrix component that multiplies \(\tilde{\eta}\) to compute \(A_m\).
    • AmU matrix component that multiplies \(\tilde{u}\) to compute \(A_m\).
    • AmV matrix component that multiplies \(\tilde{v}\) to compute \(A_m\).
    • ApN matrix component that multiplies \(\tilde{\eta}\) to compute \(A_p\).
    • ApU matrix component that multiplies \(\tilde{u}\) to compute \(A_p\).
    • ApV matrix component that multiplies \(\tilde{v}\) to compute \(A_p\).
  • components of \(S\)
    • NA0 matrix component that multiplies \(A_0\) to compute \(\tilde{\eta}\).
    • NAm matrix component that multiplies \(A_m\) to compute \(\tilde{\eta}\).
    • NAp matrix component that multiplies \(A_p\) to compute \(\tilde{\eta}\).
    • UA0 matrix component that multiplies \(A_0\) to compute \(\tilde{u}\).
    • UAm matrix component that multiplies \(A_m\) to compute \(\tilde{u}\).
    • UAp matrix component that multiplies \(A_p\) to compute \(\tilde{u}\).
    • VA0 matrix component that multiplies \(A_0\) to compute \(\tilde{v}\).
    • VAm matrix component that multiplies \(A_m\) to compute \(\tilde{v}\).
    • VAp matrix component that multiplies \(A_p\) to compute \(\tilde{v}\).
    • WAm matrix component that multiplies \(A_m\) to compute \(\tilde{w}\).
    • WAp matrix component that multiplies \(A_p\) to compute \(\tilde{w}\).
• Potential Vorticity & Enstrophy
  • Multiplicative factors
    • A0_QGPV_factor multiplicative factor that multiplies \(A_0\) to compute quasigeostrophic potential vorticity (QGPV).
    • A0_TZ_factor multiplicative factor that multiplies \(A_0^2\) to compute quasigeostrophic enstrophy.
• State Variables
  • F0 non-linear flux into A0
  • Fm non-linear flux into Am
  • Fp non-linear flux into Ap
  • rho_e excess density
  • rho_total total potential density
  • ssh sea-surface height
  • ssu x-component of the fluid velocity at the surface
  • ssv y-component of the fluid velocity at the surface
  • uvMax max horizontal fluid speed
  • wMax max vertical fluid speed
  • zeta_z vertical component of relative vorticity
• Internal
  • WVTransform initialize a WVTransform instance
  • addToVariableCache add variable to internal cache, in case it is needed again
  • clearVariableCache clear the internal cache
  • clearVariableCacheOfTimeDependentVariables clear the internal cache of variables that claim to be time dependent
  • fetchFromVariableCache retrieve a set of variables from the internal cache
  • performOperation computes (runs) the operation
  • performOperationWithName computes (runs) the operation
  • stateVariables retrieve variables either from cache or by computation
• Metadata
  • Dimensions
    • addDimensionAnnotations add one or more WVDimensions
    • dimensionAnnotationWithName retrieve a WVDimension by name
• Flow components
  • addFlowComponent add a flow component
  • addPrimaryFlowComponent add a primary flow component, automatically added to the flow
  • flowComponent retrieve a WVFlowComponent by name
  • primaryFlowComponent retrieve a WVPrimaryFlowComponent by name
• Utility function
  • spectralVariableWithResolution create a new variable with different resolution
  • Metadata
    • addOperation add a WVOperation
    • addPropertyAnnotations add a property annotation
    • addVariableAnnotations add a variable annotation
    • operationWithName retrieve a WVOperation by name
    • propertyAnnotationWithName retrieve a WVPropertyAnnotation by name
    • removeOperation remove an existing WVOperation
    • removeVariableAnnotations add a variable annotation
    • variableAnnotationWithName retrieve a WVVariableAnnotation by name
    • variableNames retrieve the names of all available variables
• Write to file
  • concatenateVariablesAlongTimeDimension Concatenate variables along the time dimension
  • createNetCDFFileForTimeStepOutput Output the WVTransform to file with variable time dimension
  • writeToFile Output the WVTransform to file.
• Operations
  • Transformations
    • convertFromWavenumberToFrequency Summary
    • transformFromSpatialDomainWithFg transforms from the spatial domain (z,:,:) to the spectral domain (j,:,:) using the geostrophic F-modes
    • transformFromSpatialDomainWithFio transforms from the spatial domain (z,:,:) to the spectral domain (j,:,:) using the inertial oscillation F-modes
    • transformFromSpatialDomainWithGg transforms from the spatial domain (z,:,:) to the spectral domain (j,:,:) using the geostrophic G-modes
    • transformToKLAxes transforms in the spectral domain from (j,kl) to (kAxis,lAxis,j)
    • transformToRadialWavenumber transforms in the spectral domain from (j,kl) to (j,kRadial)
    • transformToSpatialDomainWithF transforms from the spectral domain (k,l,j) to the spatial domain (x,y,z) using the F-modes
    • transformToSpatialDomainWithFAllDerivatives transforms from the spectral domain (k,l,j) to the spatial domain (x,y,z) using the F-modes, returning the transformed variable an its derivatives.
    • transformToSpatialDomainWithG transforms from the spectral domain (k,l,j) to the spatial domain (x,y,z) using the G-modes
    • transformToSpatialDomainWithGAllDerivatives transforms from the spectral domain (k,l,j) to the spatial domain (x,y,z) using the G-modes, returning the transformed variable an its derivatives.
    • transformUVEtaToWaveVortex transform fluid variables \((u,v,\eta)\) to wave-vortex coefficients \((A_+,A_-,A_0)\).
    • transformWaveVortexToUVWEta transform wave-vortex coefficients \((A_+,A_-,A_0)\) to fluid variables \((u,v,\eta)\).
• Properties
  • effectiveHorizontalGridResolution returns the effective grid resolution in meters
• Nonlinear flux and energy transfers
  • energyFluxFromNonlinearFlux converts nonlinear flux into energy flux
  • nonlinearFlux returns the flux of each coefficient as determined by the nonlinear flux operation
  • nonlinearFluxForFlowComponents returns the flux of each coefficient as determined by the nonlinear flux operation
  • nonlinearFluxOperation The operation responsible for computing the nonlinear flux
  • nonlinearFluxWithGradientMasks returns the flux of each coefficient as determined by the nonlinear flux operation
  • nonlinearFluxWithMask returns the flux of each coefficient as determined by the nonlinear flux
• Index Gymnastics
  • indexFromModeNumber return the linear index into a spectral matrix given (k,l,j)
  • isValidConjugateModeNumber returns a boolean indicating whether (k,l,j) is a valid conjugate mode number
  • isValidModeNumber returns a boolean indicating whether (k,l,j) is a valid mode number
  • isValidPrimaryModeNumber returns a boolean indicating whether (k,l,j) is a valid primary (non-conjugate) mode number
• Masks
  • maskA0Conj returns a mask indicating where conjugate solutions live in the A0 matrix.
  • maskA0Primary returns a mask indicating where primary solutions live in the A0 matrix.
  • maskAmConj returns a mask indicating where conjugate solutions live in the Am matrix.
  • maskAmPrimary returns a mask indicating where primary solutions live in the Am matrix.
  • maskApConj returns a mask indicating where conjugate solutions live in the Ap matrix.
  • maskApPrimary returns a mask indicating where primary solutions live in the Ap matrix.
• Other
  • A0 geostrophic coefficients at reference time t0 (m)
  • A0Z
  • Am negative wave coefficients at reference time t0 (m/s)
  • Ap positive wave coefficients at reference time t0 (m/s)
  • ApmD
  • ApmN
  • K2
  • Lr2 squared Rossby radius
  • PA0
  • conjugateDimension
  • dftBuffer
  • dftConjugateIndex
  • dftPrimaryIndex
  • diffX
  • diffY
  • 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)
  • dimensionAnnotationNameMap
  • dk
  • dl
  • dynamicalVariable
  • enstrophyFluxFromF0
  • flowComponentNameMap
  • h_0 [Nj Nkl]
  • h_pm [Nj Nkl]
  • hasMeanPressureDifference checks if there is a non-zero mean pressure difference between the top and bottom of the fluid
  • horizontalModes
  • iOmega
  • initializePrimaryFlowComponents
  • isHydrostatic
  • isequal
  • kAxis k coordinate
  • kl dimension of the interleaved k-l wavenumber coordinate
  • knownDynamicalVariables
  • lAxis l coordinate
  • modeNumberFromIndex
  • operationForDynamicalVariable This function is designed with the following goals:
  • operationNameMap
  • operationVariableNameMap
  • primaryFlowComponentNameMap
  • propertyAnnotationNameMap
  • qgpvFluxFromF0
  • spectralVanishingViscosityFilter Builds the spectral vanishing viscosity operator
  • summarizeDegreesOfFreedom
  • summarizeDynamicalVariables
  • summarizeFlowComponents
  • timeDependentVariablesNameMap
  • totalEnergy
  • totalEnergyOfFlowComponent
  • totalEnergySpatiallyIntegrated
  • totalEnstrophy
  • totalEnstrophySpatiallyIntegrated
  • totalHydrostaticEnergy
  • transformFromSpatialDomainWithFourier
  • transformToSpatialDomainWithFourier
  • transformToSpatialDomainWithFourierAtPosition
  • transformWithG_wg
  • variableAnnotationNameMap
  • variableCache
  • variables access the dynamical variables
  • variablesAtPosition access the dynamical variables at any position in the domain
  • velocityField Return the velocity field, which is the sum of the gridded
  • version
  • waveCoefficientsAtTimeT
  • waveVortexTransformWithResolution
  • wvBuffer
  • wvConjugateIndex

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