WVNarrowBandGeostrophicForcing

Initialize and hold a narrow band of geostrophic coefficients.

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Declaration

classdef WVNarrowBandGeostrophicForcing < WVFixedAmplitudeForcing

Overview

WVNarrowBandGeostrophicForcing selects the radial band \(k_f-\Delta k/2<K_h<k_f+\Delta k/2\) at vertical mode j_f and holds those A0 coefficients fixed while they continue to participate in nonlinear interactions. Active WVAdaptiveDamping support is excluded by the inherited fixed-amplitude selection behavior.

The diagnostic modelSpectrum is a function of radial wavenumber \(k\) in radians per meter. It returns the legacy geostrophic energy spectrum in \(\mathrm{m^{3}\,s^{-2}}\),

\[E(k)=\begin{cases} \kappa_\epsilon k_r^{-5/3-m}k^m, & k<k_r,\\ \kappa_\epsilon k^{-5/3}, & k_r\le k\le k_f,\\ \kappa_\epsilon k_f^{4/3}k^{-3}, & k>k_f, \end{cases} \qquad m=3/2.\]

Supplying r makes it authoritative and derives the effective k_r. Otherwise k_r is authoritative and derives the effective r. Both effective values are stored. The hydrostatic/stratified and barotropic branches retain their distinct surface scaling.

Construction has an intentional transform side effect unless initialPV="none". The default "narrow-band" draws the configured random spectrum and assigns only the selected band to wvt.A0; "full-spectrum" assigns the complete draw. Both choices consume the global random stream. "none" leaves wvt.A0 unchanged and fixes its current values in the selected band. Restart and resolution conversion use persisted selected state, reconstruct modelSpectrum from the scalar configuration, and do not initialize the target transform or consume random numbers.

Example

wvt = WVTransformBarotropicQG([40e3,40e3],[8,8],latitude=45,shouldAntialias=false);
force = WVNarrowBandGeostrophicForcing(wvt,k_f=2*wvt.dk,u_rms=0.1);
wvt.addForcing(force);
E = force.modelSpectrum(wvt.kRadial);

Topics

• Create the forcing
  • WVNarrowBandGeostrophicForcing Create narrow-band geostrophic fixed-amplitude forcing.
• Inspect forcing configuration
  • A0_indices Linear indices of the selected A0 coefficients.
  • r Effective large-scale damping rate in inverse seconds.
  • A0bar Prescribed A0 values in \(\mathrm{m^{2}\,s^{-1}}\).
  • k_r Effective arrest wavenumber \(k_r\) in radians per meter.
  • Ap_indices Linear indices of the selected Ap coefficients.
  • k_f Center wavenumber \(k_f\) of the forced band in radians per meter.
  • Apbar Prescribed Ap values in \(\mathrm{m\,s^{-1}}\).
  • j_f Forced vertical geostrophic-mode number.
  • Am_indices Linear indices of the selected Am coefficients.
  • u_rms Target surface root-mean-square speed in meters per second.
  • Ambar Prescribed Am values in \(\mathrm{m\,s^{-1}}\).
  • initialPV Potential-vorticity initialization choice.
  • modelSpectrum Configured radial geostrophic energy-spectrum function.
• Configure forcing
  • setWaveForcingCoefficients Select positive- and negative-frequency coefficients to fix.
  • setGeostrophicForcingCoefficients Select zero-frequency coefficients to fix.
  • setNarrowBandGeostrophicForcing Deprecated 4.x helper for narrow-band geostrophic forcing.

Developer Topics

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

• Forcing persistence
  • classRequiredPropertyNames Return configuration and selected state required for restart.

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