WVFixedAmplitudeForcing

Hold selected wave-vortex coefficients at prescribed amplitudes.

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Declaration

WVFixedAmplitudeForcing < WVForcing

Overview

This forcing keeps selected wave-vortex coefficients at prescribed amplitudes while those modes continue to participate in nonlinear interactions.

As a simple example, one can set an internal wave mode with amplitude \(1\ \mathrm{cm\,s^{-1}}\), and that mode will continue to oscillate and maintain its amplitude. The wave will participate in all the nonlinear dynamics, but its amplitude will be maintained/restored at each time step.

There are several different ways to write this style of forcing mathematically. The equations of motion, written in the spectral domain, take the following form

\[\frac{\partial}{\partial t} A^{klj} = \sum_i F_i^{klj}\]

where \(F_i\) are the contributions from the registered forcing objects. The transform evaluates physical-space forcing, spectral forcing, and then spectral-amplitude forcing. This forcing is evaluated last: it zeros the tendency at selected indices and restores the prescribed coefficient values after the integration step, giving \(\partial_t A^{k\ell j}=0\) for those modes.

In practice, of course, we simply restore the amplitudes to their desired value at the last step, e.g.,

A0(self.A0_indices) = self.A0bar

Notes

• This approach is commonly used in forced-dissipative turbulence to maintain some fixed forcing.
• Every fixed mode removes a degree of freedom because it no longer evolves freely. The setter methods therefore ignore coefficients below \(10^{-6}\) times the largest supplied magnitude unless an explicit mask is provided.
• Avoid selecting modes in a closure’s damping range. When WVAdaptiveDamping is registered, the setter methods automatically remove requested modes with \(K_h>k_\mathrm{damp}\).

Example

wvt = WVTransformConstantStratification([40e3,30e3,2e3],[8,6,5],N0=5.2e-3,latitude=45,isHydrostatic=true);
wvt.setGeostrophicModes(kMode=1,lMode=0,j=1,u=0.01);
force = WVFixedAmplitudeForcing(wvt,name="geostrophic-mean-flow");
force.setGeostrophicForcingCoefficients(wvt.A0);
wvt.addForcing(force);

In practice you can initialize the flow in any way you want with any arbitrary structure, and then pass those coefficients to the forcing. The WVFixedAmplitudeForcing looks for coefficients that are small and ignores those.

Topics

• Create the forcing
  • WVFixedAmplitudeForcing Create fixed-amplitude forcing for selected coefficients.
• Inspect forcing configuration
  • A0_indices Linear indices of the selected A0 coefficients.
  • A0bar Prescribed A0 values in \(\mathrm{m^{2}\,s^{-1}}\).
  • Ap_indices Linear indices of the selected Ap coefficients.
  • Apbar Prescribed Ap values in \(\mathrm{m\,s^{-1}}\).
  • Am_indices Linear indices of the selected Am coefficients.
  • Ambar Prescribed Am values in \(\mathrm{m\,s^{-1}}\).
• 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 Returns the required property names for the class

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