WVMeanFlowForcing

Resonant forcing at the natural frequency of each mode

---

Declaration

WVNonlinearFluxForced < WVNonlinearFlux

Overview

The unforced model basically looks likes like this,

\[\frac{\partial}{\partial t} A^{klj} = F_\textrm{inertial}^{klj} + F_\textrm{damp}^{klj}\]

for each of the three components. The forcing adds a new term,

\[\frac{\partial}{\partial t} A^{klj} = \underbrace{M_{A}^{klj} \left(\bar{A}^{klj} - A^{klj} \right)/ \tau}_{F_\textrm{force}} + F_\textrm{inertial}^{klj} + F_\textrm{damp}^{klj}\]

which forces those select modes to relax to their \(\bar{A}^{klj}\) state with time scale \(\tau\). If the time scale is set to 0, then the mean amplitudes remain fixed for all time. In that limit, the equations can be written as,

\[\frac{\partial}{\partial t} A^{klj} = \neg M_{A}^{klj} \left( F_\textrm{inertial}^{klj} + F_\textrm{damp}^{klj} \right)\]

This is most often used when initializing a model, e.g.,

  model = WVModel(wvt,nonlinearFlux=WVNonlinearFluxForced(wvt,uv_damp=wvt.uvMax));

Topics

• Set forcing
  • setGeostrophicForcingCoefficients set forcing values for the geostrophic part of the flow
  • setWaveForcingCoefficients set forcing values for the wave part of the flow
• Other
  • A0_indices Forcing mask, A0. 1s at the forced modes, 0s at the unforced modes
  • A0bar A0 ‘mean’ value to relax to
  • Am_indices Forcing mask, Am. 1s at the forced modes, 0s at the unforced modes
  • Ambar Am ‘mean’ value to relax to
  • Ap_indices Forcing mask, Ap. 1s at the forced modes, 0s at the unforced modes
  • Apbar Ap ‘mean’ value to relax to
  • WVMeanFlowForcing initialize the WVNonlinearFlux nonlinear flux
  • classRequiredPropertyNames
  • setNarrowBandGeostrophicForcing
  • tau0 A0 relaxation time
  • tauM Am relaxation time
  • tauP Ap relaxation time

---