WVPseudoTopographicWaveGeneration

Generate internal waves from prescribed barotropic flow over topography.

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Declaration

classdef WVPseudoTopographicWaveGeneration < WVForcing

Overview

WVPseudoTopographicWaveGeneration prescribes a horizontally uniform barotropic velocity

\[\mathbf{U}_{\mathrm{bt}}(t) =R(\tau)\operatorname{Re}\left\{ \widehat{\mathbf{U}}_{\mathrm{bt}}e^{-i\omega\tau}\right\}, \qquad \tau=t-t_s,\]

where \(t_s\) is startTime, \(\omega\) is frequency, and \(R\) is either unity or a half-cosine startup ramp. For upward-positive topographic height \(h(x,y)\), the linearized bottom kinematic boundary condition is

\[g_b(x,y,t)=w(z_b)=\mathbf{U}_{\mathrm{bt}}(t)\cdot\nabla_H h,\]

with Fourier representation

\[\widehat{g}_b=U_{\mathrm{bt},x}(ik\widehat h) +U_{\mathrm{bt},y}(i\ell\widehat h).\]

Let \(\pi_\pm(z_b)\) denote the kinematic bottom pressure of a unit current-time wave coefficient and let \(E_\pm\) denote its Apm_TE_factor. The projected current-time tendencies are

\[\dot A_{\pm,t} =\frac{\pi_\pm^*(z_b)\widehat g_b}{E_\pm}.\]

The implementation precomputes the pressure-gradient response and converts these tendencies to the stored reference-time coefficients with conjPhase for Ap and phase for Am. This normalization makes modal energy input equal the bottom pressure work.

Generation is limited to the valid Ap and Am wave masks, the requested horizontal-wavenumber and vertical-mode bounds, and, by default, the exact zero-damping support of active WVAdaptiveDamping objects. The incoming A0 tendency is unchanged. Select a standard constituent with darwinSymbol, or supply a custom angular frequency.

forcing = WVPseudoTopographicWaveGeneration(wvt,topographicHeight=h,barotropicVelocityAmplitude=[0.05; 0],darwinSymbol="M2");
wvt.removeAllForcing();
wvt.addForcing(forcing);

Topics

• Create the forcing
  • WVPseudoTopographicWaveGeneration Create a prescribed bottom wave-generation forcing.
• Inspect forcing configuration
  • topographicHeight Upward-positive topographic height \(h(x,y)\) in meters.
  • barotropicVelocityAmplitude Complex barotropic velocity amplitude in meters per second.
  • frequency Barotropic angular frequency \(\omega\) in radians per second.
  • darwinSymbol Darwin symbol used to select the tidal frequency.
  • rampDuration Duration of the half-cosine startup ramp in seconds.
  • startTime Time at which the prescribed barotropic forcing begins, in seconds.
  • shouldAvoidAdaptiveDamping Whether generation avoids active adaptive damping.
  • maximumForcedHorizontalWavenumber Largest radial horizontal wavenumber forced, in radians per meter.
  • maximumForcedVerticalMode Largest vertical wave-mode index forced.
• Evaluate prescribed forcing
  • barotropicVelocityAtTime Evaluate the prescribed horizontally uniform current.
  • bottomVelocityAtTime Evaluate the bottom kinematic velocity.
  • spectralGenerationMask Return the spectral region eligible for bottom-wave generation.
• Generate forcing inputs
  • goffAbyssalHillTopography Generate periodic Goff abyssal-hill topography.

Developer Topics

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

• Forcing persistence
  • classRequiredPropertyNames Return the forcing properties required for restart.
• Forcing internals
  • barotropicVelocityComponent Coordinate for the barotropic-velocity components.

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