Infragravity Waves Forced by Surface Wind Waves in the Central North Pacific Ocean Yusuke Uchiyama...
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![Page 1: Infragravity Waves Forced by Surface Wind Waves in the Central North Pacific Ocean Yusuke Uchiyama and James C. McWilliams (CESR, IGPP, UCLA) Ocean bottom.](https://reader038.fdocuments.us/reader038/viewer/2022103100/56649f2a5503460f94c448fb/html5/thumbnails/1.jpg)
Infragravity Waves Forced by Surface Wind Waves in the Central North Pacific Ocean
Yusuke Uchiyama and James C. McWilliams(CESR, IGPP, UCLA)
Ocean bottom pressure spectra(Webb, 1998)
Pa
2/H
z
Hz
tide, inertial oscillation etc..
IG long-waves
gravity waves
capillary waves
Pacific
Atlantic
Arctic
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What are infragravity (IG) long-waves:
• Non-linear interaction between short primary waves (modulation) + varying topography ~ O(10-2)-O(10-3)Hz• Forced (bound) & free waves [Herbers et al, 1994; 1995]• Surf beat (surf zone) [Munk, 1949; Huntley et al., 1981]• Edge waves (trapped & leaky) [Bowen & Inmann, 1971]
IG waves are generally known to have small amplitudes in deep ocean only << O(10-2) m.
amplified significantly in nearshore regions
• Is the hypothesis proposed by seismologists true?• If so, how large is amplitude of IG waves?• Dynamics: bound vs. freely propagating IG waves?
Continuous seismic oscillations ~ “Earth’s hum”~M6[Webb, 1998; Rhie and Romanowicz, 2004; Tanimoto, 2005]
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Asymptotic equations developed in MRL04(McWilliams, Restrepo and Lane, 2004)
• wave-averaged effects on currents & long waves• primary waves ~ 2nd order in wave slope (=Ak)• scale separation in time and horizontal space• Eulerian reference frame observations & models
• Vortex force (curl u Vst)• Bernoulli head ~ pressure correction (set-up/down)• Evolution due to Stokes drift
vs. Classical “radiation stress” formalism (c.f. Longuet-Higgins and Stewart, 1960, 1962, 1964)
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Equations for long-wave dynamics derived in MRL04
wave-averaged term
Momentum:
Continuity:
Wave-averaged term:
Momentum:
Continuity:
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Evaluation of the primary wave-averaged forcing term
Stokes transport:
wave set-down:
Using the ECMWF 2D wavenumber (frequency-directional) spectral data,G (, ) [m2 s /rad], every 6 hours on a 1.5o grid (w/ interpolation)
Data source: ECWMF/UCAR (http://dss.ucar.edu/datasets/ds123.0/)
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• based on 2D-ROMS with the wave-averaged term• containing advection, Coriolis, bottom drag terms• ~1/8o geographical grid (1568 1152 cells)• te=18 s
Bathymetry h (km) of the Pacific Ocean
open boundary with a modified Orlanski condition
Numerical Configuration
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IG wave solution at 0 AM UTC on 27th Julian day, 2000
wave
en
erg
yHHs s & k& k
lwlwTTmm
s s & T& Tstst
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wave
en
erg
yHHs s & k& k
lwlwTTmm
s s & T& Tstst
IG wave solution at 0 AM UTC on 28th Julian day, 2000
![Page 9: Infragravity Waves Forced by Surface Wind Waves in the Central North Pacific Ocean Yusuke Uchiyama and James C. McWilliams (CESR, IGPP, UCLA) Ocean bottom.](https://reader038.fdocuments.us/reader038/viewer/2022103100/56649f2a5503460f94c448fb/html5/thumbnails/9.jpg)
wave
en
erg
yHHs s & k& k
lwlwTTmm
s s & T& Tstst
IG wave solution at 0 AM UTC on 29th Julian day, 2000
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wave
en
erg
yHHs s & k& k
lwlwTTmm
s s & T& Tstst
IG wave solution at 0 AM UTC on 30th Julian day, 2000
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wave
en
erg
yHHs s & k& k
lwlwTTmm
s s & T& Tstst
IG wave solution at 0 AM UTC on 31st Julian day, 2000
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January 31, 2000
• Seismically quiet, but “hum” was apparent in the IG frequency band ~ M6 (Rhie & Romanowics, 2004)
• Forced IG waves are evident, but free IG waves are unclear and amplitude is small ~10-4m.
Tst and s
simulated lwwave-averaged term, F
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(1)(2)
Time series of lw at two locations on January 31, 2000
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6h
1.6h
48min
(1) Off Alaska (230o02’ E & 44o59’E)
(2) West of Hawaii (170o03’ E & 34o58’E)
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January 31, 2000
Applying Fourier low-pass time filter to extract IG wave energy
RMS for whole freq.
RMS for higher (~IG) freq.
Fourier low-pass filteredf<2 x 10-4 Hz (T>1.38h)
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Ratio of RMS :
RMS for IG freq.RMS for whole freq.
• Forced IG long-waves are predominant over slower variations in deeper ocean
• larger in the northern part because of storms
• tends to be larger near ridges, canyons and island chains
fairly consistent with seismologists’ hypothesis
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Summary
• A 2D barotropic ROMS is modified by incorporating long-wave dynamics based on MRL04 for generation of infragravity wave in basin scale,
• ECMWF/UCAR 2D wavenumber spectral data is utilized to evaluate the wave-averaged forcing term,
• Long waves in the North Pacific are evidently exited as forced (far) infragravity waves.
• Remaining questions are : - peak frequency is slightly lower than IG freq. band. - amplitudes of IG waves are small inconsistent with bottom pressure spectra. Why? - do free IG waves exist? (nearshore-generated?)
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Dominant Frequency of the Model-produced
IG wave dispersion relation
Why is dominant frequency lower than IG freq.?
Long waves at T=100s have wave lengths of L < 10km
A finer grid may be needed~regional simulations
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Comparison of wave data: ECMWF vs. NDBC buoys
#46001Off Alaska
#51028Off Hawaii
Validity of Spatial/Temporal Resolution of Wave Data
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ECMWF vs. NDBC buoys (off Alaska)
significant wave height
mean wave period
principal wave direction
magnitude of Stokes transport
Julian day in 2000
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Comparison of |Tst| PSD: ECMWF vs. NDBC buoys
#46001 off Alaska #51028 off Hawaii
Higher frequency (thus high wavenumber) components are not well resolved with less energy in the ECWMF data.
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Primary surface wave field (magnitude of Stokes transport)
apply filter functionFourier transform inverse Fourier transform
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Comparison between vortex force & radiation stress formalisms
c.f. Lane, Restrepo and McWilliams (2006, JFM)
U=
• Scale separation both in time and horizontal space
• Substitute into momentum and continuity equations
analogous to Reynolds equation
analogous to Bernoulli equation
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Radiation stress and vortex force formalisms are identical
Radiation stress Vortex force
Bernoulli head
Horizontal vortex forceNot transparent
• Wave dynamics is non-linear, but weak compared to turbulence• Non-linearity enters only through the surface B.C.• Lowest order ~ radiation stress merely captures set-up effect
IG wave equation using radiation stress
0
qHt x
SH
gt
1q
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Incorporation of wave-averaged term into 2D ROMS
+ advection, Coriolis, linear bottom drag terms
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Modified Orlanski’s Radiation Scheme for Open Boundaries(for 2D barotropic ROMS)
c: phase speed of each variable (, u, v): nudging coefficient [T-1]: coefficient for pressure-gradient mass correction (n.d.)
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Volume (or area) averaged PE, KE, and wave energy
potential energy
kinetic energy
surface elevation
wave energy