Infragravity Waves Forced by Surface Wind Waves in the Central North Pacific Ocean
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Transcript of Infragravity Waves Forced by Surface Wind Waves in the Central North Pacific Ocean
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
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]
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)
Equations for long-wave dynamics derived in MRL04
wave-averaged term
Momentum:
Continuity:
Wave-averaged term:
Momentum:
Continuity:
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/)
• 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
IG wave solution at 0 AM UTC on 27th Julian day, 2000
wave
en
erg
yHHs s & k& k
lwlwTTmm
s s & T& Tstst
wave
en
erg
yHHs s & k& k
lwlwTTmm
s s & T& Tstst
IG wave solution at 0 AM UTC on 28th Julian day, 2000
wave
en
erg
yHHs s & k& k
lwlwTTmm
s s & T& Tstst
IG wave solution at 0 AM UTC on 29th Julian day, 2000
wave
en
erg
yHHs s & k& k
lwlwTTmm
s s & T& Tstst
IG wave solution at 0 AM UTC on 30th Julian day, 2000
wave
en
erg
yHHs s & k& k
lwlwTTmm
s s & T& Tstst
IG wave solution at 0 AM UTC on 31st Julian day, 2000
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
(1)(2)
Time series of lw at two locations on January 31, 2000
6h
1.6h
48min
(1) Off Alaska (230o02’ E & 44o59’E)
(2) West of Hawaii (170o03’ E & 34o58’E)
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)
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
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?)
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
Comparison of wave data: ECMWF vs. NDBC buoys
#46001Off Alaska
#51028Off Hawaii
Validity of Spatial/Temporal Resolution of Wave Data
ECMWF vs. NDBC buoys (off Alaska)
significant wave height
mean wave period
principal wave direction
magnitude of Stokes transport
Julian day in 2000
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.
Primary surface wave field (magnitude of Stokes transport)
apply filter functionFourier transform inverse Fourier transform
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
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
Incorporation of wave-averaged term into 2D ROMS
+ advection, Coriolis, linear bottom drag terms
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.)
Volume (or area) averaged PE, KE, and wave energy
potential energy
kinetic energy
surface elevation
wave energy