An Empirical Investigation of Nonlinear Energy Transfer from the M2 Internal Tide to Diurnal Wave Motions in the Kauai Channel, Hawaii Sherry H.. CARTER, Thomas DECLOEDT Department of Oc
Trang 1An Empirical Investigation of Nonlinear Energy Transfer from the M2 Internal Tide to Diurnal Wave Motions in the Kauai Channel, Hawaii
Sherry H CHOU, Douglas S LUTHER, Martin D GUILES, Glenn S CARTER, Thomas DECLOEDT
Department of Oceanography, School of Ocean and Earth Science and Technology, University of Hawaii at Manoa, Honolulu, Hawaii, USA
Key Points:
● Strong semi-diurnal and diurnal internal tide beams are observed in the Kauai Channel
● Energy at M2 subharmonic (M2/2) is weak at all depths, including within M2 beam
● Bispectra can falsely indicate nonlinear interactions if diurnal tides are present
Fig 4 Top two panels show the full time series of horizontal velocities
(u,v), strongly modulated by a spring-neap tidal cycle; bottom two panels are two-day insets of (u,v) showing semi-diurnal, anticyclonic waves.1
Observations: Long records of current profiles from the Hawaii Ocean Mixing Experiment
(HOME) A2 and C2 moorings (Fig 3) show clear internal tide signals (Fig 4) at the
semi-diurnal frequency, modulated by a strong spring-neap cycle.
Fig 3 Locations of the HOME A2 and C2 moorings,
as well as the Nearfield location of the FLoating Instrument Platform (FLIP) are shown on a
bathymetry map with contour lines every 500 m.2
Fig 5 Velocity
Power Spectral
Density (PSD) (left
two panels;
barotropic tide
currents have been
subtracted from
measured currents)
and vertical shear
PSD (right two
panels)
from HOME
moorings C2 (top
panels) and A2
(lower two panels).1
Fig 6 Rotary spectra of horizontal velocity and vertical shear at (a,b) 660 m and
(c,d) 1124 m are shown with 95% confidence intervals (C.I.).2
Fig 7
PSDs calculated as mean of 3 adjacent discrete Fourier transform harmonics centered at the noted frequency and scaled
by the buoyancy
frequency N Depth
averaging with 80 m (50% overlapping) windows.2
Auto-spectra: Well-resolved velocity and shear auto-spectra (Figs 5-7) consistently exhibit maxima at
possibly significant interaction for [O1, K1, M2] triad Tests with synthetic data reveal that bispectrum and bicoherence estimators can yield significant values, thus misleading results.
Fig 8 (left)
Bispectra (log scale) and bicoherence for complex
velocity u+iv at 660 m
on the A2 mooring (top panels; a, b)
and (lower panels; c, d) for synthetic data
containing linear sinusoidal inputs at eight major tidal frequencies (M2, S2, N2, K2; K1, O1, P1, Q1), and white Gaussian noise (10
dbs).2
Fig 9 Bispectra and bicoherence of [-M1, -M1, -M2]
and [-O1, -K1, -M2] are shown with 80% and 90% significance levels.2
Discussion: Does the presented spectral evidence support a hypothesis of resonant nonlinear
energy transfer from the M2 tide to internal wave motions at O1 and K1?
Poster #1344
schou@hawaii.edu
Presenting 2/24 (4-5 pm)
Numerical simulations indicate observed O1 and K1 signals are from locally generated internal tides
Fig 10 Harmonic fits
of the K1 frequency are calculated for 5 months
of A2 mooring velocities (blue, with 95% C.I In gray) and output from
1 km resolution model (red) Results are
consistent in both amplitude and phase, especially in the depth range where M2 tide is strongest (550-800 m).2
Maxima in diurnal-band velocity PSD do not coincide with semidiurnal maxima, suggesting the two are not coupled
Fig 11 Semidiurnal band (1.88-2.06 cpd, left) and diurnal-band
(0.96-1.11 cpd, right) PSDs of A2 mooring velocities.2
Conclusion: Resolving the diurnal tides is essential to meaningfully assess nonlinear energy transfer from M2 tide to diurnal waves.
Table 1 Frequencies of interest are shown in the first row and
column, in cycles per day (cpd); differences shown in matrix
Nearest Discrete Fourier Transform (DFT) harmonics for record
length T = 163.5 days shown for comparison (bottom 2 rows).1
Resonance conditions for triad of waves
with wave numbers kj and frequencies ω j:
k 1 + k 2 = k 3
ω 1 + ω 2 = ω 3
Fig 1 Wave number diagram of a Parametric
Subharmonic Instability (PSI) wave triad.1
Possible PSI wave triad at 22˚N
Fig 2 Mode-1 M2 internal tide at A2
(see Fig 3) could form PSI triad with secondary waves of vertical wavelengths
~50 m, separated in freq by <0.04 cpd.1
1 Figures 1, 2, 4, 5 and Table 1 are from Chou, S (2013), An Empirical Investigation of Energy Transfer from the M2 tide to M2 Subharmonic Wave Motions
in the Kauai Channel, M.S thesis, Department of Oceanography, Univ of Hawaii at Manoa, Honolulu, Hawaii
2 Figures 3, 6-11 are from Chou, S.H., D.S Luther, M.D Guiles, G.S Carter, and T Decloedt (2014), An empirical investigation of nonlinear energy transfer
from the M2 internal tide to diurnal wave motions in the Kauai Channel, Hawaii, Geophys Res Lett., 41, doi:10.1002/2013GL058320.
Horizontal and vertical axes indicate the first and second waves of a triad
(ω 1 , ω 2 ), and the diagonal axis corresponds to the sum frequency ω 3 = ω 1 + ω 2