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Cosine Transform
Fine Structure
Internal Waves
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SpaceTime scales of internal waves
SpaceTime scales of internal waves,10.1080/03091927208236082,Geophysical and Astrophysical Fluid Dynamics,Christopher Garrett,Walter Munk
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SpaceTime scales of internal waves
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Citations: 287
)
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Christopher Garrett
,
Walter Munk
We have contrived a model E() 1p+1(2omegai2)+ for the distribution of internal
wave energy
in horizontal wavenumber, frequencyspace, with wavenumber alpha extending to some upper limit mu(omega) alpha omegar1 (omega2omegai2)½, and frequency omega extending from the inertial frequency omegai to the local Väisälä frequency n(y). The
spectrum
is portrayed as an equivalent continuum to which the modal structure (if it exists) is not vital. We assume horizontal isotropy, E(alpha, omega) = 2pialphaE(alpha1, alpha2, omega), with alpha1, alpha2 designating components of alpha. Certain moments of E(alpha1, alpha2, omega) can be derived from observations. (i) Moored (or freely floating) devices measuring horizontal current u(t), vertical displacement eta(t),..., yield the frequency spectra F(u,eta,...)(omega) = ∫∫(U2, Z2,...)E(alpha1, ∞2, omega) dalpha1 dalpha2, where U, Z,... are the appropriate wave functions. (ii) Similarly towed measurements give the wavenumber
spectrum
F(...)(alpha1) = ∫∫...dalpha2 domegaR(X, omega) which is related to the horizontal
cosine transform
∫∫ E(alpha1, alpha2 omega) cos alpha1 Xdalpha1 dalpha1. (iv) Moored measurements vertically separated by Y yield R(Y, omega) and (v) towed measurements vertically separated yield R(Y, alpha1), and these are related to similar vertical Fourier transforms. Away from inertial frequencies, our model E(alpha, omega) alpha omegapr for alpha <= mu; omegaomegar, yields F(omega) ∞ omegap, F(alpha1) alpha 1q, with q = (p + r  1)/r. The observed moored and towed spectra suggest p and q between 5/3 and 2, yielding r between 2/3 and 3/2, inconsistent with a value of r = 2 derived from Webster's measurements of moored vertical coherence. We ascribe Webster's result to the oceanic finestructure. Our choice (p, q, r) = (2, 2, 1) is then not inconsistent with existing evidence. The
spectrum
is E(∞ , omega) ∞ omega1(omega2omegai21, and the alphabandwith mu ∞ (omega2omegai2)+ is equivalent to about 20 modes. Finally, we consider the frequencyofencounter spectra F(sgrave ) at any towing speed S, approaching F(omega) as S <= So, and F(alpha1) for alpha1 = sgrave /S as S >= So, where So = 0(1 km/h) is the relevant Doppler velocity scale.
Journal:
Geophysical and Astrophysical Fluid Dynamics  GEOPHYS ASTROPHYS FLUID DYNAM
, vol. 3, no. 1, pp. 225264, 1972
DOI:
10.1080/03091927208236082
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Citation Context
(47)
...Internal waves are prominent features in the ocean with wellknown dispersion relations and characteristics (Garrett and Munk
1972
)...
Tamay M. Özgökmen
,
et al.
CFD application to oceanic mixed layer sampling with Lagrangian platfo...
...Energy of the internal wave field is taken to be that specified by Garrett and Munk [
29
], [30]...
...This spectrum is a curve fit to a great many observations in many oceans [
29
], [30] but it does not account completely for particular features in certain areas...
...This is entirely due to internal waves following the standard spectrum [
29
], [30] as they are the only phenomenon in the model...
...In this paper, the energy was taken from the literature because it is a best fit to many in situ observations, and is remarkably stable in space and time [
29
], [30]...
John L. Spiesberger
.
Internal Waves' Role in Determining Probability Distribution of Cohere...
...This effect was recognized for towed observations by Voorhis and Perkins [1966] and was considered by
Garrett and Munk [1972]
in the first exposition of the internal wave spectrum...
...To the extent that there exists a canonical internal wave spectrum [
Garrett and Munk, 1972, 1975;
Munk, 1981], high‐frequency variability should not vary much in the open ocean away from generation sites...
Daniel L. Rudnick
,
et al.
On sampling the ocean using underwater gliders
...[29] Indeed, as described in section 3.1, the spectral falloff rate with frequency w at the high‐frequency band (0.1–1.0 cph) becomes higher (close to w −3 ) than the canonical GM [
Garrett and Munk, 1972, 1975
] spectra (w −2 )...
...breaking. Persistent formation (by tidal forcing) and dissipation of an internal bolus over short time scales causes the high‐frequency (periods from 1 to 10 h) spectral falloff rate of water temperature near the bottom to deviate from canonical GM [
Garrett and Munk, 1972, 1975
] spectra (w −2 ) toward the spectra of nonlinearly transformed internal waves (w −3 )[ Filonov and Novotryasov, 2005] during the stratified season...
SungHyun Nam
,
et al.
Direct evidence of deep water intrusions onto the continental shelf vi...
...These waves occupy a vast continuum of spatial and temporal scales (
Garret and Munk 1972
, 1975), with horizontal scales ranging from few tens of meters to few kilometers and temporal scales from inertial to local BruntVaiisala frequency...
P. V. Hareesh Kumar
,
et al.
Internal Tides in the Coastal Waters of NE Arabian Sea: Observations a...
References
(21)
1962: Coupling of internal and surface waves in water of variable depth
(
Citations: 42
)
C. S. Cox
,
H. Sandstrom
Published in 1975.
Hydrodynamics of Oceans and Atmospheres
(
Citations: 101
)
C. Eckart
Published in 1960.
Internal Wave Spectra in the Presence of FineStructure
(
Citations: 31
)
Christopher Garrett
,
Walter Munk
Journal:
Journal of Physical Oceanography  J PHYS OCEANOGR
, vol. 1, no. 3, pp. 196202, 1971
Spectral Characteristics of some Deep Current Records from the Eastern North Atlantic
(
Citations: 11
)
W. J. Gould
Journal:
Philosophical Transactions of The Royal Society A: Mathematical, Physical and Engineering Sciences
, vol. 270, no. 1206, pp. 437450, 1971
Typical features of internal wave spectra
(
Citations: 1
)
W. Krauss
Journal:
Progress in Oceanography  PROG OCEANOGR
, vol. 5, pp. 95101, 1969
Sort by:
Citations
(287)
CFD application to oceanic mixed layer sampling with Lagrangian platforms
Tamay M. Özgökmen
,
Paul F. Fischer
Journal:
International Journal of Computational Fluid Dynamics  INT J COMPUT FLUID DYNAMICS
, vol. aheadofp, no. aheadofp, pp. 112, 2012
Left pulmonary artery sling with right lung aplasia
Charlotte Pierron
,
Anne SigalCinqualbre
,
Virginie Lambert
,
Emmanuel Le Bret
Journal:
Journal of Pediatric Surgery  J PEDIAT SURG
, vol. 46, no. 11, pp. 21902194, 2011
Impact of internal waves on the acoustic field at a coastal station off Paradeep, east coast of India
B. Sridevi
,
T. V. Ramana Murty
,
Y. Sadhuram
,
V. S. N. Murty
Journal:
Natural Hazards
, vol. 57, no. 3, pp. 563576, 2011
Internal Waves' Role in Determining Probability Distribution of Coherent Integration Time Near 133 Hz and 3709 km in North Pacific Ocean
John L. Spiesberger
Journal:
IEEE Journal of Oceanic Engineering  IEEE J OCEANIC ENG
, vol. 36, no. 4, pp. 760771, 2011
On sampling the ocean using underwater gliders
Daniel L. Rudnick
,
Sylvia T. Cole
Journal:
Journal of Geophysical Research
, vol. 116, no. C8, 2011