Academic
Publications
Space-Time scales of internal waves

Space-Time scales of internal waves,10.1080/03091927208236082,Geophysical and Astrophysical Fluid Dynamics,Christopher Garrett,Walter Munk

Space-Time scales of internal waves   (Citations: 287)
BibTex | RIS | RefWorks Download
We have contrived a model E() -1-p+1(2-omegai2)-+ for the distribution of internal wave energy in horizontal wavenumber, frequency-space, with wavenumber alpha extending to some upper limit mu(omega) alpha omegar-1 (omega2-omegai2)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 omega-p-r for alpha <= mu; omegaomegar, yields F(omega) ∞ omega-p, F(alpha1) alpha 1-q, 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 fine-structure. Our choice (p, q, r) = (2, 2, 1) is then not inconsistent with existing evidence. The spectrum is E(∞ , omega) ∞ omega-1(omega2-omegai2-1, and the alpha-bandwith mu ∞ (omega2-omegai2)+ is equivalent to about 20 modes. Finally, we consider the frequency-of-encounter 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.
Cumulative Annual
View Publication
The following links allow you to view full publications. These links are maintained by other sources not affiliated with Microsoft Academic Search.
    • ...Internal waves are prominent features in the ocean with well-known dispersion relations and characteristics (Garrett and Munk 1972)...

    Tamay M. Özgökmenet 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. Rudnicket 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 Namet 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 Brunt-Vaiisala frequency...

    P. V. Hareesh Kumaret al. Internal Tides in the Coastal Waters of NE Arabian Sea: Observations a...

Sort by: