Oceanic internal-wave field : theory of scale-invariant spectra

View/ Open
Date
2010-12Author
Lvov, Yuri V.
Concept link
Polzin, Kurt L.
Concept link
Tabak, Esteban G.
Concept link
Yokoyama, Naoto
Concept link
Metadata
Show full item recordCitable URI
https://hdl.handle.net/1912/4343As published
https://doi.org/10.1175/2010JPO4132.1DOI
10.1175/2010JPO4132.1Keyword
Waves; Oceanic; Internal waves; Spectral analysisAbstract
Steady scale-invariant solutions of a kinetic equation describing the statistics of oceanic internal gravity waves based on wave turbulence theory are investigated. It is shown in the nonrotating scale-invariant limit that the collision integral in the kinetic equation diverges for almost all spectral power-law exponents. These divergences come from resonant interactions with the smallest horizontal wavenumbers and/or the largest horizontal wavenumbers with extreme scale separations.
A small domain is identified in which the scale-invariant collision integral converges and numerically find a convergent power-law solution. This numerical solution is close to the Garrett–Munk spectrum. Power-law exponents that potentially permit a balance between the infrared and ultraviolet divergences are investigated. The balanced exponents are generalizations of an exact solution of the scale-invariant kinetic equation, the Pelinovsky–Raevsky spectrum. A small but finite Coriolis parameter representing the effects of rotation is introduced into the kinetic equation to determine solutions over the divergent part of the domain using rigorous asymptotic arguments. This gives rise to the induced diffusion regime.
The derivation of the kinetic equation is based on an assumption of weak nonlinearity. Dominance of the nonlocal interactions puts the self-consistency of the kinetic equation at risk. However, these weakly nonlinear stationary states are consistent with much of the observational evidence.
Description
Author Posting. © American Meteorological Society, 2010. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 40 (2010): 2605–2623, doi:10.1175/2010JPO4132.1.
Collections
Suggested Citation
Journal of Physical Oceanography 40 (2010): 2605–2623Related items
Showing items related by title, author, creator and subject.
-
Counts of Mysidacea species collected during the International Indian Ocean Expeditions (IIOE) aboard multiple cruises in the Indian Ocean from 1962-1965 (IIOE project)
Nair, Vijayalakshmi R. (Biological and Chemical Oceanography Data Management Office (BCO-DMO). Contact: bco-dmo-data@whoi.edu, 2019-11-01)Counts of Mysidacea species collected during the International Indian Ocean Expeditions (IIOE) in the Indian Ocean. Mysidacea were collected by several ships that took part in the IIOE from 1962 to 1965. Though collections ... -
Effects of internal waves on low frequency, long range, acoustic propagation in the deep ocean
Xu, Jinshan (Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, 2007-09)This thesis covers a comprehensive analysis of long-range, deep-ocean, low-frequency, sound propagation experimental results obtained from the North Pacific Ocean. The statistics of acoustic fields after propagation ... -
The role of external inputs and internal cycling in shaping the global ocean cobalt distribution : insights from the first cobalt biogeochemical model
Tagliabue, Alessandro; Hawco, Nicholas J.; Bundy, Randelle M.; Landing, William M.; Milne, Angela; Morton, Peter L.; Saito, Mak A. (John Wiley & Sons, 2018-04-16)Cobalt is an important micronutrient for ocean microbes as it is present in vitamin B12 and is a co‐factor in various metalloenzymes that catalyze cellular processes. Moreover, when seawater availability of cobalt is ...