ALBERT

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.

Description: 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: This research is supported by NSF CMG Grants 0417724, 0417732 and 0417466. YL is also supported by NSF DMS Grant 0807871 and ONR Award N00014-09-1-0515.

Description: Author Posting. © American Geophysical Union, 2011. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Reviews of Geophysics 49 (2011): RG4003, doi:10.1029/2010RG000329.

Description: Many major oceanographic internal wave observational programs of the last 4 decades are reanalyzed in order to characterize variability of the deep ocean internal wavefield. The observations are discussed in the context of the universal spectral model proposed by C. J. R. Garrett and W. H. Munk. The Garrett and Munk model is a good description of wintertime conditions at Site D on the continental rise north of the Gulf Stream. Elsewhere and at other times, significant deviations in terms of amplitude, separability of the 2-D vertical wavenumber-frequency spectrum, and departure from the model's functional form are reported. Specifically, the Garrett and Munk model overestimates annual average frequency domain spectral levels both at Site D and in general. The bias at Site D is associated with the Garrett and Munk model being a fit to wintertime data from Site D and the presence of an annual cycle in high-frequency energy in the western subtropical North Atlantic having a maximum in winter. The wave spectrum is generally nonseparable, with near-inertial waves typically having greater bandwidth (occupying smaller vertical scales) than continuum frequency waves. Separability is a better approximation for more energetic states, such as wintertime conditions at Site D. Subtle geographic differences from the high-frequency and high vertical wavenumber power laws of the Garrett and Munk spectrum are apparent. Such deviations tend to covary: whiter frequency spectra are partnered with redder vertical wavenumber spectra. We review a general theoretical framework of statistical radiative balance equations and interpret the observed variability in terms of the interplay between generation, propagation, and nonlinearity. First, nonlinearity is a fundamental organizing principle in this work. The observed power laws lie close to the induced diffusion stationary states of the resonant kinetic equation describing the lowest-order nonlinear transfers. Second, eddy variability and by implication wave mean interactions are also an organizing principle. Observations from regions of low eddy variability tend to be outliers in terms of their parametric spectral representation; other data tend to cluster in two regions of parameter space. More tentatively, the seasonal cycle of high-frequency energy is in phase with the near-inertial seasonal cycle in regions of significant eddy variability. In regions of low eddy variability, the seasonal cycle in high-frequency energy lags that of near-inertial energy. The induced diffusion stationary states are approximate analytic solutions to the resonant kinetic equation, and the Garrett and Munk spectrum represents one such analytic solution. We present numerical solutions of the resonant kinetic equation, however, that are inconsistent with the Garrett and Munk model representing a stationary state, either alone or in combination with other physical mechanisms. We believe this to be the case for other regional characterizations as well. We argue that nonstationarity of the numerical solutions is related to local transfers in horizontal wavenumber, whereas the analytic induced diffusion stationary states consider only nonlocal transfers in vertical wavenumber. Consequences for understanding the pathways by which energy is transferred from sources to sinks are considered. Further progress likely requires self-consistent solutions to a broadened kinetic equation.

Description: We gratefully acknowledge funding provided by a Collaborations in Mathematical Geosciences (CMG) grant from the National Science Foundation. Y.L. additionally acknowledges NSF DMS grant 0807871 and ONR award N00014‐09‐1‐0515.

Description: 2012-05-10

Description: Author Posting. © American Geophysical Union, 2010. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 115 (2010): C12049, doi:10.1029/2010JC006331.

Description: The generation, propagation, and dissipation processes of large-amplitude nonlinear internal waves in Massachusetts Bay during the stratified season were examined using the nonhydrostatic Finite-Volume Coastal Ocean Model (FVCOM-NH). The model reproduced well the characteristics of the high-frequency internal waves observed in Massachusetts Bay in August 1998. The model experiments suggested that internal waves over Stellwagen Bank are generated by the interaction of tidal currents with steep bottom topography through a process of forming a large-density front on the western slope of the bank by the release of an initial density perturbation near ebb-flood transition, nonlinear steepening of the density front into a deep density depression, and disintegrating of the density depression into a wave train. Earth's rotation tends to transfer the cross-bank tidal kinetic energy into the along-bank direction and thus reduces the intensity of the density perturbation at ebb-flood transition and density depression in the flood period. The internal wave packet propagates as a leading edge feature of the internal tidal wave, and the faster propagation speed of the high-frequency internal waves in Massachusetts Bay is caused by Earth's rotation. The model experiments suggested that bottom friction can significantly influence the cross-bank scale of the density perturbation and thus the density depression during wave generation and the dissipation during the wave's shoaling. Inclusion of vertical mixing using the Mellor-Yamada level 2.5 turbulence closure model had only a marginal effect on wave evolution. The model results support the internal wave theory proposed by Lee and Beardsley (1974) but are in disagreement with the lee-wave mechanism proposed by Maxworthy (1979).

Description: This research was supported by NOAA g r a n t s DOC/NOAA/NA04NMF4720332 and DOC/NOAA/ NA05NMF4721131, U.S. GLOBEC Northwest Atlantic/Georges Bank Program NSF grants (OCE‐0606928, OCE‐0712903, OCE‐0732084, OCE‐0726851, OCE0814505), and MIT Sea Grant funds (2006‐RC‐103 and 2010‐R/RC‐116), NOAA NERACOOS Program for the UMASSD team and the Smith Chair in Coastal Oceanography, and NOAA grant (NA‐17RJ1223) for R.C. Beardsley. C. Chen’s contribution is also supported by Shanghai Ocean University under grants A‐2302‐10‐0003 and 09320503700 and the State Key Laboratory for Estuarine and Coastal Research, East China Normal University.