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): 789-801, doi:10.1175/2009JPO4039.1.

Description: The issue of internal wave–mesoscale eddy interactions is revisited. Previous observational work identified the mesoscale eddy field as a possible source of internal wave energy. Characterization of the coupling as a viscous process provides a smaller horizontal transfer coefficient than previously obtained, with vh 50 m2 s−1 in contrast to νh 200–400 m2 s−1, and a vertical transfer coefficient bounded away from zero, with νυ + (f2/N2)Kh 2.5 ± 0.3 × 10−3 m2 s−1 in contrast to νυ + (f2/N2)Kh = 0 ± 2 × 10−2 m2 s−1. Current meter data from the Local Dynamics Experiment of the PolyMode field program indicate mesoscale eddy–internal wave coupling through horizontal interactions (i) is a significant sink of eddy energy and (ii) plays an O(1) role in the energy budget of the internal wave field.

Description: Author Posting. © American Meteorological Society, 2008. 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 38 (2008): 2556-2574, doi:10.1175/2008JPO3666.1.

Description: Vertical profiles of horizontal velocity obtained during the Mid-Ocean Dynamics Experiment (MODE) provided the first published estimates of the high vertical wavenumber structure of horizontal velocity. The data were interpreted as being representative of the background internal wave field, and thus, despite some evidence of excess downward energy propagation associated with coherent near-inertial features that was interpreted in terms of atmospheric generation, these data provided the basis for a revision to the Garrett and Munk spectral model. These data are reinterpreted through the lens of 30 years of research. Rather than representing the background wave field, atmospheric generation, or even near-inertial wave trapping, the coherent high wavenumber features are characteristic of internal wave capture in a mesoscale strain field. Wave capture represents a generalization of critical layer events for flows lacking the spatial symmetry inherent in a parallel shear flow or isolated vortex.

Description: Salary support for this analysis was provided by Woods Hole Oceanographic Institution bridge support funds.

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: Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 1992

Description: Oceanic profiles of temperature, salinity, horizontal velocity, rate of dissipation of turbulent kinetic energy (ε) and rate of dissipation of thermal variance (χ) are used to examine the parameterization of turbulent mixing in the ocean due to internal waves. Turbulent mixing is quantified through eddy diffusivity parameterizations of the mass (Kρ; Osborn, 1980) and heat fluxes (Kτ; Osborn and Cox, 1972) in turbulent production/dissipation balances. Turbulence in the ocean is generally held to result from the occurrence of shear instability in regions where the Richardson number is locally supercritical (i.e. Ri ≤ 1/4), permitting the growth of small-scale waves which break and result in turbulent mixing. The occurrence of shear instability results from the local intensification of the shear in the internal wave field. The energy dissipated in such events is provided by the energy flux to higher wavenumber due to nonlinear wave/wave interactions on scales of 10's to 100's of meters. In turn, the strength of the wave/wave interactions depends generally on the energy content of the internal wave field, which can vary considerably over even larger scales due to the presence of topography or background flows. The magnitude of turbulent mixing is linked to internal wave dynamics by equating the turbulent dissipation with the energy flux through the vertical wavenumber spectrum under the priviso that the model spectrum which forms the basis for the analysis is statistically stationary with respect to the nonlinear interactions. Dynamical models (McComas and Muller, 1981; Henyey et al., 1986) indicate that the Garrett and Munk (GM; Munk, 1981) spectrum is stationary. Observations from the far field of a seamount in a region of negligible large-scale flow were examined to address the issue of the buoyancy scaling of ε. These data exhibited large variations in background stratification with depth, but the internal wave characteristics were not substantially differentiable from the GM prescription. The magnitude of ε and its functional dependence upon internal wave energy levels (E) and buoyancy frequency (N) was best described by the dynamical model ofHenyey et al. (1986) (ε ~ E2N2). The Richardson number scaling model of Kunze et al. (1990) produced consistent estimates. A second dynamical model, McComas and Muller (1981), predicted an appropriate (E,N) scaling, but overestimated the observed dissipation rates by a factor of five. Two kinematical dissipation parameterizations (Garmett and Holloway (1984) and Munk (1981)) predicted buoyancy scalings of N3/2 which were inconsistent with the observed scaling. Data from an upper-ocean front, a warm core ring and a region of steep topography were analyzed in order to examine the parameter dependence of E in internal wave fields which exhibited potentially nonstationary characteristics. Evidence was provided which implied the internal wave field in an upper ocean front was interacting with and modified by the background flow. Inhomogeneity and anisotropy of the internal wave field were noted in that data set. The model of Gregg (1989), which in turn was based upon the model of Henyey et al., effectively collapsed the observed diffusivity estimates from the front. The warm core ring profiles were noted to be anisotropic, dominated by near-inertial frequencies and to have a peaked vertical wavenumber shear spectrum. The data from a region of steep topography were noted to have a peaked vertical wavenumber spectrum and were characterized by higher than GM frequency motions. For the latter two data sets, application of a frequency based correction to the Henyey et al. model (Henyey, 1991) reduced more than an order of magnitude scatter in the parameterized estimates of E to less than a factor of four. Of the possible non-equilibrium conditions in the internal wave field, the (E,N) scaled dissipation rates were most sensitive to deviations in wave field frequency content. On the basis of a number of theoretical Richardson number probability distributions (Ri = N2/S2, where S2 is the sum of the squared vertical derivatives of horizontal velocity), the nominal dissipation scaling of the Kunze et al. model was determined to be E2N3. This scaling is altered to the observed ε ~ E2N2 scaling by a statistical dependence between N2 and S2 which reduces the occurrence of supercritical Ri values. This statistical dependence is hypothesized to be an effect of the turbulent momentum and buoyancy fluxes on the internal wave shear and strain profiles caused by shear instability. The statistical dependence between N2 and S2 exhibited a buoyancy scaling which was interpreted as resulting from the decreasing ratio between the time scale of the shear instability mechanism [T- 2π/N] and the adiabatic time scale [T - 2π/(Nf)1/2] of the internal wave field (f is the Coriolis parameter). This phenomenology is interpreted in light of saturated spectral theories which suggest that the magnitude and shape of the vertical wavenumber spectrum is controlled by instability mechanisms at large wavenumber ( ≥ .1 cpm). We argue that saturated spectral theories are valid only in the limit where a separation exists between the two time scales, i.e. for large N, low internal wave frequency content, and small f. These results have immediate implications for oceanic mixing driven by internal wave motions. First, background diffusivities are small: at GM energy levels, Kρ - .03x10-4 m2/s (Kρ = .25ε/N2). Secondly, since Kρ is independent of N at constant E, some process or collection of processes must be responsible for heightened E values in the abyss if internal waves cause the 0(1-10x10-4 m2/s) diffusivities generally inferred from deep ocean hydrographic data. We view internal wave reflection and/or internal wave generation associated with topographic features to be likely candidates.

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 Meteorological Society, 2013. 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 43 (2013): 259–282, doi:10.1175/JPO-D-11-0194.1.

Description: This study reports on observations of turbulent dissipation and internal wave-scale flow properties in a standing meander of the Antarctic Circumpolar Current (ACC) north of the Kerguelen Plateau. The authors characterize the intensity and spatial distribution of the observed turbulent dissipation and the derived turbulent mixing, and consider underpinning mechanisms in the context of the internal wave field and the processes governing the waves’ generation and evolution. The turbulent dissipation rate and the derived diapycnal diffusivity are highly variable with systematic depth dependence. The dissipation rate is generally enhanced in the upper 1000–1500 m of the water column, and both the dissipation rate and diapycnal diffusivity are enhanced in some places near the seafloor, commonly in regions of rough topography and in the vicinity of strong bottom flows associated with the ACC jets. Turbulent dissipation is high in regions where internal wave energy is high, consistent with the idea that interior dissipation is related to a breaking internal wave field. Elevated turbulence occurs in association with downward-propagating near-inertial waves within 1–2 km of the surface, as well as with upward-propagating, relatively high-frequency waves within 1–2 km of the seafloor. While an interpretation of these near-bottom waves as lee waves generated by ACC jets flowing over small-scale topographic roughness is supported by the qualitative match between the spatial patterns in predicted lee wave radiation and observed near-bottom dissipation, the observed dissipation is found to be only a small percentage of the energy flux predicted by theory. The mismatch suggests an alternative fate to local dissipation for a significant fraction of the radiated energy.

Description: SW acknowledges the support of the Grantham Institute for Climate Change, Imperial College London. ACNG acknowledges the support of a NERC Advanced Research Fellowship (Grant NE/C517633/1). KLP acknowledges support from Woods Hole Oceanographic Institution bridge support funds.

Description: 2013-08-01

Description: Author Posting. © American Meteorological Society, 2014. 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 44 (2014): 2938–2950, doi:10.1175/JPO-D-13-0201.1.

Description: Direct observations in the Southern Ocean report enhanced internal wave activity and turbulence in a kilometer-thick layer above rough bottom topography collocated with the deep-reaching fronts of the Antarctic Circumpolar Current. Linear theory, corrected for finite-amplitude topography based on idealized, two-dimensional numerical simulations, has been recently used to estimate the global distribution of internal wave generation by oceanic currents and eddies. The global estimate shows that the topographic wave generation is a significant sink of energy for geostrophic flows and a source of energy for turbulent mixing in the deep ocean. However, comparison with recent observations from the Diapycnal and Isopycnal Mixing Experiment in the Southern Ocean shows that the linear theory predictions and idealized two-dimensional simulations grossly overestimate the observed levels of turbulent energy dissipation. This study presents two- and three-dimensional, realistic topography simulations of internal lee-wave generation from a steady flow interacting with topography with parameters typical of Drake Passage. The results demonstrate that internal wave generation at three-dimensional, finite bottom topography is reduced compared to the two-dimensional case. The reduction is primarily associated with finite-amplitude bottom topography effects that suppress vertical motions and thus reduce the amplitude of the internal waves radiated from topography. The implication of these results for the global lee-wave generation is discussed.

Description: This research was supported by the National Science Foundation under Award CMG-1024198.

Description: 2015-05-01

Description: Author Posting. © American Geophysical Union, 2015. 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: Oceans 120 (2015): 7997–8019, doi:10.1002/2015JC010892.

Description: This paper examines two internal lee wave closures that have been used together with ocean models to predict the time-averaged global energy conversion rate into lee waves and dissipation rate associated with lee waves and topographic blocking: the Garner (2005) scheme and the Bell (1975) theory. The closure predictions in two Southern Ocean regions where geostrophic flows dominate over tides are examined and compared to microstructure profiler observations of the turbulent kinetic energy dissipation rate, where the latter are assumed to reflect the dissipation associated with topographic blocking and generated lee wave energy. It is shown that when applied to these Southern Ocean regions, the two closures differ most in their treatment of topographic blocking. For several reasons, pointwise validation of the closures is not possible using existing observations, but horizontally averaged comparisons between closure predictions and observations are made. When anisotropy of the underlying topography is accounted for, the two horizontally averaged closure predictions near the seafloor are approximately equal. The dissipation associated with topographic blocking is predicted by the Garner (2005) scheme to account for the majority of the depth-integrated dissipation over the bottom 1000 m of the water column, where the horizontally averaged predictions lie well within the spatial variability of the horizontally averaged observations. Simplifications made by the Garner (2005) scheme that are inappropriate for the oceanic context, together with imperfect observational information, can partially account for the prediction-observation disagreement, particularly in the upper water column.

Description: National Science Foundation Grant Number: OCE-0960820; Office of Naval Research (ONR) Grant Number: N00014-11-1-0487; Australian Research Council Grant Number: (DE120102927 and CE110001028); National Science and Engineering Research Council of Canada Grant Number: (22R23085)

Description: 2016-06-17

Description: © The Author(s), 2017. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Fluids 2 (2017): 36, doi:10.3390/fluids2030036.

Description: There is no theoretical underpinning that successfully explains how turbulent mixing is fed by wave breaking associated with nonlinear wave-wave interactions in the background oceanic internal wavefield. We address this conundrum using one-dimensional ray tracing simulations to investigate interactions between high frequency internal waves and inertial oscillations in the extreme scale separated limit known as “Induced Diffusion”. Here, estimates of phase locking are used to define a resonant process (a resonant well) and a non-resonant process that results in stochastic jumps. The small amplitude limit consists of jumps that are small compared to the scale of the resonant well. The ray tracing simulations are used to estimate the first and second moments of a wave packet’s vertical wavenumber as it evolves from an initial condition. These moments are compared with predictions obtained from the diffusive approximation to a self-consistent kinetic equation derived in the ‘Direct Interaction Approximation’. Results indicate that the first and second moments of the two systems evolve in a nearly identical manner when the inertial field has amplitudes an order of magnitude smaller than oceanic values. At realistic (oceanic) amplitudes, though, the second moment estimated from the ray tracing simulations is inhibited. The transition is explained by the stochastic jumps obtaining the characteristic size of the resonant well. We interpret this transition as an adiabatic ‘saturation’ process which changes the nominal background wavefield from supporting no mixing to the point where that background wavefield defines the normalization for oceanic mixing models.

Description: Kurt L. Polzin gratefully acknowledges support from Woods Hole Oceanographic Institution’s Investment in Science Program (WHOI’s ISP) program. The authors gratefully acknowledge support from a collaborative National Science Foundation grant, award Nos. 1634644 (KP) and 1635866 (YVL).

Description: Author Posting. © American Meteorological Society, 2014. 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 44 (2014): 1466–1492, doi:10.1175/JPO-D-12-0154.1.

Description: Simultaneous full-depth microstructure measurements of turbulence and finestructure measurements of velocity and density are analyzed to investigate the relationship between turbulence and the internal wave field in the Antarctic Circumpolar Current. These data reveal a systematic near-bottom overprediction of the turbulent kinetic energy dissipation rate by finescale parameterization methods in select locations. Sites of near-bottom overprediction are typically characterized by large near-bottom flow speeds and elevated topographic roughness. Further, lower-than-average shear-to-strain ratios indicative of a less near-inertial wave field, rotary spectra suggesting a predominance of upward internal wave energy propagation, and enhanced narrowband variance at vertical wavelengths on the order of 100 m are found at these locations. Finally, finescale overprediction is typically associated with elevated Froude numbers based on the near-bottom shear of the background flow, and a background flow with a systematic backing tendency. Agreement of microstructure- and finestructure-based estimates within the expected uncertainty of the parameterization away from these special sites, the reproducibility of the overprediction signal across various parameterization implementations, and an absence of indications of atypical instrument noise at sites of parameterization overprediction, all suggest that physics not encapsulated by the parameterization play a role in the fate of bottom-generated waves at these locations. Several plausible underpinning mechanisms based on the limited available evidence are discussed that offer guidance for future studies.

Description: The SOFine project is funded by the United Kingdom’s Natural Environmental Research Council (NERC) (Grant NE/G001510/1). SW acknowledges the support of anARCDiscovery Early CareerResearchAward (Grant DE120102927), as well as the Grantham Institute for Climate Change, Imperial College London, and the ARC Centre of Excellence for Climate System Science (Grant CE110001028). ACNG acknowledges the support of a NERC Advanced Research Fellowship (Grant NE/C517633/1).KLP acknowledges support fromWoods Hole Oceanographic Institution bridge support funds.

Description: 2014-11-01