ALBERT

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): 380-399, doi:10.1175/2007JPO3728.1.

Description: Barotropic to baroclinic conversion and attendant phenomena were recently examined at the Kaena Ridge as an aspect of the Hawaii Ocean Mixing Experiment. Two distinct mixing processes appear to be at work in the waters above the 1100-m-deep ridge crest. At middepths, above 400 m, mixing events resemble their open-ocean counterparts. There is no apparent modulation of mixing rates with the fortnightly cycle, and they are well modeled by standard open-ocean parameterizations. Nearer to the topography, there is quasi-deterministic breaking associated with each baroclinic crest passage. Large-amplitude, small-scale internal waves are triggered by tidal forcing, consistent with lee-wave formation at the ridge break. These waves have vertical wavelengths on the order of 400 m. During spring tides, the waves are nonlinear and exhibit convective instabilities on their leading edge. Dissipation rates exceed those predicted by the open-ocean parameterizations by up to a factor of 100, with the disparity increasing as the seafloor is approached. These observations are based on a set of repeated CTD and microconductivity profiles obtained from the research platform (R/P) Floating Instrument Platform (FLIP), which was trimoored over the southern edge of the ridge crest. Ocean velocity and shear were resolved to a 4-m vertical scale by a suspended Doppler sonar. Dissipation was estimated both by measuring overturn displacements and from microconductivity wavenumber spectra. The methods agreed in water deeper than 200 m, where sensor resolution limitations do not limit the turbulence estimates. At intense mixing sites new phenomena await discovery, and existing parameterizations cannot be expected to apply.

Description: This work was funded by the National Science Foundation as a component of the Hawaii Ocean Mixing Program. Added support for FLIP was provided by the Office of Naval Research.

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): 686-701, doi:10.1175/2007JPO3826.1.

Description: The disintegration of a first-mode internal tide into shorter solitary-like waves is considered. Since observations frequently show both tides and waves with amplitudes beyond the restrictions of weakly nonlinear theory, the evolution is studied using a fully nonlinear, weakly nonhydrostatic two-layer theory that includes rotation. In the hydrostatic limit, the governing equations have periodic, nonlinear inertia–gravity solutions that are explored as models of the nonlinear internal tide. These long waves are shown to be robust to weak nonhydrostatic effects. Numerical solutions show that the disintegration of an initial sinusoidal linear internal tide is closely linked to the presence of these nonlinear waves. The initial tide steepens due to nonlinearity and sheds energy into short solitary waves. The disintegration is halted as the longwave part of the solution settles onto a state close to one of the nonlinear hydrostatic solutions, with the short solitary waves superimposed. The degree of disintegration is a function of initial amplitude of the tide and the properties of the underlying nonlinear hydrostatic solutions, which, depending on stratification and tidal frequency, exist only for a finite range of amplitudes (or energies). There is a lower threshold below which no short solitary waves are produced. However, for initial amplitudes above another threshold, given approximately by the energy of the limiting nonlinear hydrostatic inertia–gravity wave, most of the initial tidal energy goes into solitary waves. Recent observations in the South China Sea are briefly discussed.

Description: KRH was supported by a Woods Hole Oceanographic Institution Mellon Independent Study Award and ONR Grant N000140610798.

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: Submitted in partial fulfillment of the requirements for the degree of Master of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution August 1989

Description: Given well known environmental conditions, matched field processing has been shown to be a promising signal processing technique for the localization of acoustic sources. However, when environmental data are incomplete or inaccurate, a 'mismatch' occurs between the measured field and model field which can lead to a severe degradation of the localization estimator. We investigate the possible mismatch effects of surface and internal waves on matched field processing in a shallow water waveguide. We utilize a modified ray theory, based on the work of Tindle, to calculate the acoustic pressure field. This allows us to simply incorporate range dependent environmental conditions as well as to generalize our work to deeper waveguides. In general, the conventional (Bartlett) matched field beamformer does not provide sufficient resolution to unambiguously locate a source, even in a perfectly matched environment. The maximum likelihood method (MLM) matched field beamformer has much better resolution but is extremely susceptible to mismatch. The mismatch due to surface roughness can result in a large reduction of the estimator peak. Part, but not all, of the peak can be regained by 1)using a model which includes incomplete reflection at the surface based on actual sea surface statistics and 2) short time averaging of the measured signal, with times on the order of the period of the surface waves. Mismatch due to internal waves can also result in a large degradation of the estimator. Averaging over the same time period as surface waves provides little improvement and leads one to surmise that internal waves may be a limiting constraint on matched field processing. Finally, we combine the surface and internal wave fields with a slowly moving source. This example highlights the necessity for the development of a beamformer which has a broader mainlobe while maintaining adequate sidelobe suppression, and we address this issue by looking at two such beamformers.

Description: Author Posting. © American Meteorological Society, 2012. 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 42 (2012): 1981–2000, doi:10.1175/JPO-D-12-028.1.

Description: Packets of nonlinear internal waves (NLIWs) in a small area of the Mid-Atlantic Bight were 10 times more energetic during a local neap tide than during the preceding spring tide. This counterintuitive result cannot be explained if the waves are generated near the shelf break by the local barotropic tide since changes in shelfbreak stratification explain only a small fraction of the variability in barotropic to baroclinic conversion. Instead, this study suggests that the occurrence of strong NLIWs was caused by the shoaling of distantly generated internal tides with amplitudes that are uncorrelated with the local spring-neap cycle. An extensive set of moored observations show that NLIWs are correlated with the internal tide but uncorrelated with barotropic tide. Using harmonic analysis of a 40-day record, this study associates steady-phase motions at the shelf break with waves generated by the local barotropic tide and variable-phase motions with the shoaling of distantly generated internal tides. The dual sources of internal tide energy (local or remote) mean that shelf internal tides and NLIWs will be predictable with a local model only if the locally generated internal tides are significantly stronger than shoaling internal tides. Since the depth-integrated internal tide energy in the open ocean can greatly exceed that on the shelf, it is likely that shoaling internal tides control the energetics on shelves that are directly exposed to the open ocean.

Description: This research was supported by ONR Grants N00014-05-1-0271, N00014-08-1-0991, N00014-04- 1-0146, and N00014-11-1-0194.

Description: 2013-05-01

Description: Submitted in partial fulfillment of the requirements for the degree of Master of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution August 1996

Description: A field experiment was undertaken during July and August of 1995 aimed at understanding the interaction of acoustic signals with the internal wave field off the coast of New Jersey. As part of SWARM (Shallow Water Acoustics in a Random Medium), physical data were collected in 75 m of water near 39°15.34'N, 72°56.59'W with three thermistor strings, a bottom-mounted ADCP, and yo-yo CTDs. These data spanned a two-week period of the month-long study. With the exception of a time following a storm event, during which the generation mechanism near the shelf break was effectively switched off, large-amplitude (up to 20 meters), rank-ordered groups of internal solitons were observed traveling through the region approximately every 12.4 hours. These groups of solitons progressed across the shelf with phase speeds of 61.8 ± 14.9 cm/s with a heading of 280 ± 31° T. Two-layer finite-depth theory was tested on this data and shown to consistently overpredict the phase speed of the internal solitons within each group. Predictions of horizontal scale, particle velocities, and displacements were in qualitative agreement with two-layer finite-depth dynamics.

Description: Support for this work was provided by a National Science Foundation grant OCE-9313670.

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 June 1997

Description: As part of the Shallow Water Acoustics in a Random Medium (SWARM) experiment [1], a sixteen element WHOI vertical line array (WVLA) was moored in 70 meters of water off the New Jersey coast. This array was sampled at 1395 Hz or higher for the seven days it was deployed. Tomography sources with carrier frequencies of 224 and 400 Hz were moored about 32 km shoreward, such that the acoustic path was anti-parallel to the primary propagation direction for shelf generated internal wave solitons. Two models for the propagation of normal modes through a 2-D waveguide with solitary internal wave (soliton) scattering included are developed to help in understanding the very complicated mode arrivals seen at the WVLA. The simplest model uses the Preisig and Duda [2] sharp interface approximation for solitons, allowing for rapid analysis of the effects of various numbers of solitons on mode arrival statistics. The second model, using SWARM thermistor string data to simulate the actual SWARM waveguides, is more realistic, but much slower. The analysis of the actual WVLA data yields spread, bias, wander, and intensity fluctuation signals that are modulated at tidal frequencies. The signals are consistent with predicted relationships to the internal wave distributions in the waveguides.

Description: The funds for my education were provided by the Office of Naval Research through an ONR Fellowship (MIT award 002734-001); the funds for SWARM were also provided by the Office of Naval Research through ONR Grant N00014-95-0051.

Description: Submitted in partial fulfillment of the requirements for the degree of Master of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2015

Description: The scattering of low-mode internal tides by ocean-floor topography is extensively studied through analytical models and field observations at the Line Islands Ridge (LIR). An existing Green function method is utilized to examine the generation of internal tides by idealized topographic shapes as well as realistic transects of the LIR. The method is also applied to examine the scattering of a mode-1 internal tide at these topographies to determine the relative high mode energy flux due to generated and scattered internal tides at the realistic transects. A method of determining the modal content of an internal wave field is advanced to account for arbitrary stratification and rotation. It is then adjusted to allow for image loss as is common to oceanographic studies. Its performance is compared to the existing regression method widely used by oceanographers to determine the modal content of internal tides. The results from this comparison are used to inform the analysis of the field observations. This thesis concludes by examining the modal content of the LIR as determined from measurements taken during the 150-day EXperiment on Internal Tide Scattering (EXITS) NSF field study. Motivated by satellite altimetry data and three-dimensional numerical model studies, the EXITS cruise sought to observe the internal tide scattering process in the ocean for the first time. The data from three moorings equipped with moored profilers, spanning total depths of 3000-5000 m is analyzed to determine the modal content of the southward propagating internal tide before and after it encounters the ridge for evidence of topographic scattering.

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 February, 1980

Description: The structure of the inertial peak in deep ocean kinetic energy spectra is studied here. Records were obtained from Polymode arrays deployed in the Western North Atlantic Ocean (40°W to 70°W, 15°N to 42°N). The results are interpreted both in terms of local sources and of turning point effects on internal waves generated at lower latitudes. In most of the data, there is a prominent inertial peak slightly above f; however, the peak height above the background continuum varies with depth and geographical environment. Three classes of environment and their corresponding spectra emerge from peak height variations: class 1 is the 1500 m level near the Mid-Atlantic Ridge, with the greatest peak height of 18 db; class 2 includes (a) the upper ocean (depth less than 2000 m), (b) the deep ocean (depth greater than 2000 m) over rough topography, and (c) the deep ocean underneath the Gulf Stream, with intermediate peak height of 11.5 db; class 3 is the deep ocean over smooth topography, with the lowest peak height of 7.5 db. Near f, the horizontal coherence scale is 0(60 km) at depths from 200 m to 600 m, and the vertical coherence scale is O(200 m) just below the main thermocline. A one turning point model is developed to describe inertial waves at mid-latitudes, based on the assumption that inertial waves are randomly generated at lower latitudes (global generation) where their frequency-wavenumber spectrum is given by the model of Garrett and Munk (1972 a, 1975). Using the globally valid wave functions obtained by Munk and Phillips (1968), various frequency spectra near f are calculated numerically. The model yields a prominent inertial peak of 7 db in the horizontal velocity spectrum but no peaks in the temperature spectrum. The model is latitudinally dependent: the frequency shift and bandwidth of the inertial peak decrease with latitude; energy level near f is minimum at about 30° and higher at low and high latitudes. The observations of class 3 can be well-described by the model; a low zonal wavenumber cutoff is required to produce the observed frequency shift of the inertial peak. The differences between the global generation model and the observations of class 1 and class 2 are interpreted as the effects of local sources. A locally forced model is developed based on the latitudinal modal decomposition of a localized source function. Asymptotic eigensolutions of the Laplace's tidal equation are therefore derived and used as a set of expansion functions. The forcing is through a vertical velocity field specified at the top or bottom boundaries of the ocean. For white noise forcing, the horizontal velocity spectrum of the response has an inertial peak which diminishes in the far-field. With the forcing located at either the surface or the bottom, several properties of the class 2 observations can be described qualitatively by a combination of the global and local models. The reflection of inertial waves from a turbulent benthic boundary layer is studied by a slab model of given depth. Frictional effects are confined to the boundary layer and modelled by a quadratic drag law. For given incident waves, reflection coefficients are found to be greater than 0.9 for the long waves which contain most of the energy. This result suggests that energy-containing inertial waves can propagate over great distance as is required by the validity of the model of global generation.

Description: This work was supported by the National Science Foundation through grant OCE 76-80210 and its continuation OEE 78-19833.

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 August 1982

Description: The development of nonlinear surface and internal wave groups is investigated. Surface wave evolution was observed in an unusually long wave channel as a function of steepness and group length. Dissipation and frequency downshifting were important characteristics of the long-time evolution. The amplitude and phase modulations were obtained using the Hilbert transform and specified as an initial condition to the cubic nonlinear Schrodinger equation, which was solved numerically. This equation is known to govern the slowly varying complex modulation envelope of gravity waves on deep water. When dissipation was included, the model compared quite well with the observations. Phase modulation was used to interpret the long-time behavior, using the phase evolution of exact asymptotic solutions as a guide. The wave groups exhibited a long-time coherence but not the recurrence predicted by the inviscid theory. An oceanic field study of the generation of groups of large amplitude internal waves by stratified tidal flow over a submarine ridge indicates that the large amplitude and asymmetry of the topography are critical in determining the type of flow response. The calculated Froude numbers response length scale and duration differ markedly between the two phases of the tide due to the asymmetry.

Description: Research assistantship provided by the Office of Naval Research contract no. N00014-80-C-0273