ALBERT

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 2009

Description: Observations and inverse models suggest that small-scale turbulent mixing is enhanced in the Southern Ocean in regions above rough topography. The enhancement extends 1 km above the topography suggesting that mixing is supported by breaking of gravity waves radiated from the ocean bottom. In other regions, gravity wave radiation by bottom topography has been primarily associated with the barotropic tide. In this study, we explore the alternative hypothesis that the enhanced mixing in the Southern Ocean is sustained by internal waves generated by geostrophic motions flowing over bottom topography. Weakly-nonlinear theory is used to describe the internal wave generation and the feedback of the waves on the zonally averaged flow. A major finding is that the waves generated at the ocean bottom at finite inverse Froude numbers drive vigorous inertial oscillations. The wave radiation and dissipation at equilibrium is therefore the result of both geostrophic flow and inertial oscillations and differs substantially from the classical lee wave problem. The theoretical predictions are tested versus two-dimensional and three-dimensional high resolution numerical simulations with parameters representative of the Drake Passage region. Theory and fully nonlinear numerical simulations are used to estimate internal wave radiation from LADCP, CTD and topography data from two regions in the Southern Ocean: Drake Passage and the Southeast Pacific. The results show that radiation and dissipation of internal waves generated by geostrophic motions reproduce the magnitude and distribution of dissipation measured in the region.

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 April, 1977

Description: A total of four moorings from POLYMODE Array I and II were analyzed in an investigation of internal wavefield-mean flow interactions. In particular, evidence for wave-mean flow interaction was sought by searching for time correlations between the wavefield vertically-acting Reynolds stress (estimated using the temperature and velocity records), and the mean shear. No significant stress-shear correlations were found at the less energetic moorings, indicating that the magnitude of the eddy viscosity was under 200 cm2/sec, with the sign of the energy transfer uncertain. This is considerably below the 0(4500 cm2/sec) predicted by Müller (1976). An extensive error analysis indicates that the large wave stress predicted by the theory should have been clearly observable under the conditions of measurement. Theoretical computations indicate that the wavefield "basic state" may not be independent of the mean flow as assumed by Müller, but can actually be modified by large-scale vertical shear and still remain in equilibrium. In that case, the wavefield does not exchange momentum with a large-scale vertical shear flow, and, excepting critical layer effects, a small vertical eddy viscosity is to be expected. Using the Garrett-Munk (1975) model internal wave spectrum, estimates were made of the maximum momentum flux (stress) expected to be lost to critical layer absorption. Stress was found to increase almost linearly with the velocity difference across the shear zone, corresponding to a vertical eddy viscosity of -100 cm2 s -1. Stresses indicative of this effect were not observed in the data. The only significantly non-zero stress correlations were found at the more energetic moorings. Associated with the 600 m mean velocity and the shear at the thermocline were a positively correlated stress at 600 m, and a negatively correlated stress at 1000 m. These stress correlations were most clearly observable in the frequency range corresponding to 1 to 8 hour wave periods. The internal wavefield kinetic and potential energy were modulated by the mean flow at both levels, increasing by a factor of two with a factor of ten in the mean flow. The observed stress correlations and energy level changes were found to be inconsistent with ideas of a strictly local eddy viscosity, in which the spectrum of waves is only slightly modified by the shear. When Doppler effects in the temperature equation used to estimate vertical velocity were considered, the observations of stress and energy changes were found to be consistent with generation of short (0.4 to 3 km) internal waves at the level of maximum shear, about 800 m. The intensity of the generated waves increases with the shear, resulting in an effective vertical eddy viscosity (based on the main thermocline shear) of about +100 cm2 s-1 The stresses were not observable at the 1500 m level, indicating that the waves were absorbed within 500 m of vertical travel. The tendency for internal wave currents to be horizontally anisotropic in the presence of a mean current was investigated. Using the Garrett- Munk (1975) model internal wave spectrum, it was found that critical layer absorption cannot induce anisotropies as large as observed. A mechanical noise problem was found to be the cause of large anisotropies measured with Geodyne 850 current meters. It could not be decided, however, whether or not the A.M.F. Vector Averaging Current Meter is able to satisfactorily remove the noise with its averaging scheme.

Description: The research reported here was provided by Office of Naval Research Contract Numer N00014-76-C-0197 NR 083-400.

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

Description: © 2009 The Authors. This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License. The definitive version was published in ICES Journal of Marine Science: Journal du Conseil 67 (2010): 379-394, doi:10.1093/icesjms/fsp242.

Description: In principle, measurements of high-frequency acoustic scattering from oceanic microstructure and zooplankton across a broad range of frequencies can reduce the ambiguities typically associated with the interpretation of acoustic scattering at a single frequency or a limited number of discrete narrowband frequencies. With this motivation, a high-frequency broadband scattering system has been developed for investigating zooplankton and microstructure, involving custom modifications of a commercially available system, with almost complete acoustic coverage spanning the frequency range 150–600 kHz. This frequency range spans the Rayleigh-to-geometric scattering transition for some zooplankton, as well as the diffusive roll-off in the spectrum for scattering from turbulent temperature microstructure. The system has been used to measure scattering from zooplankton and microstructure in regions of non-linear internal waves. The broadband capabilities of the system provide a continuous frequency response of the scattering over a wide frequency band, and improved range resolution and signal-to-noise ratios through pulse-compression signal-processing techniques. System specifications and calibration procedures are outlined and the system performance is assessed. The results point to the utility of high-frequency broadband scattering techniques in the detection, classification, and under certain circumstances, quantification of zooplankton and microstructure.

Description: The work was supported by the US Office of Naval Research (Grant # N000140210359).

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, 1976

Description: Measurements of horizontal and vertical current by propeller cluster current meters and temperature by thermistors mounted on a rigid array 8 m high and 20 m long moored in the oceanic main thermocline near Bermuda are interpreted in terms of thermocline-trapped internal wave modes in the presence of temperature and density fine-structure. Two turning-point uniformly valid asymptotic solutions to the internal wave equation are developed to describe the wave functions. Mode decay beyond the turning point in depth or frequency produces a sharp cutoff in vertical current spectra above the local buoyancy frequency N(z). An internal wave wavenumber-frequency spectral model Ε(α,ω) = E(ω/No)-2 (α./α0)-2 describes vertical current spectra and potential energy to horizontal kinetic energy ratios. The red wavenumer shape suppresses peaks in both these quantities at frequencies near N(z). The data are consistent with time-averaged horizontal isotropy of the wave field. A dip in the vertical current spectra at 0.5 cph not predicted by the model appears related to the bottom slope. Temperature fine-structure is modeled as a passive vertical field advected by internal waves. Quasi-permanent fine-scale features of the stratification and vertically small-scale internal waves are indistinguishable in this study. The model of McKean (1974) is generalized to include fine-structure fields specified by their vertical wavenumber spectra as well as different Poisson-distributed layer models. Together with the trapped internal wave model, moored temperature spectra, temperature vertical difference spectra, and coherence over vertical separations are described using a fine-structure vertical wavenumber spectrum PT(k) =ATk-5/2 which agrees with other spectra made using vertical profiling instruments in the range 0.1 to 1.0 cpm. Horizontal current fine-structure is also modeled as a passive field advected vertically by long internal waves. The model describes moored horizontal current spectra (least successfully at frequencies near N(z)) and finite-difference vertical shear spectra. Contours of temperature in depth versus time indicate possible mixing events. These events appear concurrently with high shear and Richardson numbers O. 25≤ R ≤ 1.0. Over 7 m a cutoff in Ri at 0.25 is observed, indicating saturation of the internal wave spectrum. Spectra of finite-difference approximations to shear and buoyancy frequency are dominated by fine-structure contributions over nearly the whole internal wave range, suggesting that breaking is enhanced by fine-structure. Breaking appears equally likely at all frequencies in the internal wave range.

Description: This research was supported by Office of Naval Research contract N00014-67-0204-0047 and continuation contract NOOOl4-75-C-0291.

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 May 1982

Description: Velocity and temperature time series from Hudson Submarine Canyon and hydrographic surveys of seven canyons of the Middle Atlantic Bight indicate that the effects of storms, tides, and incoming internal waves are intensified in submarine canyons. Storms with strong eastward and westward wind stress were found to cause strong upwelling and downwelling through the upper layers of Hudson Canyon. Storm-forced upwelling also caused strong down-canyon flows at the canyon floor. Internal waves were found to be concentrated in the canyon head and near the floor, in agreement with theoretical predictions. Slope water apparently circulates slowly through the outer part of the canyon and is mixed in near-floor layers which could be caused by breaking internal waves. Internal tides are generated at the floor in the central part of the canyon. Oscillations at tidal frequencies dominate the near-floor velocity field below the thermocline, and are accompanied by high-frequency spikes that may be nonlinear interface waves propagating on the top of the bottom mixed layer. A numerical model was used to calculate mixing in the canyon's bottom boundary layer caused by an unstable density gradient during flood tide. Energetic internal wave activity is apparently responsible for sediment sorting in the canyon head; the internal waves become more energetic as the sediment grain size increases. Below the thermocline, the tidal oscillations vary in amplitude with the phases of the moon; the observed deposition of mud can easily occur during weeks of low velocity.

Description: Foundation graduate fellowship and by the Office of Naval Research under Contracts N00014-75-C-029l and N00014-80-C-0273.

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 April, 1975

Description: This thesis reports on an investigation into the structure, energetics and propagation of tidal frequency internal waves. Data from Site D, near the New England continental slope, Muir Seamount northeast of Bermuda, and the Mid-Ocean Dynamics Experiment in the deep Sargasso Sea were used. Site D, in the near-field of a near-critical semidiurnal generation region, shows variable tidal currents and a marked surface intensification of M2 energy at the southern Site, related to the beam-like nature of the internal tide. The M2 tide dominates the semidiurnal band, with about 3 times more energy than at adjacent frequencies at 1/15 cpd separation. There is a significant phase locking between the M2 baroclinic currents and the equilibrium tide, and evidence for southward propagation of internal wave energy, suggesting generation at the slope to the north. The M2 baroclinic energy density is about 40% as great as the total barotropic energy density, but the internal tides have more horizontal kinetic energy. A seaward energy flux of .6 x 106 erg/s cm in the first three baroclinic M2 modes is much less than the .2 x 1010 erg/s cm shoreward energy flux in the surface tide. Difficul ties in interpreting the measurements are ascribed to the near-singular generation case. The MODE-l semidiurnal internal tides are also dominated by the M2 frequency, with a 3-fold energy increase over adjacent frequencies at 1/15 cpd separation. MODE-l is far from any major source of internal tides, but the measurements are much less variable than those from Site D. The extensive temperature measurements defining the MODE-l M2 internal tide are significantly coherent (phase locked) with the equilibrium tide, with about 80% of the coherent energy deriving from the first baroclinic mode, typical thermocline displacements being 3 m. A horizontal wavenumber spectrum estimate for the first mode M2 displacement fluctuations gives a peak at 160 km wavelength, in excellent agreement with the theoretical dispersion relation. The coherent first mode propagates on a bearing of 125°T, with a horizontal energy flux of .3 x 108 erg/s cm. Use of the weaker S2 internal tide and the dispersive nature of oceanic internal waves yields an estimate of 700 km to a common semidiurnal source region. The inferred range and bearing are consistent with generation at the Blake Escarpment and the continental slope to the northwest of the experiment. In one special case current and temperature measurements are combined in a local demonstration of the first mode M2 propagation, and the less extensive current data gives estimates of the barotropic tidal currents. Mooring motion, measured by pressure recorders on the mooring lines, accounts for about 15% of the semidiurnal temperature variance, but it is incoherent with the equilibrium tide. Diurnal tides were examined at all three locations. At the MODE-1 site - near the critical latitude for diurnal period internal waves - the current and temperture fields are dominated by high mode, incoherent, inertial-character morions which mask the tidal currents. About 25% of the diurnal band temperature variance is related to mooring motion. Muir Seamount provides a clear example of diurnal period internal tides trapped to their source region north of the critical latitude. A simple analytical model is developed for the diurnal period flow adjustment in a seamount geometry. Site D shows some evidence for diurnal period internal tides, but most of the energy in the diurnal currents is not simply related to the tidal forcing. Diurnal barotropic currents measured at Site D are combined with currents on the New England shelf, showing that the diurnal tidal wave behaves as a Kelvin-Stokes mode trapped to the slope, propagating along the depth contours to the west. Some aspects of simple generation models are considered. The slope north of Site D is not at all well described as an abrupt step for the M2 generations problem, but a more realistic model of Baines (1974) predicts the coherent fields observed. But the relatively small energy conversion from the surface tide to internal modes suggests that the globally near-critical slope north of Site D is a poor generator of internal tides in the deep sea, although the local energy density is high. The step shelf generation model is well suited for the steep Blake Escarpment, and predicts a seaward energy flux of .4 x 108 erg/s cm in the first mode, comparable to the measurements at MODE-1. This confirms theoretical expectations that the first baroclinic mode is not significantly damped by turbulent diffusion after propagating through the 700 km of ocean between the generation region and the MODE-1 deep ocean site.

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, 1975

Description: A set of vertical profiles of horizontal ocean currents, obtained by electro-magnetic profilers in the Atlantic Ocean southwest of Bermuda in the spring of 1973, has been analyzed in order to study the vertical structure and temporal behavior of internal waves, particularly those with periods near the local inertial period. An important feature of the observed structure is the polarization of horizontal velocity components in the vertical. This polarization, along with temporal changes of the vertical wave structure seen in a time series of profiles made at one location, has been related to the direction of vertical energy flux due to the observed waves. Whereas the observed vertical phase propagation can be affected by horizontal advection of waves past the point of observation, the use of wave polarization to infer the direction of vertical energy propagation has the advantage that it is not influenced by horizontal advection. The result shows that at a location where profiles were obtained over smooth topography, the net energy flux was downward, indicating that the energy sources for these waves were located at or near the sea surface. An estimate of the net, downward energy flux (~ .2 - .3 erg/cm2/sec) has been obtained. Calculations have been made which show that a frictional bottom boundary layer can be an important energy sink for near-inertial waves. A rough estimate suggests that the observed, net, downward energy flux coul d be accounted for by energy losses in this frictional boundary layer. A reflection coefficient for the observed waves as they reflect off the bottom has been estimated. In contrast, some profiles made over a region of rough topography indicate that the rough bottom may also be acting to generate near-inertial waves which propagate energy upward. Ca1culations of vertical flux of horizontal kinetic energy, using an empirical form for the energy spectrum of internal waves, show that this vertical flux reaches a maximum for frequencies 10% - 20% greater than the local inertial frequency. Comparison with profiler velocity data and frequency spectra supports the conclusion that the dominant waves had frequencies 10% - 20% greater than the inertial frequency. The fact that the waves were propagating energy in the vertical is proposed as the reason for the observed frequency shift. Finally, energy spectra in vertical wave number have been calculated from the profiles in order to compare the data with an empirical model of the energy density spectrum for internal waves proposed by C. Garrett and W. Munk (1975). The result shows that although the general shape and magnitude of the observed spectrum compares well with the empirica1 model, the two-sided spectrum is not symmetric in vertical wave number. This asymmetry has been used to infer that more energy was propagating downward than upward. These calculations have also been used to obtain the coherence between profiles made at the same location, but separated in time (the so-called dropped, lagged, rotary coherence). This coherence is compared with the aforementioned empirical model. The coherence results show that the contribution of the semidiurnal tide to the energy of the profiles is restricted to long vertical wave lengths.

Description: Support for the experiment which is described in this report was provided by the Office of Naval Research under contracts N00014-66-C-0241, NR 083-004 and N00014-74-C-0262, NR 083-004.