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 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: Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute and the Woods Hole Oceanographic Institution August 1975

Description: This thesis is made of two separate, but interrelated parts. In Part I the instability of a baroclinic Rossby wave in a two-layer ocean of inviscid fluid without topography, is investigated and its results are applied in the ocean. The velocity field of the basic state (the wave) is characterized by significant horizontal and vertical shears, non-zonal currents, and unsteadiness due to its westward propagation. This configuration is more relevant to the ocean than are the steady, zonal 'meteorological' flows, which dominate the literature of baroclinic instability. Truncated Fourier series are used in perturbation analyses. The wave is found to be unstable for a wide range of the wavelength; growing perturbations draw their energy from kinetic or potential energy of the wave depending upon whether the wavelength, 2πL, is much smaller or larger than 2πLρ, respectively, where Lρ is the internal radius of deformation. When the shears are comparable dynamically, L~Lρ , the balance between the two energy transfer processes is very sensitive to the ratios L/Lρ and U/C as well, where U is a typical current speed, and C a typical phase speed of the wave. For L = Lρ they are augmenting if U 〈 C, yet they detract from each other if U 〉 C. The beta-effect tends to stabilize the flow, but perturbations dominated by a zonal velocity can grow irrespective of the beta-effect. It is necessary that growing perturbations are comprised of both barotropic and baroclinic modes vertically. The scale of the fastest growing perturbation is significantly larger than L for barotropically controlled flows (L 〈 Lρ ), reduces to the wave scale L for a mixed kind (L ~ Lρ ) and is fixed slightly larger than Lρ for baroclinically controlled flows (L 〉 Lρ ). Increasing supply of potential energy causes the normalized growth rate, αL/U, to increase monotonically as L → Lρ from below. As L increases beyond Lρ, the growth rate αLρ /U shows a slight increase, but soon approaches an asymptotic value. In a geophysical eddy field like the ocean this model shows possible pumping of energy into the radius of deformation (~ 40 km rational scale, or 250 km wavelength) from both smaller and larger scales through nonlinear interactions, which occur without interference from the beta-effect. The e-folding time scale is about 24 days if U = 5 cm/sec and L = 90 km. Also it is strongly suggested that, given the observed distribution of energy versus length scale, eddy-eddy interactions are more vigorous than eddy-mean interaction, away from intènse currents like the Gulf Stream. The flux of energy toward the deformation scale, and the interaction of barotropic and baroclinic modes, occur also in fully turbulent 'computer' oceans, and these calculations provide a theoretical basis for source of these experimental cascades. In Part II an available potential energy (APE) is defined in terms appropriate to a limited area synoptic density map (e.g., the 'MODE-I' data) and then in terms appropriate to time-series of hydrographic station at a single geographic location (e. g., the 'Panulirus' data). Instantaneously the APE shows highly variable spatial structure, horizontally as well as vertically, but the vertical profile of the average APE from 19 stations resembles the profile of vertical gradient of the reference stratification. The eddy APE takes values very similar to those of the average kinetic energy density at 500 m, 1500 m and 3000 m depth in the MODE area. In and above the thermocline the APE has roughly the same level in the MODE area (centered at 28°N, 69° 40'W) as at the Panulirus station (32° 10'N, 64° 30'W), yet in the deep water there is significantly more APE at the Panulirus station. This may in part indicate an island effect near Bermuda.

Description: This research has been supported by the National Science Foundation grant IDO 73-09737, formerly GX-36342.

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 2007

Description: Oceanic spreading centers are sites of magmatic, tectonic, and hydrothermal processes. In this thesis I present experimental and seismological constraints on the evolution of these complex regions of focused crustal accretion and extension. Experimental results from drained, triaxial deformation experiments on partially molten olivine reveal that melt extraction rates are linearly dependent on effective mean stress when the effective mean stress is low and non-linearly dependent on effective mean stress when it is high. Microearthquakes recorded above an inferred magma reservoir along the TAG segment of the Mid-Atlantic Ridge delineate for the first time the arcuate, subsurface structure of a long-lived, active detachment fault. This fault penetrates the entire oceanic crust and forms the high-permeability pathway necessary to sustain long-lived, high-temperature hydrothermal venting in this region. Long-lived detachment faulting exhumes lower crustal and mantle rocks. Residual stresses generated by thermal expansion anisotropy and mismatch in the uplifting, cooling rock trigger grain boundary microfractures if stress intensities at the tips of naturally occurring flaws exceed a critical stress intensity factor. Experimental results coupled with geomechanical models indicate that pervasive grain boundary cracking occurs in mantle peridotite when it is uplifted to within 4 km of the seafloor. Whereas faults provide the high-permeability pathways necessary to sustain high-temperature fluid circulation, grain boundary cracks form the interconnected network required for pervasive alteration of the oceanic lithosphere. This thesis provides fundamental constraints on the rheology, evolution, and alteration of the lithosphere at oceanic spreading centers.

Description: Research was funded by a MIT Presidential Fellowship and NSF grants OCE-0095936, OCE-9907224, OCE-0137329, OCE-6892222, and OCE-6897400.

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, 1978

Description: A two-layer linear analytic model is used to study the response of the mid-latitude ocean to the seasonal variation of the windstress. The most important component of the response is a barotropic quasi-steady Sverdrup balance. A meridional ridge such as the Antilles Arc is modeled as an infinitely thin meridional barrier that blocks the lower layer but does not protrude into the upper layer. It is found that such a barrier has little effect on the upper layer flow across the barrier. This result is obtained provided the frequency of the motion is low enough so that free short Rossby waves are essentially nondivergent. In this case there is little coupling between the layers for energy propagating to the east away from the barrier. A study of the dynamics of flow over a sloping bottom is made and the results are used to determine the effect on seasonal oscillations of eastern boundary slopes and triangular ridges. It is found that the presence of a slope at the eastern boundary has little effect. A meridional ridge that does not reach the interface may cause substantial scattering of free Rossby waves, but unless the ridge is steep its effect on the quasi-steady Sverdrup balance is minimal. However, if the ridge height is a substantial fraction of the lower layer depth and the width is comparable to the scale of free short Rossby waves, the ridge will tend to block flow in the lower layer, acting like the infinitely thin barrier. The theory suggests that the Antilles Arc should have the effect of a thin barrier, while the Mid-Atlantic Ridge should have little effect on the response of the ocean to seasonal wind variations.

Description: For three and a half years of generous financial support I am grateful to the John and Fannie Hertz Foundation, from which I received a Graduate Fellowship. Research money and other support were provided by the National Science Foundation under contract OCE 77 15600.

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, 1978

Description: A linearized theory for the response of a circular pendulum spar in 2-dimensional waves and a uniform current is developed. The linear forces on the cylinder are predicted using an approximate potential flow theory for slender bodies. The dynamic equations are then amended to account for the wake effects of viscous bluff body flow by including a quadratic drag law and neglecting wave damping. A spectral model for the forces on a cylinder due to an oscillating wake, modeling the force as a frequency modulation process, is proposed. The non-linear equations of motion which result are then solved, assuming constant force coefficients, by linearization for use with a Gaussian random sea. The method of equivalent linearization is extended to include mean flow effects and a spatially distributed process. Some numerical experiments are then used to test the performance of the linearization. For a variety of environments, the linearization predicts the standard deviation of the simulation response to within 10% and the mean angle of inclination to within 30%. Results of the numerical experiments indicate that there is significant variation (order of magnitude changes) in both response and mean angle of inclination. Thus, significant changes are followed by the linearization. A laboratory experiment was carried out to test the linearized spar model in a realistic fluid environment. Only the low Keulegan Carpenter number regime was investigated. With some minimal manipulations, good agreement is obtained between the experiment and the linearized estimates. It appears that the drag coefficients for vortex induced in-line forces may be an order of magnitude larger than those reported in the literature, .5 instead of .06, and that the shedding of vortices due to steady flow may reduce the added mass coefficient significantly, as observed in oscillating flows with significant vortex shedding.

Description: The National Science Foundation provided tuition and stipend support under an NSF Graduate Fellowship for three years. I was fortunate to have been selected by the Board of Trustees of the Naval Postgraduate School Foundation as the first recipient of the Carl E. Menneken Fellowship for Scientific Research, which provided partial support during 1976-77.

Description: Submitted in partial fulfillment of the requirements for the Degree of Doctor of Philosophy at the Woods Hole Oceanographic Institution and the Massachusetts Institute of Technology April 1979

Description: Observational work by Thompson (1977) and others has demonstrated that free topographic Rossby waves propagate northward up the continental rise south of New England. To study the dynamical implications of these waves as they approach the shelf, Beardsley, Vermersch, and Brown conducted an experiment in 1976 (called NESS76) in which some moored instruments were strategically placed across the New England continental margin to measure current, temperature, and bottom pressure for about six months. An analytical model has been constructed to study the propagation of free topographic Rossby waves in an infinite wedge filled with a uniformly stratified fluid. The problem is found after some coordinate transformations to be identical to the corresponding surface gravity wave problem in a homogeneous fluid, but with the roles of the surface and bottom boundaries interchanged. Analytical solutions are thus available for both progressive and trapped waves, forming continuous and discrete spectra in the frequency space. The separation occurs at a nondimensional frequency δ = S, defined as (N/f) tanθ*, where N and f are the Brunt-Väisälä and inertial frequencies, and tanθ* is the bottom slope. Since an infinite wedge has no intrinsic length scales, the only relevant nondimensiona1 parameters are the frequency δ and the Burger number S. Thus, stratification and bottom slope play the same dynamical role, and the analysis is greatly simplified. Asymptotic solutions for the progressive waves have been obtained for both the far field and small S which enable us to examine the parameter dependence of some of the basic wave properties in the far field, and the spatial evolution of the wave amplitude and phase as they approach the apex when S is small. The general solution is then presented and discussed in some detail. The eigenfrequencies of the trapped modes decrease when S decreases and reduce to the short wave limit of Reid's (1958) second class, barotropic edge waves when S approaches zero. The modal structure broadens as S increases to some critical value above which no such coastally-trapped modes exist. To simulate more closely the dynamical processes occurring near the continental margin, a numerical model incorporating a more realistic topography than an infinite wedge has been constructed. With stratification imposing an additional harrier, the model suggests that the maximum energy flux transmission coefficient obtained in Kroll and Niiler's barotropic model (1976) is likely an upper bound. Also in the presence of the finite slope changes, the baroclinic fringe waves generated near the slope-rise junction may form an amphidromic point at some mid-depth and locally reverse the direction of the phase propagation above it. These baroclinic fringe waves also cause an offshore heat flux over the continental rise which, combined with the onshore heat flux generated over the slope region in a frictionless model, induces, across the transect, a mean flow pattern of two counter-rotating gyres with downwelling occurring near the slope-rise junction. Bottom friction always generates an offshore heat flux and therefore modifies this mean flow pattern over the slope region. The induced longshore mean flow is approximately geostrophically balanced and generally points to the left facing the shoreline, but its direction can be reversed where the baroclinic fringe waves dominate. The mean thermal wind relation implies a generally denser slope water than that farther offshore. Some of the model predictions are compared with the data taken from NESS76. The comparisons are generally consistent, suggesting that topographic Rossby wave dynamics may play an important role for the low frequency motions near continental margins.

Description: This work is supported at Woods Hole Oceanographic Institution by the National Science Foundation under grant numbers OCE 76-0l813 and OCE 78-19513.

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 September 2007

Description: Surfzone wave height transformation and wave-breaking-driven increases in the mean sea level (setup) are examined on alongshore-uniform beaches with alongshore homogeneous and inhomogeneous wave forcing. While previously derived models predict wave heights adequately (root-mean-square errors typically less than 20%), the models can be improved by tuning a free parameter or by using a new parameterization based on the deep-water wave height. Based on a sensitivity analysis of the cross-shore momentum balance used to predict setup, a one-dimensional (1-D) model is developed that includes wave rollers and bottom stress owing to the mean offshore-directed flow. The model predicts setup accurately at three alongshore homogeneous field sites, as well as at a site where the incident wave field is alongshore non-uniform, suggesting that setup is driven primarily by the cross-shore (1-D) forcing. Furthermore, alongshore gradients of setup can be important to driving alongshore flows in the surfzone, and the 1-D setup model predicts these gradients accurately enough to simulate the observed flows.

Description: I would like to thank the National Science Foundation (OCE-0622844), the Office of Naval Research (G000783, G000782, N00014-99-10193, N00014-02- 10145), the MIT/WHOI Academic Programs Office, and the MIT Presidential Graduate Fellowship Program for their generous support of my research.

Description: Submitted in partial fulfillment of the requirements for the degree of Oceanographic Engineer at the Woods Hole Oceanographic Institution and the Massachusetts Institute of Technology and for the degree of Master of Science in Ocean Engineering at the Massachusetts Institute of Technology February 1979

Description: The development and application of an autonomous field instrumentation system consisting of four current meters and four wave gauges, along with a field monitor and digital recorder, is documented. The flow sensors are electromagnetic current meters, which employ the principle of electromagnetic induction to sense an induced electrical potential from the flow of water through an imposed magnetic field. The 10 cm diameter, discus-shaped sensor was tested in the laboratory under a wide variety of conditions, including both steady and oscillatory flow tests. The results of these tests indicate an excellent response in terms of linearity and horizontal cosine. The vertical cosine response is close to ideal in the region of ±30°, but beyond a negative angle of attack of approximately -30° the response is compromised by the onset of separation under dominantly steady flow conditions. The wave gauges are surface-piercing digital sensors, relying on the presence or absence of water at 128 individual sensing electrodes spaced 1.5 cm apart along the front surface of the wave gauge. On command, the instantaneous water surface elevation is measured, then telemetered digitally to the shorebased monitor and recorder. Field measurements of waves and currents at four stations across the width of the surf zone were made, using this system at a beach along the southern coast of Maine. Spilling breakers (approximately 1.0 m in height with an angle at breaking of about 8°), translated across the 30 m surf zone, generated an observed net longshore current during the four hour measurement period. The subsequently analyzed data from this experiment showed a strong longshore current which varied across the width of the surf zone, having a maximum of about 15 cm/ sec just inside the breaker line. A net offshore current was observed at all four stations, and averaged approximately 10 cm/sec to 15 cm/sec. Using a simplified force balance model for the generation of longshore currents on a plane, uniform beach, the data was further analyzed to investigate the validity and parameterization of the momentum flux forces and bottom friction forces within the surf zone. There was an observed shoreward loss in momentum flux across the width of the surf zone, from about -150,000 dynes/cm outside the breakers to near zero close to the shoreward extent of the surf zone. The computed friction coefficient from the balancing longshore current-induced bottom friction was found to be relatively unstable during periods of changing wave and current conditions, but was observed to be between 0.10 and 0.15 during more stable conditions.

Description: The support of the NOAA Sea Grant Program through the MIT Sea Grant Program, along with the MIT/WHOI Joint Research Seed Funds is acknowledged.

Description: Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Woods Hole Oceanographic Institution February 1980

Description: The existence of resonant, baroclinic, equatorially-trapped inertia-gravity waves (discovered by Wunsch and Gill (1976)) is confirmed in the mid-Pacific by spectral analysis of long sea level records. The energy of the low-mode inertia-gravity waves is found to decrease toward the meridional boundaries. A simple spectral model, acknowledging the dispersive characteristics of the equatorial waves, adequately reproduces the observed mid-Pacific sea level spectra in the 1-6 day band. Model spectra computed at latitudes outside the equatorial waveguide of the gravest meridional modes suggest the presence of "inertial" peaks in several observed sea level spectra. Resonant, low-mode inertia-gravity waves may also exist in the Indian Ocean. Sea level fluctuations along the Pacific equator are found to have Kelvin wave characteristics in the 35-80 day band, and, in particular, propagation from the western Pacific to the coast of South America is observed. The Kelvin waves are atmospherically-forced in the central- western Pacific and have a computed equivalent depth corresponding to the first-baroc1inic mode. Outside of the equatorial mid-Pacific, a non-static ocean response to air pressure in the 4-6 day band is dominated by a basin-wide, barotropic, planetary mode. The low Q of this mode suggests that the ocean is viscous with respect to large-scale barotropic oscillations. The dynamical components of the observed long-period tides have been isolated for the first time using the "self-consistent" equilibrium tide of Agnew and Farrell (1978). The tides are slightly non-equilibrium with large horizontal scales. The relatively short-scale Rossby modes predicted by Wunsch (1967) are not observed, perhaps because of the poor spatial coverage of the dataset. Considering the low Q of the 4-6 day planetary basin mode, it is suggested that the long-period tides are frictionally-controlled. The 4- and 5-day equatorial inertia-gravity waves, the 35-80 day Kelvin waves and the 4-6 day planetary basin mode are clearly atmospherically forced, and, perhaps surprisingly, they are forced by atmospheric waves that have similar horizontal structures, i.e., 4-5 day Rossby-gravity waves, 40-50 day Kelvin waves and a 5-day global barotropic mode. The surface expressions of these atmospheric waves are determined in order to understand the nature of the oceanic response, e.g., resonant or forced. Much of the information about the surface atmospheric fields that has been collected, including frequency-wavenumber descriptions, awaits an accurate model of the coupling between wind stress and internal ocean waves.

Description: Monetary support for this research was provided by the National Science Foundation through contract OCE73-0l384. At various times, tuition and living expenses were paid by funds from the NSF contract above, the Office of Naval Research (contract N00014-C-75-029l), the Cecil and Ida Green Professorship in Earth Sciences, the J. P. Luther Educational Fund and by an M.I.T. Educational Tuition Award.

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 December 1997

Description: A new tomographic technique is employed to investigate the structure and dynamics of the Pacific upper mantle. We invert band-center travel times of ScS reverberations and frequency-dependent travel times of direct S phases, upper-mantle guided waves such as SS and SSS, and the R1 and G1 surface waves for the 2D composite structure in the plane of two Pacific corridors. The frequency-dependent travel times of the turning and surface waves are measured from all three components of ground motion as phase delays relative to a radially-anisotropic, spherically-symmetric oceanic mantle model, and their 2D Fréchet kernels are constructed by a coupled-mode algorithm. The travel times of the primary ScSn and sScSn phases and their first-order reverberations from the 410 and 660 discontinuities are measured as individual phases and the 2D Fréchet kernels for these band-limited signals are calculated using the paraxial ray approximation. The model parameters include shear-speed variations throughout the mantle, perturbations to radial shear-wave anisotropy in the uppermost mantle, and the topography of the 410 and 660 discontinuities. We construct vertical tomograms through two mantle corridors: one between the Tonga subduction zone and Oahu, Hawaii, which traverses the central Pacific Ocean; and the other between the Ryukyu subduction zone and Oahu, which samples the northern Philippine Sea, the western Pacific, and the entire Hawaiian swell. Tests demonstrate that the data sets for the two corridors resolve the lateral structure in the upper mantle with a scale length of a few hundreds kilometers and greater but that the resolving power decreases rapidly in the lower mantle. The model for the Tonga-Hawaii corridor reveals several interesting features, the most significant being a regular pattern of high and low shear velocities in the upper mantle between Tonga and Hawaii. These variations, which are well resolved by the data set, have a horizontal wavelength of 1500 km, a vertical dimension of 700 km, and an amplitude of about 3%, and they show a strong positive correlation with seafloor topography and geoid-height variations along this corridor. The geoid highs correspond to a series of northwest-trending swells associated with the major hotspots of the Society, Marquesas, and Hawaiian Islands. Where these swells cross the corridor, they are underlain by high shear velocities throughout the uppermost mantle, so it is unlikely that their topography is supported by thermal buoyancy. This result is substantiated by the model from the Ryukyu-Hawaii corridor, which exhibits a prominent, fast region that extends beneath the entire Hawaiian swell. This anomaly, which resides in the uppermost 200-300 km of the mantle, is also positively correlated with the undulations of the Hawaiian-swell height. The other dominant features in the Ryukyu-Hawaii model include the high-velocity subducting slabs beneath the Ryukyu and Izu-Bonin seismic zones, which extend throughout the entire upper mantle; a very low-velocity in the uppermost 160 km of the mantle beneath the northern Philippine Sea, which is ascribed to the presence of extra water in this region; and a pronounced minimum in the amount of radial anisotropy near Hawaii, which is also seen along the Tonga-Hawaii corridor. A joint inversion of the data from the two corridors reveals the same anomaly pattern and clearly demonstrates that the swells in the Central Pacific are underlain by fast velocities. It is therefore implied that the topography of the swells in the central Pacific is supported by a chemical buoyancy mechanism which is generated by basaltic volcanism and the formation of its low-density peridotitic residuum. While the basaltic depletion mechanism can produce high shear velocities in the uppermost 200 km, it cannot explain the depth extent of the fast anomalies beneath the swells which, along Tonga-Hawaii corridor, extend well into the transition zone. It is therefore hypothesized that the central Pacific is underlain by a system of convective rolls that are confined above the 660-km discontinuity. It is likely that these rolls are predominantly oriented in the direction of plate motion (like "Richter rolls ") but the limited depth of the fast anomaly beneath the Hawaiian swell (200-300 km) suggests that their pattern is probably more complicated. Nevertheless, this convection pattern appears to be strongly correlated with the locations of the Tahitian, Marquesan, and Hawaiian hotspots, which raises interesting questions for Morgan's hypothesis that these hotspots are the surface manifestations of deep-mantle plumes.

Description: This research was supported by the National Science Foundation under grant EAR- 9628351 and by the Defense Special Weapons Agency under grant DSW A-F49620-95-1- 0051.

Description: Submitted in partial fulfillment of the requirements of the degree of Master of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution June 2004

Description: Laterally extensive, well-developed clinoforms have been mapped in Early Cretaceous deposits located in the northeastern 27,000 km2 of the Colvile Basin, North Slope of Alaska. Using public domain 2-D seismic data, well logs, core photographs, and grain size data, depositional geometries within the Nanushuk and Torok formations were interpreted in order to constrain the transport conditions associated with progradation of the shoreline and construction of the continental margin out of detritus shed from the ancestral Brooks Range. Using STRATA, a synthetic stratigraphic modeling package, constructional clinoform geometries similar to those preserved in the North Slope clinoform volume (32,400 km3) were simulated. Sediment flux, marine and nonmarine diffusivities, and basin subsidence were systematically varied until a match was found for the foreset and topset slopes, as well as progradation rates over a 6 milion year period. The ability of STRATA to match the seismically interpreted geometries allows us to constrain measures of possible water and sediment discharges consistent with the observed development of the Early Cretaceous c1inoform suite. Simulations indicate that, in order to reproduce observed geometries and trends using constant input parameters, the subsidence rate must be very small, only a fraction of the most likely rate calculated from the seismic data. Constant sediment transport parameters can successfully describe the evolution of the prograding margin only in the absence of tectonic subsidence. However, further work is needed to constrain the absolute magnitude of these values and determine a unique solution for the NPR-A clinoforms.

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, 1976

Description: Two numerical applications of two-level quasigeostrophic theory are used to investigate the interrelationships of the mean and mesoscale eddy fields in a closed-basin ocean model. The resulting techniques provide a more accurate description of the local dynamics, origins, and parametric dependences of the eddies than that available in previous modelling studies. First, we propose a novel and highly efficient quasigeostrophic closed-domain model which has among its advantages a heightened resolution in the boundary layer regions. The pseudospectral method, employing an orthogonal expansion in Fourier and Chebyshev functions, relies upon a discrete Green's function technique capable of satisfying to spectral accuracy rather arbitrary boundary conditions on the eastern and western (continental) walls. Using this formulation, a series of four primary numerical experiments tests the sensitivity of wind-driven single and double-gyred eddying circulations to a transition from free-slip to no-slip boundary conditions. These comparisons indicate that, in the absence of topography, no-slip boundaries act primarily to diffuse vorticity more efficiently. The interior transport fields are thus reduced by as much as 50%, but left qualitatively unchanged. In effect, once having separated from the western wall, the internal jet has no know1edge, apart from its characteristic flow speed, of the details of the boundary layer structure. Next, we develop a linearized stability theory to analyze the local dynamic processes responsible for the eddy fields observed in these idealized models. Given two-dimensional (x, z) velocity profiles of arbitrary horizontal orientation, the resulting eigenfunction problems are solved to predict a variety of eddy properties: growth rate, length and time scales, spatial distribution, and energy fluxes. This simple methodology accurately reproduces many of the eddy statistics of the fully nonlinear fields; for instance, growth rates of 10-100 days predicted for the growing waves by the stability analysis are consistent with observed model behavior and have been confirmed independently by a perturbation growth test. Local energetic considerations indicate that the eddy motions arise in distinct and recognizable regions of barotropic and baroclinic activity. The baroclinic instabilities deîend sensitively on the vertical shear which must exceed 0(5 cm sec-1) across the thermocline to induce eddy growth. As little as a 10% reduction in |uz|, however, severely suppresses the cascade of mean potential energy to the eddy field. In comparison, the barotropic energy conversion process scales with the horizontal velocity shear, |uy|, whose threshold values for instability, a (2 x 10-6 sec-1), is undoubtedly geophysically realizable. A simple scatter diagram of |uy| versus |uz| for all the unstable modes studied shows a clear separation between the regions of barotropic and baroclinic instability. While the existence of baroclinic modes can be deduced from either time mean or instantaneous flow profiles, barotropic modes cannot be predicted from mean circulation profiles (in which the averaging process reduces the effective horizontal shears). Finally, we conduct a separate set of stability experiments on analytically generated jet profiles. The resulting unstable modes align with the upper level velocity maxima and, although highly sensitive to local shear amplitude, depend much less strongly on jet separation and width. Thus, the spatial and temporal variability of the mesoscale statistics monitored in the nonlinear eddy simulations can be attributed almost entirely to time-dependent variations in local shear strength. While these results have been obtained in the absence of topography and in an idealized system, they yet have strong implications for the importance of the mid-ocean and boundary layer regions as possible eddy generation sites.

Description: This research has been made possible by National Science Foundation grant OCE74-03001 A03, formerly DES73-00528, and the National Science Foundation funded National Center for Atmospheric Research.

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 October, 1971

Description: The objective of this study was to describe the mechanics of wind wave generation and spectral development. Intermittency, high frequency microstructure in wind and wave fields, and strong nonlinear coupling involving a wide range of scales are shown to be crucial elements in the transfer of momentum to, from, and within the wave field. None of these elements are included in available theories. Measurements of wave height and of the turbulent atmospheric and subsurface boundary layers were made, from a small surface following platform and from a stable 38.5m spar buoy. The structure of moving gust patterns (cat's paws) is described and related to the generation of surface waves. Results from this and other background studies are then applied to a discussion of spectral growth during a two day period of active wave generation. Cat's paws contain 'bursts' of intense turbulent stress and buoyancy fluctuations separated by quiescent 'intervals'. There is a difference of over three orders of magnitude in fluctuation strength between these features. Rapid growth rate generation of high frequency surface waves and atmospheric turbulence occurs during the bursts. The resultant microscale components aid the growth of lower frequency instabilities by strong nonlinear coupling between scales of motion and by acting as drag or roughness elements. Evidence of strong coupling between frequency bands and of weakly resonant capillary-gravity wave interactions is presented. Thermal stratification has a strong influence on fluctuation magnitude and can delay the onset of surface wave generation. Major spectral growth is highly unsteady. Much of the momentum flux from air to sea occurs during intermittent events that are similar in nature to cat's paws, and goes directly into high frequency waves. The bursts occur predominantly over large groups of surface waves and involve strong nonlinear interactions between media and frequency bands. The long-term equilibrium balance between wind and water is disrupted by variations in surface currents. There are 'critical' wind speeds characterized by anomalous relationships between parameters of the predominantly logarithmic velocity profile.

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 January, 1971

Description: Observations of the ocean in the vicinity of Bermuda on two different occasions show systematic distortions of the isotherms close to the island and an area of intensive mixing on the northern coast. Two mechanisms are investigated and each produces some agreement with data from different flow regimes. Firstly, the island is modeled as a circularly symmetric obstacle with steep sides and a small aspect ratio. A steady, rotating, and stratified flow which, far from the island, is uniform in the horizontal and a linear function of the vertical coordinate is taken to be flowing past the island. Neglecting circulation effects, the problem is solved to first order in a small parameter, α, which measures the steepness of the island and a small Rossby number, ε. This allows a calculation of the depth contours of isotherms to 0(ε2,εα). For one set of data the flow is such that the slope effect of 0(εα) predominates while for another period of observation both slope and Rossby number influences are of the same magnitude. In both cases qualitative agreement between fact and theory is remarkably good. In addition, it is shown that the north slope (for a west-east current) is the most favored area for mixing as there the Richardson number is a minimum and the flow is most likely to separate from the boundary. A second means of producing isotherm distortion and mixing areas close to the island concerns the nonlinear effects of shoaling internal gravity waves. For normal incidence on a two-dimensional beach the Reynolds stresses produced by the fundamental wave motion are shown to force a mean Eulerian current which is equal hut opposite in sense to the Stokes drift. This causes the mean Lagrangian current to vanish so that the physical constraint that there be no net motion of fluid particles along isopycnals into the beach is satisfied. In addition, isotherms are distorted in a fashion analogous to the surface set-down produced by shoaling surface waves. The mean isopycnal shift can be as much as 10m where the theory has some validity. Distortions of the predicted form are observed in the data from a period when the mean currents were small. Consideration of the oblique incidence problem shows that this generalization has little effect on the expected magnitude of the shifts but that a significant longshore current can be forced by the breaking of the waves.

Description: This study was supported by the Office of Naval Research under contracts Nonr 1841(74) and Nonr 3963(31) with the Massachusetts Institute of Technology. Additional support came from the National Science Foundation in the form of a summer fellowship and computer time under contract NSF GJ-133 with the Woods Hole Oceanographic Institution.

Description: The purpose of this paper is to discuss the nature of the electrical field induced in the ocean by particular types of velocity distribution. It is believed that these examples will be helpful in the interpretation of measurements by towed electrodes in the sea. The electrical field induced by waves and tidal streams, originally predicted by Faraday (1832), was first measured experimentally by Young, Gerrard and Jevons (1920), who used both moored and towed electrodes in their observations. Recently, the technique of towed electrodes has been developed by von Arx (1950, 1951) and others into a useful means of detecting water movements in the deep ocean. While the method has been increasingly used, the problem of interpreting the measurements in terms of water movements has become of great importance. Two of the present authors have made theoretical studies (Longuet-Higgins 1949, Stommel 1948) dealing with certain cases of velocity fields, and Malkus and Stern (1952) have proved some important integral theorems. There seems, however, to be a need for a more extended discussion of the principles underlying the method, and for the computation of additional illustrative examples. This is all the more desirable since some of the theoretical discussions published previously have been misleading.

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.