The quasi-geostrophic equations (QGE) are usually discretized in space by the finite difference method. The finite element (FE) method, however, offers several advantages over the finite difference method, such as the easy treatment of complex boundaries and a natural treatment of boundary conditions [Myers1995]. Despite these advantages, there are relatively few papers that consider the FE method applied to the QGE. Most FE discretizations of the QGE have been developed for the streamfunction-vorticity formulation. The reason is simple: The streamfunction-vorticity formulation yields a second order \\emph{partial differential equation (PDE)}, whereas the streamfunction formulation yields a fourth order PDE. Thus, although the streamfunction-vorticity formulation has two variables ($q$ and $\\psi$) and the streamfunction formulation has just one ($\\psi$), the former is the preferred formulation used in practical computations, since its conforming FE discretization requires low-order ($C^0$) elements, whereas the latter requires a high-order ($C^1$) FE discretization. We present a conforming FE discretization of the QGE based on the Argyris element and we present a two-level FE discretization of the Stationary QGE (SQGE) based on the same conforming FE discretization using the Argyris element. We also, for the first time, develop optimal error estimates for the FE discretization QGE. Numerical tests for the FE discretization and the two-level FE discretization of the QGE are presented and theoretical error estimates are verified. By benchmarking the numerical results against those in the published literature, we conclude that our FE discretization is accurate. �Furthermore, the numerical results have the same convergence rates as those predicted by the theoretical error estimates. / Ph. D.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Meteorology and Physical Oceanography, 1982. / Microfiche copy available in Archives and Science / Bibliography: leaves 228-233. / Lynne D. Talley. / Ph.D.

Thesis (S.M.)--Joint Program in Physical Oceanography (Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences; and the Woods Hole Oceanographic Institution), 2012. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 121-123). / Interactions between the ocean circulation in sub-ice shelf cavities and the overlying ice shelf have received considerable attention in the context of observed changes in flow speeds of marine ice sheets around Antarctica. Modeling these interactions requires parameterizing the turbulent boundary layer processes to infer melt rates from the oceanic state at the ice-ocean interface. Here we explore two such parameterizations in the context of the MIT ocean general circulation model coupled to the z-coordinates ice shelf cavity model of Losch (2008). We investigate both idealized ice shelf cavity geometries as well as a realistic cavity under Pine Island Ice Shelf (PIIS), West Antarctica. Our starting point is a three-equation melt rate parameterization implemented by Losch (2008), which is based on the work of Hellmer and Olbers (1989). In this form, the transfer coefficients for calculating heat and freshwater fluxes are independent of frictional turbulence induced by the proximity of the moving ocean to the fixed ice interface. More recently, Holland and Jenkins (1999) have proposed a parameterization in which the transfer coefficients do depend on the ocean-induced turbulence and are directly coupled to the speed of currents in the ocean mixed layer underneath the ice shelf through a quadratic drag formulation and a bulk drag coefficient. The melt rate parameterization in the MITgcm is augmented to account for this velocity dependence. First, the effect of the augmented formulation is investigated in terms of its impact on melt rates as well as on its feedback on the wider sub-ice shelf circulation. We find that, over a wide range of drag coefficients, velocity-dependent melt rates are more strongly constrained by the distribution of mixed layer currents than by the temperature gradient between the shelf base and underlying ocean, as opposed to velocity-independent melt rates. This leads to large differences in melt rate patterns under PIIS when including versus not including the velocity dependence. In a second time, the modulating effects of tidal currents on melting at the base of PIIS are examined. We find that the temporal variability of velocity-dependent melt rates under tidal forcing is greater than that of velocity-independent melt rates. Our experiments suggest that because tidal currents under PIIS are weak and buoyancy fluxes are strong, tidal mixing is negligible and tidal rectification is restricted to very steep bathymetric features, such as the ice shelf front. Nonetheless, strong tidally-rectified currents at the ice shelf front significantly increase ablation rates there when the formulation of the transfer coefficients includes the velocity dependence. The enhanced melting then feedbacks positively on the rectified currents, which are susceptible to insulate the cavity interior from changes in open ocean conditions. / by Véronique Dansereau. / S.M.

Thesis: Ph. D., Joint Program in Physical Oceanography (Massachusetts Institute of Technology, Department of Earth, Atmospheric, and Planetary Sciences; and the Woods Hole Oceanographic Institution), 2014. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 155-162). / This work concerns the nitrogen fixation and abundance of Trichodesmium colonies in the western subtropical-tropical North Atlantic and their connections with physical processes. Data were collected in fall 2010 and spring 2011, primarily using the Video Plankton Recorder (VPR). A data processing procedure for estimating the abundance of rare taxa was devised to take advantage of the accuracy of manual classification and the effort savings of automatic classification. The procedure entails selecting a subset of the original dataset, classifying it with automated software, and then manually correcting each classification. The method was validated through comparisons with fully classified VPR data and with abundance data based on microscopic enumeration on preserved samples. Correlations of Trichodesmium colony abundance with the eddy field emerged in two subsets of the VPR observations. In fall 2010, local maxima in abundance were observed in a series of cyclones. We hypothesized Ekman transport convergence/ divergence in cyclones/anticyclones as a driving mechanism. We investigated the process using idealized three-dimensional models of buoyant colonies in eddies. Elevated abundances in anticyclones in spring 2011 were correlated with anomalously fresh water, suggesting riverine input as a driver of the relationship. Finally, we evaluated the hypothesis of Davis and McGillicuddy (2006) that Trichodesmium nitrogen fixation in the North Atlantic may be underestimated by conventional sampling methods, based on their VPR observations of higher than expected colony abundances at depth in the subtropical North Atlantic. A bio-optical model was developed based on carbon-normalized nitrogen fixation rates measured in fall 2010 and spring 2011 and used to estimate nitrogen fixation over the VPR transects. Estimates of abundance and nitrogen fixation were similar in magnitude and vertical and geographical distribution to estimates compiled in a database by Luo et al. (2012). In the mean, VPR-based estimates of volume-specific nitrogen fixation rates at depth in the tropical North Atlantic were not inconsistent with estimates derived from conventional sampling methods. Based on this analysis, if Trichodesmium nitrogen fixation is underestimated, it is unlikely that it is attributable to underestimation of deep colony abundances due to mechanical disturbance during net-based sampling. / by Elise Marie Black Olson. / Ph. D.

Thesis (Ph. D.)--Joint Program in Physical Oceanography (Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences; and the Woods Hole Oceanographic Institution), 2009. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 219-222). / Interaction between the Antarctic Circumpolar Current and the continental slope/shelf in the Marguerite Bay and west Antarctic Peninsula is examined as interaction between a wind-driven channel flow and a zonally uniform slope with a bay-shaped shelf to the south. Two control mechanisms, eddy advection and propagation of topographic waves, are identified in barotropic vortex-escarpment interactions. The two mechanisms advect the potential vorticity (PV) perturbations in opposite directions in anticyclone-induced interactions but in the same direction in cyclone-induced interactions, resulting in dramatic differences in the two kinds of interactions. The topographic waves become more nonlinear near the western(eastern if in the Northern Hemisphere) boundary of the bay, where strong cross-escarpment motion occurs. In the interaction between a surface anticyclone and a slope penetrating into the upper layer in a two-layer isopycnal model, the eddy advection decays on length scales on the order of the internal deformation radius, so shoreward over a slope that is wider than the deformation radius, the wave mechanism becomes noticeably significant. It acts to spread the cross-isobath transport in a much wider range while the transport directly driven by the anticyclone is concentrated in space. A two-layer wind-driven channel flow is constructed to the north of the slope in the Southern Hemisphere, spontaneously generating eddies through baroclinic instability. A PV front forms in the first layer shoreward of the base of the topography due to the lower-layer eddy-slope interactions. / (cont.) Perturbed by the jet in the center of the channel, the front interacts with the slope/shelf persistently yet episodically, driving a clockwise mean circulation within the bay as well as crossisobath transport. Both the transports across the slope edge and out of the bay are comparable with the maximum Ekman transport in the channel, indicative of the significance of the examined mechanism. The wave-boundary interaction identified in the barotropic model is found essential for the out-of-bay transport and responsible for the heterogeneity of the transport within the bay. Much more water is transported out of the bay from the west than from the east, and the southeastern area is the most isolated region. These results suggest that strong out-of-bay transport may be found near the western boundary of the Marguerite Bay while the southeastern region is a retention area where high population of Antarctic krill may be found. / by Yu Zhang. / Ph.D.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Meteorology, 1981. / Microfiche copy available in Archives and Science. / Bibliography: leaves 210-215. / by William Roy Young. / Ph.D.

Thesis. 1975. Ph.D.--Massachusetts Institute of Technology. Dept. of Meteorology. / Vita. / Bibliography: leaves 122-129. / by Harry Leonard Bryden, Jr. / Ph.D.

Thesis. 1978. Ph.D.--Massachusetts Institute of Technology. Dept. of Meteorology. / Microfiche copy available in Archives and Science. / Bibliography: p. 239-241. / Ph.D.

Thesis. 1975. Ph.D.--Massachusetts Institute of Technology. Dept. of Meteorology. / Vita. / Bibliography: leaves 170-173. / Ph.D.

Thesis. 1977. Ph.D.--Massachusetts Institute of Technology. Dept. of Meteorology. / Microfiche copy available in Archives and Science. / Vita. / Bibliography : p. [323-328]. / Ph.D.