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 September 1994

Description: The thesis addresses the applicability of traditional hydraulic theory to an unstable, mid-latitude jet where the only wave present is the Rossby wave modified by shear. While others (Armi 1989, Pratt 1989, Haynes et al.1993 and Woods 1993) have examined specific examples of shear flow "hydraulics", my goal was to find general criteria for the types of flows that may exhibit hydraulic behavior. In addition, a goal was to determine whether a hydraulic mechanism could be important if smaller scale shear instabilities were present. A flow may exhibit hydraulic behavior if there is an alternate steady state with the same functional relationship between potential vorticity and streamfunction. Using theorems for uniqueness and existence of two point boundary value problems, a necessary condition for the existence of multiple states was established. Only certain flows with non-constant, negative dQ(ψ)/dψ have alternate states. Using a shooting method for a given transport and a given smooth relationship between potential vorticity and streamfunction, alternate states are found over a range of beta. Multiple solutions arise at a pitchfork bifurcation as a stability parameter is raised above the stability threshold determined by the necessary condition for instability. The center branch of the pitchfork is unstable to the gravest mode, while the two outer branches do not even have discrete modes. Other pitchfork bifurcations occur as higher meridional modes become unstable. Again, the inner branch is unstable to the next gravest mode, while the outer branches do not support this discrete mode. These results place the barotropic instability problem into a large set of nonlinear systems described by bifurcation theory. However, if the eastward transport across the channel is large enough, the normal modes may stabilize and these waves have a phase speed less than the minimum velocity of the flow. In this case, the flow is analogous to sub-critical hydraulic flow. The establishment of these states and the nature of transitions between them is studied in the context of an initial value problem, solved numerically, in which the zonally uniform jet is forced to adjust to the sudden appearance of an obstacle. The time-dependent adjustment of an initially stable flow exhibits traditional hydraulic behavior such as control and influence in the far-field. However, if the flow is unstable, the instability dominates the evolution. If the topographic slope renders the flow more unstable than the ambient flow, then the resulting adjustment can be understood as a local instability. The thesis has established a connection between hydraulic adjustment and the barotropic instability of the flow. Both types of dynamics arise from adjustments among multiple equilibria in an unforced, inviscid fluid.

Description: This research was supported by National Science foundation grants OCE 91-15359 and OCE 89-16446, and also by a Department of Defense AASERT grant administered under ONR N00014-89-J-1182.

Description: Author Posting. © American Geophysical Union, 2004. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 109 (2004): C10S04, doi:10.1029/2003JC001997.

Description: Data from near-bottom instruments reveal that the mechanisms responsible for generating bottom stresses and resuspending sediment over the shelf and slope off of Lake Superior's Keweenaw peninsula exhibit distinct seasonal variations. Notably, near-bottom flows over the slope are persistently weak (〈10 cm s−1) during summer but frequently attain high speeds, in excess of 20 cm s−1, in autumn and winter. During the intense storms of autumn and winter the generation of bottom stress is enhanced by the action of near-bottom orbital velocities due to surface waves. Even at 90-m depth, orbital velocities can increase bottom stress by a factor of up to 20% during storms. Where the seasonal thermocline intersects the lake floor, bottom stress is also considerably enhanced, often by more than a factor of 2, by high-frequency motions in the internal wave band. Over the Keweenaw slope, sediment resuspension is largely confined to autumn and winter episodes of high bottom stress. Our analysis indicates that this resuspended material tends to be carried offshore, a phenomenon that is partly due to the coincidence of the direction of the buoyancy-driven component of the Keweenaw Current with downwelling favorable alongshore winds. As a result of this coincidence, currents and bottom stresses tend to be greater during periods of downwelling, as opposed to upwelling, circulation. A potential challenge to modeling storm-driven resuspension in the study region is indicated by observations that the minimum stress required for resuspension may vary significantly with time over the autumn and winter.

Description: The work described was part of the Keweenaw Interdisciplinary Transport Experiment in Superior funded by the National Science Foundation through grants 9712889 to J. Churchill and A.Williams and 9712871 to E. Ralph.

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 1991

Description: Using a semi-geostrophic, reduced gravity thin jet model, we analytically study the evolution of initial meanders into pinched-off rings. The model used is similar to the path equation developed by Flierl and Robinson {1984) for vertically coherent meanders. However, in the present model, the meanders are baroclinic, and a stretching term arises due to the motion of the interface. It can be shown that the equation governing the time-dependent meander of this jet (Pratt, 1988) can be transformed into the Modified Korteweg- deVries (MKdV) equation in intrinsic coordinates. The MKdV equation admits two types of solitary wave solutions, loop solitons and breathers. The breathers are permanent meanders which propagate on the path , and some are able to form rings. Using the inverse scattering transform , we can predict breather and ring formation for simple initial meanders. The inverse scattering t ransform is applied to S and Ω shaped meanders with piecewise constant and continuous curvature. S shaped meanders, or steps, must be multi-valued to form breathers, and must have very steep angles in order to form rings. Due to integral constraints, Ω shaped meanders, or lobes, are unable to pinch together to form rings unless they are wide enough so that the two side flanks of the lobe act as two independent steps. The numerical solutions indicate that the breathers predicted by the inverse scattering is a very good approximation to the full solution.

Description: This work has been supported by NSF contract number OCE 89-16446 and ONR contract number N00014-S9-J-1182.