ALBERT

Description: Submitted in partial fulfillment of the requirements for the degree of Doctor of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution August, 1977

Description: Stimulated by new evidence from both "in situ" oceanic observations and results from numerical modelling, a laboratory study of quasigeostrophic flow and turbulence in a rotating homogeneous fluid has been undertaken. Two dimensional turbulence driven by a uniform distribution of sources and sinks which oscillate in time, can be fairly well reproduced in this context. Inertial time scales are about ten times smaller than Ekman spinup time, and typical Reynolds numbers read 2000. The observations emphasize the spectral tendency of the energy containing eddies. The case of no topography is first discussed. In steadily forced turbulence, it is observed that the energy containing scale is significantly larger than the forcing scale. In the decaying stage the red cascade is observed and rates of interaction are measured. Theoretical arguments for both behaviors are presented; the former concerning the forced turbulence case is believed to be new. The forcing is next applied over various large scale topographies, modelling the geophysical beta effect. The polar beta plane geometry preserves the above spectral characteristics but at the same time introduces anisotropy into the flow pattern. A broad westward mean flow develops in the north and is surrounded by a belt of cyclones lying on its southward side. The calculated second-order Eulerian mean flows induced by steadily and uniformly forced Rossby waves in a long zonal channel, exhibit much of the same momentum distribution in the inertial regime. In contrast, the "sliced cylinder" geometry which possesses no closed geostrophic contours drastically modifies the above picture. Both mean flow production and a large scale tendency for the eddies are inhibited. The geographical distribution of the eddy intensities and scales is now wildly inhomogeneous. The second aspect of this work is a study of the interaction of Rossby waves with mean flows. A zonally traveling, forced wave is generated near the southern boundary of a polar beta plane. Due to energy radiation in the free interior and (or) potential vorticity mixing by the finite amplitude waves, a westward zonal flow develops. The effect of the mean flow upon the forced steady waves is to weaken the anticyclones and intensify the cyclones. Pressure time series reveal a growth of harmonics and general spectral broadening as the waves travel freely inwards, suggesting active nonlinear interactions. An experimental test of Rhines' (1977) potential vorticity mixing theory is also presented at free latitudes. The decay period when the driving is suppressed shows that a net transfer from the waves to the mean flow kinetic energy occurs. Connection with hydrodynamic stability theory is discussed. Interaction of Rossby waves with an externally generated westward mean flow allows one to make a controlled study of the critical layer problem. For small amplitude waves, the mean flow is accelerated in the entire region between the forcing and the critical latitude which acts as a wall for mean wave momentum. In nonlinear runs the steady profile of the westward flow indicates that an accelerating force is acting everywhere, revealing the increasing transmission of wave momentum through the critical layer. At the same time, pressure measurements near the critical point show considerable fine structure developing over a long time scale. The third part deals with steady isolated source-sink flows in the sliced cylinder geometry. The response of the fluid to a meridionally oriented steady dipole extends exclusively westward of the forcing. The viscously balanced solutions are discussed and relevance to oceanic abyssal circulation is emphasized. With strong driving, the combination of a cyclone to the north and an anticyclone to the south is absolutely stable although the reverse configuration is not. A connection with a certain class of free, steady, isolated, inertial solutions developed recently by Stern (1976) is made.

Description: The DGRST . (FRACE) and the Joint Program in Oceanography, Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution offered a fellowship for the first two years. The National Science Foundation under Grant OCE75-2l 674 and the Office of Naval Research under Contract N00014-74-C0262-NR-083-004 supported this study for the final two years.

Description: Interannual sea surface height variations in the Atlantic Ocean are examined from 10 years of high-precision altimeter data in light of simple mechanisms that describe the ocean response to atmospheric forcing: 1) local steric changes due to surface buoyancy forcing and a local response to wind stress via Ekman pumping and 2) baroclinic and barotropic oceanic adjustment via propagating Rossby waves and quasi-steady Sverdrup balance, respectively. The relevance of these simple mechanisms in explaining interannual sea level variability in the whole Atlantic Ocean is investigated. It is shown that, in various regions, a large part of the interannual sea level variability is related to local response to heat flux changes (more than 50% in the eastern North Atlantic). Except in a few places, a local response to wind stress forcing is less successful in explaining sea surface height observations. In this case, it is necessary to consider large-scale oceanic adjustments: the first baroclinic mode forced by wind stress explains about 70% of interannual sea level variations in the latitude band 18°–20°N. A quasi-steady barotropic Sverdrup response is observed between 40° and 50°N.

Description: The differences between the interdecadal variability under mixed and constant flux boundary conditions are investigated using a coarse-resolution ocean model in an idealized flat-bottom single-hemisphere basin. Objective features are determined that allow one type of oscillation to be distinguished versus the other. First, by performing a linear stability analysis of the steady state obtained under restoring boundary conditions, it is shown that the interdecadal variability under constant flux and mixed boundary conditions arises, respectively, from the instability of a linear mode around the mean stratification and circulation and from departure from the initial state. Based on the budgets of density variance, it is shown next that the two types of oscillations have different energy sources: Under the constant-flux boundary condition (the thermal mode), the downgradient meridional eddy heat flux in the western boundary current regions sustains interdecadal variability, whereas under mixed boundary conditions (the salinity mode), a positive feedback between convective adjustment and restoring surface heat flux is at the heart of the existence of the decadal oscillation. Furthermore, the positive correlations between temperature and salinity anomalies in the forcing layer are shown to dominate the forcing of density variance. In addition, the vertical structure of perturbations reveals vertical phase lags at different depths in all tracer fields under constant flux, while under mixed boundary conditions only the temperature anomalies show a strong dipolar structure. The authors propose that these differences will allow one to identify which type of oscillation, if any, is at play in the more exhaustive climate models.