5Dynamics ofLarge-ScaleOcean CirculationGeorge Veronis5.1 Introduction and SummaryThe past 30 years have witnessed a rapid evolution ofcirculation theory. Much of the progress can be attrib-uted to the intuition and physical balance that haveemerged from the use of simple models that isolateimportant processes. Major contributions along theselines were made by Stommel, Welander, and others.An excellent presentation of the ideas together with anumber of significant advances appears in Stem's(1975a) book. More recently numerical simulationshave provided a different attack on the problem. Proc-esses that are difficult to study with analytical modelsbecome accessible through the latter approach. Early,climatological-type studies by Bryan have now beensupplemented by numerical models oriented towardthe isolation of the effects of individual mechanisms.The papers of Rhines and Holland cited below havebeen especially instructive.The development of the theory for the dynamics oflarge-scale oceanic flows is very recent. One has onlyto look at the chapter on dynamics in Sverdrup, John-son, and Fleming (1942) to realize how primitive thetheory was in the mid-1940s. Sverdrup's (1947) impor-tant demonstration of the generation of planetary vor-ticity by wind stress was the first step in obtainingexplicit information about oceanic flow from a simpleexternal observable. Until that time the dynamicmethod (i.e., geostrophic-hydrostatic balance) wasused to obtain flow information, but this hardly con-stitutes a theory since one internal property must beused to determine another.Ekman's (1905) theory for what we now call theEkman layer was a significant early contribution, butits application to large-scale theory was not understooduntil Charney and Eliassen (1949) showed the couplingto large-scale flows via the spin-up mechanism. Ac-tually, the generation of large-scale flow by Ekmansuction in the laboratory was observed and describedby Pettersson (1931), who repeated some of Ekman's(1906) early experiments with a stratified fluid to de-termine the inhibition of vertical momentum transportby stratification. Pettersson found the large-scale cir-culation to be an annoying interference, however, inhis primary objective, determining vertical transfer ofmomentum by turbulence, and he discarded the ap-proach as unpromising.Shortly after Sverdrup's paper Stommel (1948) pro-duced the first significant, closed-basin circulationmodel showing that westward intensification ofoceanic flow is due to the variation of the Coriolisparameter with latitude. Hidaka (1949) proposed aclosed set of equations for the circulation including theeffects of lateral (eddy) dissipation of momentum.Munk (1950) continued the development by obtainingI40George Veronis---a solution that resembled Stommel's except for detailsin the boundary layers near the eastern and westernsides of the basin. He applied his solution to an ideal-ized ocean basin with observed wind stresses and re-lated a number of observed oceanic gyres to the drivingwind patterns. The first nonlinear correction to theselinearized models (Munk, Groves and Carrier, 1950)showed that inertia shifts positive vortices to the southand negative vortices to the north. Nonlinear effectsthus introduce the observed north-south asymmetryinto a circulation pattern that is predicted by steadylinear theory to be symmetric about mid-latitude whenthe wind driving is symmetric.Fofonoff (1954) approached the problem from the op-posite extreme, treating a completely inertial, non-driven model. His solution exhibits the pure effect ofinertia for steady westward flows. The circulation pat-tern is symmetric in the east-west direction and closeswith the center of a cyclonic (anticyclonic) vortex atthe south (north) edge of the basin. When linear, fric-tional effects perturb the nonlinear pattern (Niiler,1966), the center of the vortex shifts westward. Niiler'smodel had been proposed independently by Veronis(1966b) after a numerical study of nonlinear effects ina barotropic ocean, and Niiler's solution had been sug-gested heuristically by Stommel (1965).The theoretical models leading to these results forwind-driven circulation are discussed below in sections5.5 and 5.6. More general considerations in section 5.2,based on conservation integrals for the nondissipativeequations (Welander, 1971a), prepare the way for theordered system of quasi-geostrophic equations that arepresented in section 5.3. The latter are derived for afluid with arbitrary stable stratification and for a two-layer approximation to the stratification.' A large por-tion of the remainder of the paper reports results ob-tained with the simpler two-layer system.2Section 5.7 concludes the discussion of simplemodels of steady, wind-driven circulation with a sug-gested simple explanation of why the Gulf Stream andother western boundary currents leave the coast andflow out to sea (Parsons, 1969; Veronis, 1973a). Sepa-ration of the Gulf Stream from the coast occurs withinan anticyclonic gyre at a latitude where the Ekmandrift due to an eastward wind stress in the interiormust be returned geostrophically in the westernboundary layer. If the mean'thermocline depth is suf-ficiently small, i.e., if the amount of upper-layer wateris sufficiently limited, the thermocline surfaces on theonshore side of the Gulf Stream and separation occurs.The surfacing of the thermocline is enhanced by thepoleward transport by the Gulf Stream of upper-layerwater that eventually reaches polar latitudes and sinks.A review of models of thermohaline circulation isgiven in section 5.8. The open models introduced byWelander (1959) and Robinson and Stommel (1959) andthe subsequent developments by them as well as otherauthors are described. The section concludes with adescription of a closed, two-layer model in which theheating and cooling processes are parameterized by anassumed upwelling of lower-layer water across thethermocline (Veronis, 1978). The closure of the modelleads to an evaluation of the magnitude of upwellingof 1.5 x 10- 7m s-, in agreement with values obtainedfrom chemical tracers and the estimated age of
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