5 Dynamics of Large Scale Ocean Circulation George Veronis 5 1 Introduction and Summary The past 30 years have witnessed a rapid evolution of circulation theory Much of the progress can be attributed to the intuition and physical balance that have emerged from the use of simple models that isolate important processes Major contributions along these lines were made by Stommel Welander and others An excellent presentation of the ideas together with a number of significant advances appears in Stem s 1975a book More recently numerical simulations have provided a different attack on the problem Processes that are difficult to study with analytical models become accessible through the latter approach Early climatological type studies by Bryan have now been supplemented by numerical models oriented toward the isolation of the effects of individual mechanisms The papers of Rhines and Holland cited below have been especially instructive The development of the theory for the dynamics of large scale oceanic flows is very recent One has only to look at the chapter on dynamics in Sverdrup Johnson and Fleming 1942 to realize how primitive the theory was in the mid 1940s Sverdrup s 1947 important demonstration of the generation of planetary vorticity by wind stress was the first step in obtaining explicit information about oceanic flow from a simple external observable Until that time the dynamic method i e geostrophic hydrostatic balance was used to obtain flow information but this hardly constitutes a theory since one internal property must be used to determine another Ekman s 1905 theory for what we now call the Ekman layer was a significant early contribution but its application to large scale theory was not understood until Charney and Eliassen 1949 showed the coupling to large scale flows via the spin up mechanism Actually the generation of large scale flow by Ekman suction in the laboratory was observed and described by Pettersson 1931 who repeated some of Ekman s 1906 early experiments with a stratified fluid to determine the inhibition of vertical momentum transport by stratification Pettersson found the large scale circulation to be an annoying interference however in his primary objective determining vertical transfer of momentum by turbulence and he discarded the approach as unpromising Shortly after Sverdrup s paper Stommel 1948 produced the first significant closed basin circulation model showing that westward intensification of oceanic flow is due to the variation of the Coriolis parameter with latitude Hidaka 1949 proposed a closed set of equations for the circulation including the effects of lateral eddy dissipation of momentum Munk 1950 continued the development by obtaining I40 George Veronis a solution that resembled Stommel s except for details in the boundary layers near the eastern and western sides of the basin He applied his solution to an idealized ocean basin with observed wind stresses and related a number of observed oceanic gyres to the driving wind patterns The first nonlinear correction to these linearized models Munk Groves and Carrier 1950 showed that inertia shifts positive vortices to the south and negative vortices to the north Nonlinear effects thus introduce the observed north south asymmetry into a circulation pattern that is predicted by steady linear theory to be symmetric about mid latitude when the wind driving is symmetric Fofonoff 1954 approached the problem from the opposite extreme treating a completely inertial nondriven model His solution exhibits the pure effect of inertia for steady westward flows The circulation pattern is symmetric in the east west direction and closes with the center of a cyclonic anticyclonic vortex at the south north edge of the basin When linear frictional effects perturb the nonlinear pattern Niiler 1966 the center of the vortex shifts westward Niiler s model had been proposed independently by Veronis 1966b after a numerical study of nonlinear effects in a barotropic ocean and Niiler s solution had been suggested heuristically by Stommel 1965 The theoretical models leading to these results for wind driven circulation are discussed below in sections 5 5 and 5 6 More general considerations in section 5 2 based on conservation integrals for the nondissipative equations Welander 1971a prepare the way for the ordered system of quasi geostrophic equations that are presented in section 5 3 The latter are derived for a fluid with arbitrary stable stratification and for a twolayer approximation to the stratification A large portion of the remainder of the paper reports results obtained with the simpler two layer system 2 Section 5 7 concludes the discussion of simple models of steady wind driven circulation with a suggested simple explanation of why the Gulf Stream and other western boundary currents leave the coast and flow out to sea Parsons 1969 Veronis 1973a Separation of the Gulf Stream from the coast occurs within an anticyclonic gyre at a latitude where the Ekman drift due to an eastward wind stress in the interior must be returned geostrophically in the western boundary layer If the mean thermocline depth is sufficiently small i e if the amount of upper layer water is sufficiently limited the thermocline surfaces on the onshore side of the Gulf Stream and separation occurs The surfacing of the thermocline is enhanced by the poleward transport by the Gulf Stream of upper layer water that eventually reaches polar latitudes and sinks A review of models of thermohaline circulation is given in section 5 8 The open models introduced by Welander 1959 and Robinson and Stommel 1959 and the subsequent developments by them as well as other authors are described The section concludes with a description of a closed two layer model in which the heating and cooling processes are parameterized by an assumed upwelling of lower layer water across the thermocline Veronis 1978 The closure of the model leads to an evaluation of the magnitude of upwelling of 1 5 x 10 7 m s in agreement with values obtained from chemical tracers and the estimated age of deep water The normal modes for a two layer system are derived in section 5 9 and the free wave solutions are obtained for an ocean of constant depth The derivation is a generalization of the treatment by Veronis and Stommel 1956 but the method is basically the same The results include barotropic and baroclinic modes of inertiogravity and quasi geostrophic Rossby waves Brief mention is made
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