ing a horizontal cell But the leeward piling up of water is the same in the two cases Returning to the problem at high latitudes we note first that the analysis given above must be supplemented by the remaining dynamic balances The reader is referred to Veronis 1973a for the details for the wind driven model The qualitative discussion given here is simpler and clearer than in the original paper The first problem is that the Sverdrup transport for the interior vanishes with kV x and without adding to the simple argument there is no way of supplying warm water to the north of the latitude 40 N in the North Atlantic where the curl vanishes Second even supposing that warm water has somehow been supplied to the north the Sverdrup transport there is northward kiV x 0 so the southward return of the flow by a western boundary current would require that the thermocline be deeper on the western side of the boundary layer That is not possible with the boundary current in mid ocean Both of these issues can be resolved by considering what happens even farther to the north where warm water flows northward and impinges on the northern boundary In the real ocean and in a model including thermal driving Veronis 1978 this water will sink and give rise to a deep circulation and an overturning cell In a wind driven model the water travels counterclockwise as an isolated warm boundary current and rejoins the stream at the point of separation In the analysis given above this recirculating current represents an excess transport in the separated boundary current Because its transport does not depend on local winds it can transport water past the latitude of vanishing wind stress curl and supply warm water to the interior at high latitudes When it is included in the analysis a revised longitude for the separated boundary current is obtained The calculation which can be made consistent and quanitative for both the winddriven model and the one including thermal driving is contained in the two papers cited above The path of the separated Gulf Stream is reproduced in figure 5 8 It is especially interesting to note that the vestigial current in the northeastern corner of the basin corresponds to the Norwegian Current the Alaskan Current in the Pacific and that its transport is important for the separation of the Gulf Stream and also for the determination of the longitude of the current after it has separated The analysis leading to the separation of the Gulf Stream from the coast is contained in a quasi geostrophic model by Parsons 1969 It was derived independently by Veronis 1973a as part of a study of the circulation of the World Ocean The extension poleward of the latitude where the wind stress curl vanishes is contained in the latter paper Kamenkovich and Reznik 1972 included a bottom friction analy 70 60 50 40 I 30 20 10 I 8 I I 10 20 I I I 30 40 50 Figure 5 8 The path solid curve of the Gulf Stream after it has separated from the coast from a reduced gravity model by Veronis 1973a The zonal wind stress that drives the system is taken from observations and has zero curl at 40 N The Norwegian Current is the narrow jet in the northeast The dashed curve is the prediction for an isolated anticyclonic wind gyre Parsons 1969 The latter solution cannot be extended north of the latitude of zero wind stress curl Axes are latitude and longitude sis of the deep circulation induced by the separated current All of the above make use of a steady linear quasigeostrophic model and it is certain that the details e g the longitude of the separated current will be altered when a more complete dynamic model is used The key elements of the argument however are the geostrophic balance of downstream velocity in the western boundary current the Ekman wind drift and a limited amount of upper layer water As long as a different dynamic model does not drastically change those three features they are pretty rugged and can withstand a lot of battering the moje complicated dynamics can be incorporated to change the details of the results leaving the main argument unchanged By the same token the present analysis suggests that an explanation of the separation of western boundary currents from the coast must necessarily include the surfacing of the thermocline with a possible mixed layer at the surface Western boundary currents can be forced out to sea between wind driven gyres of opposite sign but that occurs at low latitudes as well where the phenomenon is qualitatively different because the thermocline does not surface In addition the argument given here depends on properties of global scale A more precise dynamic treatment based on local properties can lead to a better understanding of the detailed mechanistic balances of the separated current but the cause of separation seems to be based on global properties 5 8 Thermohaline Circulation The physical processes that are involved in the formation of the thermocline have been studied as a separate part of the general circulation The models incorporate geostrophic dynamics and steady convection I58 George Veronis view of the earlier papers is given by Veronis 1969 The variables u v and p are given in terms of P by 5 104 to 5 106 These can be substituted in 5 108 of density the latter often including vertical dif Though the analyses sometimes make use of plane the scales are really global and spherica dinates are more appropriate The real difficult3 nonlinearity in the convection of density an turns out the limited successes of the analyse been achieved as often in the spherical systen the P plane None of the nonlinear investigation a closed basin though a single eastern boun sometimes included A closed two layer basin i to give w in terms of P and the continuity equation then yields Needler s pressure equation K sin 4 cos 4 PzzPzzzz Pzz P P P PZ Pzz a x a x able see section 5 8 2 cot4PP 5 8 1 Continuous Models for an Open Basin where K 2fKa 2 Welander 1959 1971b defined the variable The starting point for these studies is the sir set of equations in spherical coordinates M 1 OP 5 104 a a cos4 O 1 0P aP a 04 f w X 0 dA sin cos M z K a xo coto MxMzzz 0 5 110 so that P Mz to obtain the simpler equation 5 105 5 105 a fu P dz a 2f sin 5 109 5 111 Pm By integrating 5 104 from to 0 and settingP 0 z 0 it is easy to see that Mif is the geostrophic wind v cos a cosz 0 driven meridional transport between and 0 and beU ap V Op ap 0K2P 5108 low level z P 0 4 z 0 means that the reference az aZ2 a
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