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The Wind-Driven Overturning Circulation of the World Ocean

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The Wind-Driven Overturning Circulation of the World Ocean Ocean Science Discussions, 2, 473–505, 2005 Ocean Science OSD www.ocean-science.net/osd/2/473/ Discussions SRef-ID: 1812-0822/osd/2005-2-473 2, 473–505, 2005 European Geosciences Union The wind-driven Papers published in Ocean Science Discussions are under overturning open-access review for the journal Ocean Science circulation of the World Ocean K. Do¨os¨ Title Page The wind-driven overturning circulation Abstract Introduction of the World Ocean Conclusions References Tables Figures K. Do¨ os¨ Department of Meteorology, Stockholm University, 10691 Stockholm, Sweden J I Received: 18 October 2005 – Accepted: 25 October 2005 – Published: 25 November 2005 J I Correspondence to: K. Do¨os¨ ([email protected]) Back Close © 2005 Author(s). This work is licensed under a Creative Commons License. Full Screen / Esc Print Version Interactive Discussion EGU 473 Abstract OSD The wind driven aspects of the meridional overturning circulation of the world ocean 2, 473–505, 2005 and the Conveyor Belt is studied making use of a simple analytical model. The model consists of three reduced gravity layers with an inviscid Sverdrupian interior and a The wind-driven 5 western boundary layer. The net north-south exchange is made possible by setting overturning appropriate western boundary conditions, so that most of the transport is confined to circulation of the the western boundary layer, while the interior is the Sverdrupian solution to the wind World Ocean stress. The flow across the equator is made possible by the change of potential vorticity by the Rayleigh friction in the western boundary layer, which is sufficient to permit water K. Do¨os¨ 10 and the Conveyor Belt to cross the equator. The cross-equatorial flow is driven by a weak meridional pressure gradient in opposite direction in the two layers on the equator at the western boundary. Title Page The model is applied to the World Ocean with a realistic wind stress. The amplitude of the Conveyor Belt is set by the northward Ekman transport in the Southern Ocean Abstract Introduction 15 and the outcropping latitude of the NADW. It is in this way possible to set the amount Conclusions References of NADW that is pumped up from the deep ocean and driven northward by the wind and converted in the surface layer into less dense water by choosing the outcropping Tables Figures latitude and the depth of the layers at the western boundary. The model has proved to be able to simulate many of the key features of the Conveyor Belt and the meridional J I 20 overturning cells of the World Ocean. This despite that there is no deep ocan mixing J I and that the water mass conversions in the this model are made at the surface. Back Close 1. Introduction Full Screen / Esc The meridional overturning is the most important mechanism of the world ocean to Print Version exchange mass and heat between latitudes and ocean basins. The density difference 25 between the cold and salty water of the North Atlantic and the fresher and warmer Interactive Discussion waters of the Pacific and the Indian Ocean is believed to drive the largest overturning EGU 474 cell in the ocean, known as the Conveyor belt (Broecker, 1991). The North Atlantic OSD Deep Water (NADW), which is formed by convection, constitutes the deeper part of the Conveyor Belt. The NADW travels south through the Atlantic into the Southern 2, 473–505, 2005 Ocean, where the NADW is ventilated or continues in the deep ocean into the Pacific 5 or Indian Oceans. Once the water emerges at the surface it can return to the North The wind-driven Atlantic along the upper part of the Conveyor Belt. The return route has been a subject overturning for discussion, whether the water comes mainly through the Drake Passage and then circulation of the flows north into the Atlantic along the “cold water route” (Rintoul, 1991) or goes from World Ocean the Pacific through the Indonesian Sea into the Indian Ocean around South Africa and 10 then into the Atlantic in the “warm water route” (Gordon, 1986). K. Do¨os¨ The Conveyor Belt is thus the greatest inter-ocean exchange of mass and heat. The Conveyor Belt is often presented as a fundamentally non-linear phenomenon and is driven by the high-latitude buoyancy flow to the atmosphere and by deep convection. Title Page Accordingly it has been mostly discussed diagnostically using numerical general cir- Abstract Introduction 15 culation models (GCMs) (e.g. Drijfhout, 1996; Speich et al., 2002). Such discussions cannot examine the broader aspects of the physics involved because of the complex- Conclusions References ities (numerical and geographical) of the GCM solutions. However, it is possible to Tables Figures address many (but not all) aspects of the Conveyor Belt with simple, mostly analytical, models; this is the idea behind this article. J I 20 The purpose of this study is to explore to what extent the ocean overturning circu- lation and in particular the Conveyor Belt can be explained by the wind driven ocean J I dynamics. This will be done by using an as simple wind driven model as possible but that still captures the basic overturning circulation as seen in General Circulation Back Close Models (GCMs). The key features of the Conveyor Belt which must be included are a Full Screen / Esc 25 pole-ward surface, and an equator-ward subsurface flow. The simplest model, which would include these, is a layered model. We choose a three-and-a-half layered model Print Version similar to that of Do¨os¨ (1994) and Nof (2003). This choice automatically brings some disadvantages, chief among which is the lack of thermodynamics. At first sight this Interactive Discussion may seen a telling difficulty, since deep convection, one essential component of the EGU 475 Conveyor Belt, is explicitly excluded in what is primarily a wind-driven model. Although OSD there are ad hoc methods for including thermodynamics in a layered model, these are unsatisfactory and remove the clarity sought in the first place. Accordingly, all areas 2, 473–505, 2005 where thermodynamics play a crucial role are placed logically and geographically be- 5 yond the boundaries of the model. The amplitude of the Conveyor Belt must then be The wind-driven provided for the model. overturning A description of the model is presented in Sect. 2. The model is applied to the World circulation of the Ocean together with a fine resolution primitive equation model in Sect. 3. The simula- World Ocean tion of the wind driven cells with a particular focus on the Conveyor Belt is presented 10 in Sect. 4 followed by a discussion and conclusions in Sect. 5. K. Do¨os¨ 2. The analytical model Title Page The dynamics of the model are Sverdrupian in the interior with a Stommel layer at Abstract Introduction the western boundary (Stommel, 1948). By including a western boundary layer it is Conclusions References possible to calculate net meridional transports and the corresponding meridional over- 15 turning stream function. Three reduced gravity layers are used, and an Ekman layer Tables Figures in the extra-equatorial regions. The physical model is shown in Figs. 1 and 2. The equations of motion for the Ekman layer are: J I T x −f vE = ρ0hE J I T y f uE = (1) ρ0hE Back Close 1 T W wE = ρ ∇ × f 0 Full Screen / Esc The equations of motion and the continuity equation for layer 1 are: ∂G1 Print Version −f v1 = − ∂x ∂G1 f u1 = − ∂y − Γ v1 (2) Interactive Discussion ∂u1 ∂v1 ∂w1 20 ∂x + ∂y + ∂z = 0 EGU 476 and for layer 2: OSD ∂G2 −f v2 = − ∂x 2, 473–505, 2005 ∂G2 f u2 = − ∂y − Γ v2 (3) ∂u2 ∂v2 ∂w2 ∂x + ∂y + ∂z = 0 The wind-driven overturning and for layer 3: circulation of the ∂G3 World Ocean −f v3 = − ∂x ∂G3 f u3 = − ∂y − Γ v3 (4) K. Do¨os¨ ∂u3 ∂v3 ∂w3 ∂x + ∂y + ∂z = 0 5 where for simplicity the coordinates are Cartesian here but all the calculations Title Page have been made with spherical coordinates. x is pointing eastward, y northward, Abstract Introduction f is the Coriolis parameter as a function of latitude, hn is the n-th layer’s thick- ness and G1≡γ1h1+G2, G2≡γ2 (h1+h2) +G3 and G3≡γ3 (h1+h2+h3). Γ is the bot- Conclusions References tom friction coefficient. Under the Boussinesq approximation a reference density 10 can be used in the denominator for the reduced gravity in each active layer so that Tables Figures X Y γn≡2g (ρn+1−ρn) / (ρn+1+ρn) is the reduced gravity. T and T are the zonal and W X Y meridional wind stresses and T T ,T is the wind stress vector. Layer 4 is inert J I due to our reduced-gravity assumption. J I The model is constructed in a similar way as Stommel (1948) solved the western Back Close 15 boundary current problem by separating the ocean in in a frictionless interior and a western boundary layer with linear friction. Full Screen / Esc 2.1. Interior of the ocean Print Version The dynamics are Sverdrupian in the interior of the ocean, i.e. under the Ekman layer Interactive Discussion and outside the western boundary layer, where the friction terms are small. The equa- 20 tions can here be solved using the equations for the ventilated thermocline by Luten EGU 477 et al. (1983) (hereafter denoted LPS). These solutions are presented in the Appendix. OSD The LPS theory has of course in its simplicity many limitations such as e.g.
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