EBUS Summer School 2019 LAZAR

Paradoxes and overlooked constraints of the dynamics and thermodynamics of EBUS Alban Lazar july 2019 ICTP Trieste !1 high frequency circulation low frequencies: common large spatial patterns… of SST variance low frequencies: common large spatial patterns… of SST variance which constrain explains these pattern ? SST intra-seasonal variability (Diakhaté et al. 2015) interannual climate variability (Kushnir 2003) bioactivity (Seawifs) mixed layer minima (De Boyer et al. 2004) Ekman vertical pumping CCM error maps (Richter, Xie 2008) Modelling large scale vertical velocities model : Nemo config : ORCA025-G70 – (DRAKKAR reference simulation) horizontal resolution: from 27 km (1/4° at equator) to 12 km (Arctic) vertical resolution : 46 levels, spaced from 6 m (surface) to 250 m (bottom) average 1980-2004 Questions - outline I. vertical velocity at low frequency: What determine vertical movements within and below the Ekman layer? In an upwelling, is the Ekman velocity really upwards? How is its surface mass divergence balanced is geostrophic ﬂow divergent? What is behind the Sverdrup integral balance? II. Control of the sea surface temperature in a large upwelling system Various variabilities Are surface temperature always cooled by upwelling? How much salinity may controls the mixed layer and its temperature? 200 10. THE WIND-DRIVEN CIRCULATION defined above which, for convenience, τ by focusing on the transport properties F we write out in component form here: of the layer by integrating vertically across it. As in Section 7.4, we split the flow 1 ∂p 1 ∂τ fv + = x ; into geostrophic and ageostrophic parts. − ρ ∂x ρ ∂z With given by Eq. 10-2, the ageostrophic ref ref F (10-3) component of Eq. 7-25 is 1 ∂p 1 ∂τy fu + = . ρref ∂y ρref ∂z 1 ∂τ f z uag = . (10-4) Equation 10-3 describes the balance of × ρref ∂z forces in the directly wind-driven circula- ! tion, but it does not yet tell us what that Multiplying Eq. 10-4 by ρref and integrating circulation is. The stress at the surface is across the layer from the surface where τ = τ , to a depth z = δ, where τ = 0 known—it is the wind stress, τwind, plot- wind − ted in Fig. 10.2—but we do not know the (see Fig. 10.4) we obtain: vertical distribution of stress beneath the f z M = τ(z = 0) = τ , surface. The wind stress will be communi- × Ek wind cated downward by turbulent, wind-stirred motions confined to the near-surface layers where ! of the ocean. The direct influence of wind- 0 forcing decays with depth (rather rapidly, MEk = ρref uagdz in a few tens of meters or so, depending "δ − on wind strength)What so thatdetermine by the vertical time movements a within and below the Ekman layer? depth z = δ has been reached, the stress is the lateral mass transport over the layer. − has vanished, τ = 0, as sketched in Fig. 10.4.EkmanNoting pumping that z z MEk = MEk, we may × × − rearrange10.1. THE WIND STRESS the AND EKMAN above LAYERS to give:201 As discussed in Chapter 7, thistau is the Ekman y (left). We have# just seen that the Ekman$ layer. transport is directed to the right of the wind!Ekman and hence! there will(vertically be a mass flux integrated) transport directed inward (as marked by the broad Conveniently, we can bypass the need to open arrows in the figure), leadingτ to con- z M divergence vergence into the center. Sincewind the mass Dek Ek flux acrossM the sea surface= is zero (neglect- × . (10-5) ing evaporationEk and precipitation, which, know the detailed vertical distribution of as discussed in Chapter 11, are typicallyf (upwelling regime) 1 1my− ), water cannot accumulate in the ± steady state, and so it must be driven down into the interior. Conversely, the cyclonic patternEkman of wind stress sketchedcurrents in Fig. 10.6 horizontal! divergence FIGURE 10.5. The mass transport of the Ekman (right) will result in a mass flux directed out- layer is directed to the right of the wind in the northern ward from the center, and therefore water hemisphere (see Eq. 10-5). Theory suggests that hori- will begenerates drawn up from below. downward vertical velocities zontal currents, uag, within the Ekman layer spiral with If the wind stress pattern varies in space depth as shown. (or, more precisely, as we shall see, if the wind stress has some ‘‘curl’’) it will there- Since z is a unit๏ vector in pointing an vertically upwellingfore result state, in vertical motionwind across driven the currents subtract mass, upwards, we see that the mass transport base of the Ekman layer. The flow within of the Ekman! layercorresponding is exactly to the right the Ekman initially layer is convergent to downward in anti- vertical velocity Wwind (!) of the surface wind (in the northern hemi- cyclonic flow and divergent in cyclonic sphere). Eq. 10-5 determines MEk, which flow, as sketched in Fig. 10.6. The conver- depends only on τwind and f. But Eq. 10-5 gent flow drives downward vertical motion does not predict typical velocities or bound- (called Ekman pumping); the divergent flow ary layer depths that๏ dependwhen on the detailssteadydrives state upward vertical is motionreached, from beneath sea surface is stable, of the turbulent boundary layer. A more (called Ekman suction). We will see that it complete analysis (carried out by Ekman, is this pattern of vertical motion from the 1 <=> W + W = 0 (boundary condition : z=0) 1905 ) shows that the horizontal velocitywindbase of surfaceEk Ekman layers that brings vectors within the layer trace out a spiral, as the interior of the ocean into motion. But shown in Fig. 10.5. Typically δ 10 100 m. ≃ − first let us study Ekman pumping and suc- So the direct effects of the wind are confined tion in isolation, in a simple laboratory z to the very surface of the ocean. experiment. 10.1.2. Ekman pumping and suction and GFD Lab XII: Ekman pumping and suction GFD Lab XII x The mechanism by which the wind drives (N.H.) Imagine a wind stress blowing over the ocean circulation through the action of northern hemisphere ocean with the general Ekman layers can be studied in a simple anticyclonic pattern sketched in Fig. 10.6 laboratory experiment in which the cyclonic 1 Vagn Walfrid Ekman (1874–1954), a Swedish physical oceanographer, is remembered for his studies of wind-driven ocean currents. The role of Coriolis forces in the wind-driven layers of the ocean was first suggested by the great Norwegian explorer Fridtjof Nansen, who observed that sea ice generally drifted to the right of the wind and proposed that this was a consequence of the Coriolis force. He suggested the problem to Ekman—at the time a student of Vilhelm Bjerknes—who, remarkably, worked out the mathematics behind what are now known as Ekman spirals in one evening of intense activity. FIGURE 10.4. The stress at the sea surface, τ(0) = τ , the wind stress, diminishes to zero at a depth z = δ. wind − The layer directly affected by the stress is known as the Ekman layer. 200 10. THE WIND-DRIVEN CIRCULATION defined above which, for convenience, τ by focusing on the transport properties F we write out in component form here: of the layer by integrating vertically across it. As in Section 7.4, we split the flow 1 ∂p 1 ∂τ fv + = x ; into geostrophic and ageostrophic parts. − ρ ∂x ρ ∂z With given by Eq. 10-2, the ageostrophic ref ref F (10-3) component of Eq. 7-25 is 1 ∂p 1 ∂τy fu + = . ρref ∂y 204ρref ∂z 10. THE WIND-DRIVEN CIRCULATION1 ∂τ f z uag = . (10-4) Equation 10-3 describes the balance of × ρref ∂z forces in the directly wind-driven circula- ! tion, but it does not yet tell us what that Multiplying Eq. 10-4 by ρref and integrating circulation is. The stress at the surface is across the layer from the surface where τ = τ , to a depth z = δ, where τ = 0 known—it is the wind stress, τwind, plot- wind − ted in Fig. 10.2—but we do not know the (see Fig. 10.4) weFIGURE obtain: 10.10. A schematic showing midlatitude westerlies (eastward wind stress) and tropical easterlies vertical distribution of stress beneath the (westward stress) blowing over the ocean. Because surface. The wind stress will be communi- f z MEkthe= Ekmanτ(z = transport0) = τ iswind to, the right of the wind in × the northern hemisphere, there is convergence and cated downward by turbulent, wind-stirred downward Ekman pumping into the interior of the motions confined to the near-surface layers where ! ocean. Note that the sea surface is high in regions of of the ocean. The direct influence of wind- convergence.0 forcing decays with depth (rather rapidly, MEk = ρref uagdz We can obtain a simple expression for in a few tens of meters or so, depending "δ the pattern− and magnitude of the Ekman on wind strength)What so thatdetermine by the vertical time movements a within and below the Ekman layer? depth z = δ has been reached, the stress is the lateral masspumping/suction transport over field the in layer. terms of the − , applied wind stress as follows. Integrat- has vanished, τ = 0, as sketched in Fig. 10.4.EkmanNoting pumping that z z MEk = MEk, we may ×ing× the continuity− equation, Eq. 6-11, across As discussed in Chapter 7, this is the Ekman rearrange the abovethe Ekman to give: layer, assuming that geostrophic tauy # $ layer. !Ekmanflow! (vertically is nondivergent integrated) (but transport see footnote in Section 10.2.1): Conveniently, we can bypass the need to τwind z Dek MEk = × .

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