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Vertical Flow in the Southern Ocean Estimated from Individual Moorings

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Vertical Flow in the Southern Ocean Estimated from Individual Moorings SEPTEMBER 2015 S É VELLEC ET AL. 2209 Vertical Flow in the Southern Ocean Estimated from Individual Moorings F. SÉVELLEC,A.C.NAVEIRA GARABATO,J.A.BREARLEY,* AND K. L. SHEEN Ocean and Earth Science, National Oceanography Centre Southampton, University of Southampton, Southampton, United Kingdom (Manuscript received 14 February 2014, in final form 26 March 2015) ABSTRACT This study demonstrates that oceanic vertical velocities can be estimated from individual mooring mea- surements, even for nonstationary flow. This result is obtained under three assumptions: (i) weak diffusion (Péclet number 1), (ii) weak friction (Reynolds number 1), and (iii) small inertial terms (Rossby number 1). The theoretical framework is applied to a set of four moorings located in the Southern Ocean. For this site, the diagnosed vertical velocities are highly variable in time, their standard deviation being one to two orders of magnitude greater than their mean. The time-averaged vertical velocities are demonstrated to be largely induced by geostrophic flow and can be estimated from the time-averaged density and hori- zontal velocities. This suggests that local time-mean vertical velocities are primarily forced by the time- mean ocean dynamics, rather than by, for example, transient eddies or internal waves. It is also shown that, in the context of these four moorings, the time-mean vertical flow is consistent with stratified Taylor column dynamics in the presence of a topographic obstacle. 1. Introduction motions, and rectified mesoscale eddy flows along sloping isopycnals (Marshall and Speer 2012, and ref- Oceanic vertical flow is an important element of the erences therein). The latter two mechanisms are believed ocean circulation, playing a central role in the re- to extensively underpin vertical flow in the Southern distribution of water and tracers between (and within) Ocean, a region hosting a prominent large-scale vertical the upper-ocean mixed layer and the ocean interior. In circulation of global significance (Rintoul and Naveira the interior, the occurrence of vertical motion is asso- Garabato 2013). This view of the Southern Ocean stems ciated with a wide range of processes characterized by from simple theoretical models of the regional circula- distinct dynamics: from relatively high-frequency and tion (Olbers et al. 2004) and is found to hold in general small-scale geostrophically unbalanced flows (such as circulation models of varying degrees of idealization and internal waves and three-dimensional turbulent mo- eddy-permitting capability (Abernathey et al. 2011; tions; e.g., Polzin et al. 1997; D’Asaro et al. 2007; Hallberg and Gnanadesikan 2006; Farneti and Delworth Waterman et al. 2013; Sheen et al. 2013) to near-bottom 2010). Nonetheless, the weakness and wide spatial distri- frictional Ekman currents along sloping topographic bution of the vertical flows associated with these processes boundaries (Garrett et al. 1993), wind-driven Ekman have to date impeded their assessment from observations. Historically, the computation of vertical velocities Denotes Open Access content. has been done using the well-known omega equation (Holton 1972). This equation relates the vertical mo- tion to measurable features (density, temperature, * Current affiliation: British Antarctic Survey, Cambridge, United Kingdom. pressure, and horizontal flows) and is derived from a combination of the continuity, thermodynamic, and Corresponding author address: F. Sévellec, Ocean and Earth Science, University of Southampton, Waterfront campus, Euro- pean Way, Southampton, SO14 3ZH, United Kingdom. This article is licensed under a Creative Commons E-mail: fl[email protected] Attribution 4.0 license. DOI: 10.1175/JPO-D-14-0065.1 Ó 2015 American Meteorological Society Unauthenticated | Downloaded 09/26/21 01:53 AM UTC 2210 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 45 momentum equations. The omega equation has the ad- and analytical methodology are introduced in section 3. vantage of being a diagnostic (i.e., no time derivative) of Section 4 describes the results of our analysis. The main the state of the system, so that a single snapshot is enough findings of this work are synthesized in section 5. to determine the vertical flow. However, the equation requires a fine spatial discretization (i.e., spatial de- 2. Theory rivatives along the three spatial dimensions). It has been In this section, we use the thermodynamic equation for shown to be extremely useful in the atmosphere, where the advection of density to calculate the vertical velocity.1 radiosondes capture accurately the three-dimensional The set of equations (in Cartesian coordinates) from system’s state on a global scale at a given instant (but which our results are derived are given below. These en- repeated measurements at the same location are impos- compass the horizontal momentum equations, hydrostatic sible, that is, time derivatives are not measurable). In the balance, nondivergence (i.e., the Boussinesq approxima- ocean, spatial sampling is much sparser, making im- tion), and the evolution of density forced by advective and plementation of this equation difficult. However, ocean- diffusive processes: ographic moorings, which measure the ocean at a single 1 location but with high temporal resolution, allow an al- D u 2 f y 52 › P 1 t r x Visc, (1a) ternative approach to be adopted. Here, we derive a new 0 equation based on a combination of the momentum and 1 D y 1 fu 52 › P 1 thermodynamic equations, which utilizes the time evo- t r y Visc, (1b) 0 lution of the local horizontal velocity and density field to › P 52rg, (1c) provide robust estimates of vertical velocity. z › 1 › y 1 › 5 In this study, we characterize the vertical motion in a xu y zw 0, and (1d) 10.5 km 3 10.5 km patch of the Southern Ocean and in- D r 5 Diff . (1e) vestigate its underpinning physics using measurements t from a cluster of moorings deployed in Drake Passage as Here, t is time; x, y,andz are the zonal, meridional, and part of the Diapycnal and Isopycnal Mixing Experiment vertical coordinates; u, y,andw are the zonal, meridional, in the Southern Ocean (DIMES). Time series of vertical and vertical velocities; P is the pressure; r (r0) is the (ref- velocity profiles are estimated from individual moorings erence) density; f is the Coriolis parameter; g is Earth’s by deriving and applying an expression for the vertical gravity acceleration; ›t, ›x, ›y,and›z are the time, zonal, flow in terms of the temporal and vertical variations of meridional, and vertical partial derivatives; Dt is the ma- density and horizontal velocity, generalized from the work terial derivative (5›t 1 u›x 1 y›y 1 w›z); and Visc and of Bryden (1980) to include ageostrophic and time- Diff are viscosity and diffusivity operators, respectively. varying forcings. We show that, in this area, time-mean We simplify this set of equations further by assuming vertical motion in the deep ocean is primarily determined low viscosity (Re 1, Visc is negligible), small in- by the properties of the time-mean horizontal flow, which ertial terms (Ro 1, advective terms are negligible in the exhibits a spatial structure consistent with the occurrence horizontal momentum equations), and low diffusion of a stratified Taylor column over a topographic obstacle (Pe 1, Diff is negligible). The quantity Re is encompassed by the moorings. Unlike in classical Taylor the Reynolds number and measures the ratio of inertial to column theory for a uniform fluid, which induces a verti- viscous forces; Ro is the Rossby number and measures the cally uniform horizontal deviation in the presence of a ratio of inertial forces to the Coriolis acceleration; and Pe topographic obstacle to conserve potential vorticity, with is the Péclet number and measures the ratio of advective stratification the Taylor column is restricted to the deep to diffusive terms. (An estimation of the vertical Rossby ocean. Because stratification restricts the horizontal de- number can be found in section 5.) Applying these as- viation to the vicinity of the topographic obstacle, there sumptions, the set in (1) reduces to is a change in the horizontal flow orientation with depth. In accordance with Bryden (1980), a steady vertical flow 1 Two other methods exist to calculate the vertical velocity but are must occur in association with this change in order to inconsistent with the available dataset. One possible approach would conserve density. Here, we will demonstrate that, fol- entail the derivation of vertical velocity from the divergence of the lowing stratified Taylor column dynamics, a vertical flow horizontal velocity field. However, the spatial derivatives involved occurs above the topographic obstacle encompassed by cannot be estimated accurately by using neighboring moorings (since the moorings. these may be too far apart to resolve the scales of the key processes involved). The other alternative would be to combine the momentum The paper is organized as follows: In section 2,we and continuity equations, yet this would lead to an even more com- derive the expression used to estimate the vertical ve- plex expression with more unknowns (i.e., the equation of vorticity locity from individual mooring measurements. The data conservation in its quasigeostrophic form). Unauthenticated | Downloaded 09/26/21 01:53 AM UTC SEPTEMBER 2015 S É VELLEC ET AL. 2211 TABLE 1. Current meter and moored CTD nominal depths for the DIMES C mooring and the four corner moorings (SW, SE, NE, and NW). Data were returned between 12 Dec 2009 and 6 Dec 2010 and between 20 Dec 2010 and 5 Mar 2012. The exact instrument depths vary slightly between the four corner moorings because of subtle differences in mooring design. Both the SW and NE moorings suffered from a buoyancy implosion early in the first year of deployment, such that they only recorded ;45 days of data in that year.
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