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Tidal Effect on the Dense Water Discharge, Part 1 Analytical Model

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Tidal Effect on the Dense Water Discharge, Part 1 Analytical Model ARTICLE IN PRESS Deep-Sea Research II 56 (2009) 874–883 Contents lists available at ScienceDirect Deep-Sea Research II journal homepage: www.elsevier.com/locate/dsr2 Tidal effect on the dense water discharge, Part 1: Analytical model$ Hsien-Wang Ou a,Ã, Xiaorui Guan a, Dake Chen b a Division of Ocean and Climate Physics, Lamont-Doherty Earth Observatory, Columbia University, 61 Route 9W, Palisades, NY 10964, USA b The State Key Lab of Satellite Ocean Environment Dynamics, SIO, Hangzhou, China article info abstract Article history: It is hypothesized that tidally induced shear dispersion may significantly enhance the spread and Accepted 26 October 2008 descent of the dense water. Here, we present an analytical model to elucidate the basic physics, to be Available online 18 November 2008 followed (in Part 2) by a numerical study using a primitive-equation model. Keywords: While tides enhance the vertical mixing and thicken the Ekman layer, the tidal dispersion is seen to Shear dispersion produce a disparate benthic layer several times the Ekman depths. With its top boundary lying above Benthic layer the frictional shear, the diapycnal mixing with the overlying water would be curtailed on account of its Dense outflow Richardson-number dependence. Over the shelf, this reduced erosion of the dense water and the generation of the Ekman flow by the thermal wind within the layer would act in concert to propel the dense water much beyond the deformation radius, which thus may reach the shelf break with less densification by the air-sea fluxes. Over the slope, even with the strong Ekman flow induced by the sloping interface, the dense water remains confined to the Ekman layer in the absence of tides, hence subjected to strong diapycnal mixing that would curb its descent. With the tidal augmentation of the benthic layer beyond the Ekman depth, on the other hand, the much-reduced diapycnal mixing would allow the Ekman advection to operate more effectively, which may propel the dense water to the lower slope, as observed in the western Ross Sea. & 2008 Elsevier Ltd. All rights reserved. 1. Introduction flow induced by the along-isobath current can advect the dense water offshore (Nagata et al., 1993; Condie, 1995; Cenedese et al., Through air–sea fluxes, dense water may form in marginal seas 2004), the frictional torque acting on a detached benthic plume or on polar shelves, which then descends the continental slope to can propel it to the concave lower slope (Ou, 2005), and enter the deep ocean. Prominent examples include the Mediter- entrainment of the overlying water would augment the transport ranean Outflow—a significant salt provider to the North Atlantic, to extend its outer edge (Smith, 1975; Price and Baringer, 1994; the Denmark Strait Overflow—a major source of the North Condie, 1995; Baines and Condie, 1998). On the other hand, the Atlantic Deep Water (NADW), and the High-Salinity Shelf Water Coriolis constraint can be overcome if the dense water is (HSSW) from Antarctic shelves, which seeds the Antarctic Bottom channeled through canyons, blocked by ridges, or incorporated Water (AABW) to ventilate the deepest of the world oceans. Partly into frontal eddies (Jungclaus and Backhaus, 1994; Gawarkiewicz for the dynamic intrigue and partly for its obvious climatic and Chapman, 1995; Chapman and Gawarkiewicz, 1995; Jiang and importance, how the dense water may descend the slope and Garwood, 1995). And in polar waters, the thermobaric effect may enter the deep ocean has generated considerable research interest exert additional buoyancy force to lessen the constraint of a in the past, as attested by an extensive body of literature and neutral density level (Killworth, 1977). many recent review articles on the subject (Griffiths, 1986; Price Clearly, different processes dominate over different regions or and Baringer, 1994; Baines and Condie, 1998; Ivanov et al., 2004). stages of the phenomenon; but despite the rather exhaustive list, Given the spatio-temporal scales involved, the Earth’s rotation one dynamical aspect of the phenomenon has received scant would impose a strong constraint on the down-slope motion, attention—not even mentioned in the above reviews, which deflecting it instead to move along isobaths within about the concerns the tidally rectified effect. This is somewhat surprising deformation radius. As such, frictional and mixing processes are since tides are typically strong along some major dense- often needed in simulating the observed descent (Ezer, 2005; Legg water routes and tidal shear dispersion is a well-known and et al., 2006). Among the more prominent mechanisms, the Ekman effective transport mechanism of passive tracers (Okubo, 1967; Zimmerman, 1986). $ As the western Ross Sea is a major formation region of the Lamont-Doherty Earth Observatory Contribution Number 7218. Ã Corresponding author. AABW (Jacobs et al., 1970; Orsi and Wiederwohl, 2009), a field E-mail address: [email protected] (H.-W. Ou). program (AnSlope) was carried out in recent years to examine the 0967-0645/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.dsr2.2008.10.031 ARTICLE IN PRESS H.-W. Ou et al. / Deep-Sea Research II 56 (2009) 874–883 875 dense water formation and discharge. A hydrographic section with speed up to a half knot; and since the instruments are from AnSlope is shown in Fig. 1, which shows a benthic layer located well within the benthic layer, the temperature fluctuation about 200 m thick (on average) extending all the way to the lower is due mainly to the tidal advection of the lateral temperature slope. The topography in the experimental site is relatively gradient. While there are short bursts of energetic cascades during smooth—devoid of major canyons, and there is no evidence of the spring tide—hence likely tidally triggered (Gordon et al., prevalent meso-scale eddies given the relatively stable descent 2004)—their contribution to the net flux is nonetheless minor angle of the dense water (Gordon et al., 2009, their Fig. 17), so the compared with that due to the mean motion. mean down-slope motion is due primarily to the friction-induced The observation raises some obvious questions: If the Ekman Ekman flow. We show in Fig. 2 moored time series 20 m above the flow dominates the down-slope transport, shouldn’t the benthic bottom from a mid-slope site, which exhibit strong diurnal tides layer defined by the anomalous density be confined to the much Fig. 1. Property distributions in the western Ross Sea. Data are from the AnSlope (courtesy of Arnold Gordon and Martin Visbeck). Northward is approximately offshore. Oct 2003 Nov 2003 0.5 0.5 0 0 −0.5 −0.5 −1 −1 potential temperature −1.5 potential temperature −1.5 0 102030 0102030 60 60 40 40 20 20 0 0 −20 −20 tidal velocity(cm/s) tidal velocity(cm/s) −40 −40 0 102030 0102030 days days Fig. 2. Time series of potential temperature and cross-shore velocity measured over the slope in the western Ross Sea (20 m above the bottom in a water depth of 1750 m). Data are from the AnSlope (courtesy of Alejandro Orsi). ARTICLE IN PRESS 876 H.-W. Ou et al. / Deep-Sea Research II 56 (2009) 874–883 thinner Ekman Layer (no more than a few tens of meters, see local tidal flux may be counter-gradient, the vertically integrated Section 6)? And in the presence of diapycnal mixing, can the tidal diffusivity remains positive. That is, the passive tracer in the Ekman flow really propel the dense water to the lower slope? benthic layer, being short-circuited by vertical mixing, would Generally, how important is the tidal flux in transporting the spread in bulk from its source, the essence of the shear dispersion. dense water? It is to address these questions and to assess the To specify the tidal motion, we consider a tidal velocity tidal effect on the spread and descent of the dense water that u^ ð u0 þ iv0Þ governed by the equation motivates the study. ^ ^ ^ Our study consists of two parts pertaining to analytical and iðf À sÞðu À u1Þ¼uuzz, (2.4) numerical modeling. This part 1 of the analytical study is where f is the Coriolis parameter, assumed positive, and the organized as follows: We first derive in Section 2 the tidal vertical viscosity is taken to be the same as the vertical diffusivity diffusivity of a passive tracer, and discuss in Section 3 the genesis since they stem from the same turbulent mixing. For simplicity, of the benthic layer. The spread of the benthic layer on the shelf we assume a non-slip bottom, although a more general stress and its decent down the slope are discussed in Sections 4 and 5 condition can be easily applied, which however would introduce respectively. In Section 6, the model is applied to the western Ross an additional parameter to complicate the problem; and with the Sea to compare with the observed phenomenon. We summarize tidal shear being greater with the non-slip condition, the derived the main findings and provide further discussion in Section 7. In tidal diffusivity represents an upper bound. Given the tidal forcing part 2, a process study using a primitive-equation numerical u^ 1, we solve (2.4) and (2.1) for the tidal fields, which are then model will be carried out, both to evaluate the analytical model combined in (2.2) to obtain the tidal diffusivity. and to provide a closer simulation of the observed phenomenon. For simplicity, we non-dimensionalize the variables by the À1 scaling rules (the brackets) of [t] ¼ f ,[s] ¼ f,[z] ¼ hE (the 1/2 0 0 0 0 À1 ‘‘Ekman’’ depth)(2u/f) , ½u ¼ju1j, ½C ¼½u C¯ xf and 2.
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