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On the Theories That Underlie Our Understanding of Continental Shelf Circulation

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On the Theories That Underlie Our Understanding of Continental Shelf Circulation Journal of Oceanography, Vol. 53, pp. 207 to 229. 1997 Review On the Theories that Underlie Our Understanding of Continental Shelf Circulation G. T. CSANADY Old Dominion University, Norfolk, VA 23529, U.S.A. (Received 10 January 1996; accepted 1 October 1996) Our present understanding of continental shelf circulation rests on a few conceptual Keywords: models which yield highly idealized mathematical representations of shelf topography ⋅ Continental shelf circulation, and dynamics. This review examines several of such models in the light of experimental ⋅ evidence accumulated within the past two decades or so: what are the successes of the coastal oceanogra- models, and what overidealizations underlie their shortcomings. The coastal jet model, phy, ⋅ coastal upwelling, coastally trapped wave models, the dynamic height model, Joint Effect of Baroclinity and ⋅ coastally trapped Relief (JEBAR) models, self-advection of density and front models are discussed in turn. waves, The final section on the interaction of shelf and boundary currents draws attention to the ⋅ thermohaline lack of satisfactory models for this important aspect of shelf dynamics. coastal currents. 1. Introduction it turns out that the problem of the open boundary condition “Coastal” and “Deepwater” physical oceanography resurfaces in the different theories and is the root cause of have developed separately on account of disparate vertical their principal weaknesses. It is not too far-fetched to con- and horizontal scales, and the consequent dissimilar role of clude that these theories in one way or another fail to account such forcing effects as wind stress or freshwater runoff. for observation, because they neglect interactions with deeper Waters over continental shelves abut waters of the deep waters offshore. A study of such interactions promises to be ocean, however, so that separate treatment of their movements a rewarding research activity for the future. requires a decision on where the one ends and the other begins. Furthermore, such treatment implies a priori that 2. Coastal Upwelling continental shelf circulation can be understood in isolation, Owing to its ecologic and economic importance, coastal that any interactions with the deep ocean can be suitably upwelling is the most discussed and researched phenomenon represented in shelf circulation models. Although all our in all of coastal oceanography. In a recent review, Huyer theories of shelf circulation implicitly assume this, condi- (1990) gives a thorough and very readable summary of the tions to be imposed at the “open” boundary separating the physical processes involved in wind-induced upwelling, continental shelf from the deep ocean remain the Achilles with emphasis on the major upwelling regions off the west heel of shelf circulation models, whether analytical or nu- coast of North and South America, distinguished “by their merical. high productivity and their cool and foggy weather”. High The separation of continental shelf and deep ocean is productivity comes from nutrients brought to the surface by already drastic surgery. Irregular topography, water mass upwelling, cool and foggy weather from the associated cold distribution, wind fields force further idealization. Theories water temperatures. Although of lesser economic importance, of shelf circulation have employed different levels of ide- transient, wind-induced inner shelf upwelling (and its obvious alization in pursuing two different objectives: one, to simulate counterpart, downwelling) is commonplace on most other complex reality as faithfully as possible, two, to understand shelves (Pettigrew and Murray, 1986) and along the coasts prominent observed phenomena in terms as simple as pos- of inland seas such as the Baltic (Walin, 1972) or the Great sible. The latter approach rests on “conceptual models”, and Lakes (Mortimer, 1963). builds simple theories to explain the essential physics of A great deal of very detailed information has come to phenomena. The purpose of this article is to review several light on coastal upwelling since the early 60-s. Reviews of such “minimally complex” theories, and to adjudge how the major field programs by Smith (1981) and Brink et al. well and how completely they account for the observed (1983), and of upwelling-related phenomena in continental phenomena they are designed to explain. Not surprisingly, shelf circulation by Huyer (1990), summarize the many 207 Copyright The Oceanographic Society of Japan. Fig. 1. Temperature and velocity cross-shelf sections in the CODE II experiment: (a) Top row, two days after the start of upwelling- favorable wind; (b) Bottom row, three days later. From Lentz (1987). interesting findings. With a view to relating observations to waters come from, to replace those moving offshore in the theory, we briefly sketch here occurrences in a prototype surface layer, but Lentz’s analysis of mass balance shows it upwelling event, the “spring transition” along the U.S. west to be two-dimensional in the cross-shore plane, on the coast, particularly well documented in the course of the average during the five days of the spring transition. In CODE experiment off northern California (Lentz, 1987, and 130 m depth the flow is offshore in the top 45 m or so, other papers in the same issue). onshore below, the depth-integrated transports balancing. Temperature gradients in the top 45 m are significant even 2.1 Prototype coastal upwelling at the beginning of the upwelling event. The onshore flow is Figure 1(a) shows the distribution of cross-shore and drawn from 200–300 m depth over the continental slope, alongshore velocity and temperature less than two days after with little influence on waters deeper than 400 m. Lentz the arrival of strong upwelling favorable wind in the central (1987) gives a wealth of other detail. transect of CODE, from Lentz’s paper. The well-known This relatively straightforward picture gets more signatures of coastal upwelling are all present: upward complicated even before the first relaxation of the upwelling- sloping isotherms, a strong coastal jet, rapid offshore mo- favorable wind: 3 days later the sections look different, Fig. tion in the surface layer with strong divergence close to 1(b). The cross-shelf velocity has a stagnation point a few shore. The displacement of the isotherms is large: the km from shore, and shoreward from there the alongshore 11.5°C isotherm has moved in the preceeding 24 hours from velocity is now barotropic and poleward, opposite to the a more or less constant depth of 15 m to the surface, wind. Lentz (1987) and Send et al. (1987) demonstrate that intersecting it now at 7 km from shore. During the following this flow component is pressure-gradient driven. Later in the 24 hours the coastal jet moves offshore by some 10 km while upwelling season, when upwelling and relaxation cycles the 11.0°C isotherm also moves to the surface and offshore. alternate, alongshore pressure gradient driven flow comes to Cross-shelf advection of both temperature and momentum supply much of the upwelling fluid mass which is perma- thus plays a major role. The figures do not show where the nently removed seaward (Send et al., 1987; Winant et al., 208 G. T. Csanady 1987). On this longer time scale the mass balance thus becomes three-dimensional, the convergence of the along- shore transport balancing the surface layer divergence. How well does existing theory account for the diverse phenomena observed on occasion of wind-driven coastal upwelling, and more broadly, in the course of upwelling- downwelling cycles caused by variable wind? 2.2 Two layer coastal jet model The classical, minimally complex model of transient coastal upwelling is due to Charney (1955), the model originally meant to simulate the Gulf Stream. Transplanted to coastal oceanography in the sixties, it represents the coastal zone as a constant depth sea with a vertical coast, a light layer overlying a heavy one, extending from the coast Fig. 2. Coastal upwelling and coastal jet generation by alongshore to “infinity”. The wind stress is suddenly applied, the wind wind, according to the two-layer Charney model. From Csanady (1977). force distributed evenly over the light surface layer. Ev- erything is supposed the same in every cross-section inde- pendently of alongshore distance, including in particular the pressure distribution. Postulating time-independent cross- direct consequence of postulated alongshore uniformity. shore motion, the model portrays events in coastal upwelling Dynamically, linear superposition of barotropic and as illustrated in Fig. 2. Alongshore wind accelerates the baroclinic solutions is responsible for the entire scenario. surface layer: with interface friction absent, the surface fluid One weakness of this model is the postulate of time- speeds up, as earth rotation slowly deflects the motion independent cross-shore motion: this cannot just material- seaward. The coast, however, suppresses cross-shore motion ize as the wind begins to blow. The full analytical solution over an e-folding distance of c/f, the baroclinic radius of of the same problem, impulsively applied wind to a two- deformation (c is the phase speed of internal waves, f layer frictionless fluid bounded by a vertical wall (Crépon, Coriolis parameter). Farther out cross-shore Ekman trans- 1967), shows essentially the same behavior, with some gaps port in the surface layer comes to balance the wind stress. filled in: the cross-shore motion is set up in the wake of an Within the range of the coast’s influence wind stress re- internal gravity wave propagating offshore, in a period of mains partly unbalanced and steadily accelerates an along- order f–1, Ekman transport offshore arises in the same period, shore “coastal jet” in the surface layer, with highest velocity and is accompanied by inertial oscillations. at the coast. The near-shore divergence of the cross-shore Both Charney’s and Crépon’s model are linearized, motion in the surface layer raises the interface under the valid only for small interface displacements (compared to coastal jet, causing convergence in the lower layer, and either layer depth).
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