4.1.3. Wind-driven dynamics of the mean circulation
The distinctive regional wind forcing is key to understanding the complex thermal structure of the region and the modification of the central Pacific zonal currents of the central Pacific near the continent. West of about 110 °W the characteristic central Pacific winds are seen (Fig. 1), with trade winds converging into a well-developed ITCZ. East of 110°W and north of the equator the pattern is quite different: instead of a zonally oriented ITCZ, the winds (and especially the wind curl) are dominated by jets blowing through three gaps in the Central American cordillera: Chivela Pass at the Isthmus of Tehuantepec in Mexico, the Lake District lowlands of Nicaragua inland of the Gulf of Papagayo, and the central isthmus of Panama where the Panama Canal was built (Fig. 1).
The wind stress curl is Curl() = /x - /y, where the components of the wind stress vector are and ; the curl expresses the rotation a vertical column of air would experience in a wind field that varies in space. The Central American wind jets extend at least 500 km into the Pacific and produce distinctive curl dipoles as wind strength decreases away from the jet axis: each jet has a region of positive curl on its left flank and negative curl on its right. (In the mean, the wind jets are more clearly defined by their associated curl dipoles than in the vector winds themselves; Fig. 1.) The magnitudes of these curls are at least as large as that of the ITCZ. Positive curl on the south flank of the Papagayo jet is enhanced and extended to the west because of the westerly winds south of the jet (Mitchell et al., 1989). The three wind jets are known to vary on short (weekly) timescales, especially in association with winter high pressure systems transiting North America (Chelton et al., 2000a,b), producing oceanic eddies of various types (Willett et al., 2006). For present purposes, we are interested in the jets' impact on the low-frequency dynamics, in which Ekman pumping due to their curl is the main factor.
Ekman pumping occurs because the winds and therefore the Ekman transport vary spatially, which produces convergences and divergences in the upper layer. As a consequence, the thermocline must rise or fall to conserve mass, so Ekman pumping is interpreted as a vertical velocity at the base of the surface layer. Zonal and meridional Ekman transports are (U = /f ,V = -/f ), where f is the Coriolis parameter and the density. The divergence of the Ekman transports (U/x + V/y) equals the wind stress curl divided by f , (where f is for the moment taken as constant). The Ekman pumping velocity Curl()/f , is of fundamental importance for the ocean circulation because it produces thermocline depth variations and resulting pressure gradients, which consequently produce geostrophic flow. For example, under northern hemisphere wind jets like those west of Central America, the Ekman transport is to the right of the wind direction, and is largest at the jet axis. Approaching the jet from its left, the Ekman transport is increasing, so on this side of the jet it is divergent, leading to upwelling. To the right of the jet axis, the Ekman transport is decreasing, and is thus convergent (downwelling). The curl dipoles seen in Fig. 1 thereby produce the thermocline bowls and domes, and the corresponding highs and lows in dynamic height (Fig. 2, top).
The consequences of Ekman pumping go beyond changing the thermocline depth, however. On a rotating planet, a locally still water column has the rotation rate ("vorticity") about its vertical axis equal to the local value of the Coriolis parameter divided by two (thus it is zero at the equator and grows in magnitude towards the poles). If the column is lengthened or shortened by Ekman pumping at the top, its vorticity will be changed in proportion to its cross-sectional area. Stretching produces increasing vorticity because the column becomes narrower and the same angular momentum is achieved by a faster rotation. In the absence of other forces or friction, a stretched column would experience a rotational acceleration. Thus the wind stress curl can be seen as imposing its rotation directly on the ocean, through the intermediary mechanism of Ekman pumping, which illustrates the connection between rotation and stretching (and is why Ekman divergence is proportional to the wind stress curl). In steady state (where total vorticity is conserved) a local increase in vorticity can be balanced by moving poleward, where the vertical component of the earth's rotation (the planetary vorticity) is larger. This is the basis of the Sverdrup relation, V = Curl(), where = df/dy is the meridional gradient of the Coriolis parameter and V is the total meridional (Sverdrup) transport (Sverdrup, 1947). It expresses the fact that meridional motion is equivalent to a change in rotation rate. For example, under positive curl, as occurs on the south flank of the Papagayo jet, Ekman pumping lifts the thermocline and thus stretches the water column beneath. The vorticity of the column increases, and in steady state it must move north to a latitude where its spin equals the planetary vorticity.
The region of positive wind curl on the south flank of the Papagayo jet (Fig. 1) produces especially strong upwelling (10–20 m month, comparable to equatorial upwelling) because the Ekman transport is northward under the easterly jet itself at 10–11°N and southward under the westerly winds at 6–8°N. As a result of this surface divergence, the thermocline is lifted and the water column beneath is stretched, forming the Costa Rica Dome at 9°N (Fig. 8, top, shows a zonal slice and Fig. 6, bottom, a meridional slice through the center of the dome). The thermocline dome produces a cyclonic eddy-like geostrophic circulation at the surface (Figs. 4 and 2 (top)), but no dome is seen below the shallow thermocline. Instead, subthermocline isotherms slope up to the west over a broad region to at least 105°W (Fig. 8, top; and see Fiedler and Talley, 2006), thus the resulting geostrophic flow deeper than about 50 m under the dome is all northward (Fig. 8, bottom, or Fig. 2, bottom). This thick subthermocline flow dominates the vertical integral, and total transport is northward across the whole dome region to at least 99°W, quantitatively consistent with the Sverdrup relation under positive curl (Kessler, 2002). The cyclonic eddy circulation of the dome is found to be a very shallow feature. Thus both the rotating dome and the northward flow beneath it are part of the ocean response to the Papagayo jet.
Knowing the vertical structure of geostrophic transport (from XBT data) allows the structure of vertical motion below the directly wind-driven Ekman layer to be inferred (if both v and w are assumed to be zero at 450 m); this is found to be a transport of about 3.5 Sv upward across the 17 °C isotherm into the dome, where it diverges in the Ekman outflow (Kessler, 2002). The dome is one of the few places in the ocean where upwelling arises mostly from below the thermocline (equatorial upwelling draws water primarily from the upper levels of the thermocline), and thus constitutes a perhaps-important means of communication from the intermediate to the surface layer. Wyrtki (1964) did not realize the importance of these vorticity dynamics because the existence of the Papagayo wind jet and its curl were not known at the time, and because the very sparse thermal observations available concentrated on the position of the surface dome itself and did not extend west of about 91°W, so the clue of northward transport under the dome remained unknown.
It has not been possible to construct a heat balance for the dome because the surface flux terms are so poorly known, and vary strongly on short timescales (Chelton et al., 2000b). However, it is clear that the upwelling transport diagnosed in the Costa Rica Dome implies a large downward mixing of heat to maintain a steady balance, otherwise the isotherms would continue to be advected upward. High wind speeds under the Papagayo jet provide a plausible source of this mixing, but a quantitative assessment remains to be accomplished.
Costa Rica Dome upwelling and subsurface northward transport are linked with the northern Tsuchiya Jet that flows across the entire Pacific at about 4°N, 150–200 m depth (Fig. 6). The northward flow under and to the west of the dome seen in Fig. 8 is in fact the Tsuchiya Jet turning abruptly away from the equator (Fig. 2, bottom, and note the disappearance of both Tsuchiya Jets at 90°W, compared to the sections further west in Fig. 6). About half the roughly 7 Sv transport of the northern Tsuchiya Jet upwells into the Costa Rica Dome, while the other half turns and flows west into the lower reaches of the NEC (Fig. 2, bottom; note the large Tsuchiya Jet approaching the dome and weaker flow leaving the region at these depths, Kessler, 2002). The mechanism driving the Tsuchiya Jets remains in question, but recent theory suggests that the northern branch is in fact a consequence of Costa Rica Dome upwelling (McCreary et al., 2002), as an example of a "-plume" (Stommel, 1982). The southern branch may be similarly driven by upward motion across a broader region of the southeast Pacific (the negative curl along 5°S in Fig. 1, plus Peru upwelling), with a subthermocline dome reported near 10°S, 85°W (Voituriez, 1981); this is probably the long feature stretching from 105°W to the coast along 5–12°S in Fig. 2, bottom. The Atlantic also has Tsuchiya Jets flowing into upwelling in the Guinea and Angola Domes (Mazeika, 1967). Thus Costa Rica Dome upwelling appears to be the northeast Pacific instance of a more general phenomenon.
The mean ocean response to the Tehuantepec and Panama wind jets is also consistent with the Sverdrup relation: northward geostrophic transport is found under their left flanks and southward under their right (Kessler, 2002). Unlike Papagayo, for these jets the downwelling curl is larger than the upwelling curl (Fig. 1). In the Gulf of Tehuantepec, the mean curl dipole produces the northward bulge of the Costa Rica Dome (note the 88–92 dyn cm contours in Fig. 2, top, that go north under the upwelling curl to the east of Tehuantepec and south to its west). The Tehuantepec Bowl is consistent with a linear response to the downwelling curl stretching west from the right flank of the Tehuantepec wind jet (Kessler, 2002).
Interpreting the mean and low-frequency evolution of the Tehuantepec Bowl from sparse XBT data is tricky because it is in an area where anti-cyclonic eddies pass each winter (Giese et al., 1994; Willett et al., 2006), and it could be that the apparent mean bowl was simply a reflection of sampling many such eddies. In addition, the strength of the short timescale eddies suggests that nonlinear terms would be important. However nonlinearity seems not to be dominant for the mean circulation, which can be reasonably well diagnosed based on linear Sverdrup dynamics (Kessler, 2002). In the Panama Bight, the curl dipole produces a cyclonic circulation with northward flow along the Colombian coast, and (rather weak) southward flow at 85–90°W (Fig. 2). One of the first modern dynamical formulations for the vertical velocity due to the curl was developed by Stevenson (1970) to interpret the circulation in the Panama Bight. He estimated upwelling velocities of few m day in the central gulf, and showed a rough consistency of upwelling due to the wind curl with the cyclonic geostrophic gyre. Cool SST along the coast of Colombia might be a response to the upwelling curl, especially considering that the mean poleward winds favor coastal downwelling (Fig. 1), but, since Stevenson, relatively little work has been done in this region and a full quantitative description of its dynamics remains to be accomplished.
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