A Numerical Investigation of the Somali Current During the Southwest Monsoon

Journal of Marine Research, 46. 25-58, 1988

A numerical investigation of the Somali Current during the Southwest Monsoon

by Julian P. McCreary, Jr.' and Pijush K. Kundu1

ABSTRACT The dynamics of the Somali Current system during the Southwest Monsoon are investigated using a 21/2-layer numerical model that includes entrainment of cool water into the upper layer. Entrainment cools the upper layer, provides interfacial drag, and prevents the interface from surfacing in regions of strong coastal upwelling. Solutions are forced by a variety of wind stress fields in ocean basins with western boundaries oriented either meridionally or at a 45° angle. Solutions forced by southern hemisphere easterlies develop a strong coastal current south of the equator. When the western boundary is slanted, this current bends offshore at the equator and meanders back into the ocean interior. No cold wedge forms on the Somali Coast. These solutions suggest that the southern hemisphere trades are not an important forcing mechanism of the Somali Current circulation. Solutions forced by northward alongshore winds differ considerably depending on the orientation of the western boundary and the horizontal structure of the wind. When the boundary is meridional and the wind is uniform (a curl-free wind field), solutions continuously shed eddies which propagate northward along the coast and weaken. When the boundary is meridional and the wind weakens offshore, they reach a completely steady, eddy-free state with no coastal upwelling. If the boundary is slanted and the wind does not vary alongshore, solutions reach a steady state that now contains stationary gyres and cold wedges. If the boundary is slanted and the forcing is a strong wind patch confined north of the equator, the flow field slowly vacillates between single-gyre and double-gyre states. Solutions are also forced by an idealized representation of the observed alongshore wind field, consisting of two components: a moderate background field (-I dyn/ cm2) turned on in May, and a Findlater jet (-4 dyn/cm2) turned on gradually in June. A single gyre, the Southern Gyre, initially develops south of 4N due to the background wind, and a second gyre, the Great Whirl, develops later between 4N-9N in response to the Findlater jet. Cold wedges form on the northern flanks of both gyres. In some of the solutions, the Southern Gyre moves northward and coalesces with the Great Whirl in early September, before the monsoon begins to weaken. Thus the collapse of the two-gyre system is part of the adjustment of the model to the peak phase of the Southwest Monsoon, and is not due to a relaxation of the wind.

1. Introduction In contrast to the other major western boundary currents, the Somali Current changes direction annually. It seems to respond to the seasonal changes in the wind

I. Nova University Oceanographic Center, 8000 North Ocean Drive, Dania, Florida, 33004, U.s.A. 25 26 Journal of Marine Research [46, 1 field, being poleward during the summertime Southwest Monsoon and equatorward during the wintertime Northeast Monsoon. The development of the current throughout the Southwest Monsoon has been studied extensively, and involves the establish- ment and decay of intense gyres and wedges of cold sea-surface temperature (SST). The articles by Schott (1983), Knox and Anderson (1985), and Luther (1987) provide recent overviews of both observations and models. In late April or early May, at the beginning of the northern-hemisphere summer monsoon, the southern hemisphere tradewinds shift equatorward, and northward winds appear along the African coast near and south of the equator; a few weeks later, 2 moderate alongshore winds (-1 dyn/cm ) appear along the entire Somali Coast (Fig. la). In late April, a northward coastal current already exists south ofthe equator, and it bends offshore to form a meandering eastward flow located just south of the equator (Fig. 2a). By mid-May, the coastal current strengthens, crosses the equator, and turns offshore near 2.5N. Part of this current loops back across the equator (Fig. 2b; Leetmaa et al.. 1982; Swallow et al., 1983); we refer to this loop, and its later development, as the Southern Gyre. A wedge of cold SST, extending several hundred kilometers offshore and from 3N to 5N, forms on the northern flank of this gyre (Fig. 14 of Swallow et al., 1983). Farther to the north there is an alongshore current directed poleward, and coastal SST is cold but not wedge-like, as in a typical mid-latitude upwelling region (Schott, 1983).

(a) 16 May (b) 16 July

,~.~ ,,~~..;. .;/~::"·f , , t , , t - ...•...• ...•.- ;' ~ "'" " }::'r-c-,-~--~__'\ '\ '\ , " - - '\ , , t f . /~-\"-\;..\__~ '-'Qs\ ' " •...... •.." " , \ t f, I<:-"'_~ "-\ '\ '\ "--'-o.:-"'-' __ ~ __'\ , ~ t \\.~..~""~...~ ~.s..'''\:.'''~ " :-::_:':-...... •...... '::-,_., t'., .:>", ". , '\ , ,~ ...... •....-~..:::-~ .

Figure 1. Observed wind stress fields from the FGGE Experiment of 1979, using a drag coefficient of 0.1875 x 10-3• The left panel (a) shows them on 16 May, and the right panel (b) 2 shows them on 16 July. The contour interval is 0.5 dyn/cm • In May the southern hemisphere trades migrate northward, and moderate alongshore winds appear everywhere along the African coast. In July the Findlater jet is well developed, resulting in a region of very large 2 wind stress values (~6 dyn/cm ) over the northern Arabian Sea. [After Luther et al., 1985.] 1988] ¥cCreary & Kundu: Model of the Somali Current 27

Cal 29 April- 5 May 1979 Cbl 20 May - 2 June (ell July - 4 Aug.

Figure 2. Surface currents (arrows) and depths (m) of the 20°C isotherm in 1979 during (a) April 29-May 5, (b) May 2o-June 2, and (c) July I-Aug 4. There are indications of a weak eddy and a meandering eastward current just south of the equator in panel (a), a well-developed Southern Gyre in panel (b), and both the Southern Gyre and the Great Whirl in panel (c). [After Swallow et al., 1983.]

In early June, a strong low-level atmospheric jet (the Findlater jet) appears off nothern Somalia. It strengthens throughout June, attaining speeds of the order of 2 15 mls (T-5 dyn/cm ) in July (Fig. Ib). By the end of June, a second oceanic gyre, called the Great Whirl, develops north of 5N (Fig. 2c) and another wedge of cold SST forms on its nothern flank near 9-10N. There is usually a third gyre even farther north near the island ofSocotra (Fig. 3), and we refer to this gyre as the Socotra Eddy. The winds off Somalia weaken in September, and the Southwest Monsoon is essentially over by October. In either August or September, the Southern Gyre and its associated cold wedge have been observed to migrate northward and to interact with the Great Whirl. In 1979, for example, satellite images of SST indicate that the two gyres coalesce (Fig. 4). Coalescence, however, does not always occur; in 1978 the Great Whirl appeared to be pushed out of the way to the north by the movement of the Southern Gyre (Fig. 9 of Schott, 1983). What aspects of the wind field over the Indian Ocean force this remarkable series of events? An obvious possibility is the local alongshore wind. Such a wind forces offshore Ekman drift, coastal upwelling and a poleward surface current. A number of studies have already examined the response of the Somali Current region to a forcing of this kind (Hurlburt and Thompson, 1976; Lin and Hurlburt, 1981; Cox, 1979, 1981; Philander and Delec1use, 1983; Delec1use and Philander, 1983; Luther and O'Brien, 1985; Luther et al.• 1985; McCreary and Kundu, 1985). A second possibility is remote forcing by features of the offshore wind field that excite baroclinic Rossby waves. These waves subsequently propagate to the coast of Africa, adjust the interior ocean toward Sverdrup balance, and thereby affect the Somali Current. One type of remote 28 Journal of Marine Research [46, 1

6-11 JUly, 1976 o

20'W 100

200 10'

300

400

500 m 2'$ 0 2 4' 6' 8' 10' 12' 14' 16' 18' 20' 22'N 50'E 60'

Figure 3. Temperature section obtained during July 6-11, 1978, along the tanker lane shown in the right panel. The island of Socotra is also shown in the right panel. Note the Great Whirl between 5N-ION, and the smaller Socotra Eddy between lON-14N. The depth of the 20°C isotherm varies markedly from about 75 m at the edge of the Great Whirl to more than 200 m at its center. [After Bruce, 1979.] forcing was proposed by Lighthill (1969), who hypothesized that the onset of the Somali Current is forced entirely by remote wind curl, without any coastal wind; however, Leetmaa (1972, 1973) pointed out that this interesting hypothesis cannot be correct, noting that the Somali Current turns northward considerably before the remote winds strengthen. Another type of remote forcing, and the one that is addressed in this paper, involves wind curl associated with an alongshore wind that weakens offshore. A third possibility is forcing by local wind curl, which generates geostrophic

July 1979 (mean) 17 Aug. 25 Aug. 3 Sep.

Figure 4. Time sequence of satellite-observed temperature fronts observed during 1979. The northward propagation of the southern cold wedge and its eventual coalescence with the northern wedge are evident. [After Brown et al .• 1980.] 1988] McCreary & Kundu: Model of the Somali Current 29 currents via Ekman pumping. There is a region of very strong negative wind curl on the eastern side of the Findlater Jet just off the Somali Coast (Fig. 1b). This region drives an anticyclonic circulation, and several workers have suggested that the Great Whirl may be a directly forced response to this curl (Oiling, priv. comm.; Schott and Quadfasel, 1982; Luther et al.. 1985). The southern hemisphere trades may force a northward Somali Current near the equator. According to this mechanism, the western boundary current driven by these winds overshoots across the equator to form the Southern Gyre (Anderson and Moore, 1979; Anderson, 1981; Knox and Anderson, 1985). Finally, the relaxation of the wind field at the end of the Southwest Monsoon has frequently been suggested as being the cause of the northward movement of the Southern Gyre. Schott (1983), however, pointed out that observations do not support this idea because, in two of the three years that he analyzed, the monsoon continued at maximum strength for quite some time after the migration began. This paper investigates the dynamics of the Somali Current system during the Southwest Monsoon using a nonlinear, 2'/l-layer model (a 3-layer model with pressure gradients in the lowest layer set to zero) that includes entrainment of cool water into the upper layer. Solutions are forced by a variety of simple wind stress fields in ocean basins with western boundaries oriented either meridionally or at a 45° angle. These solutions serve to illustrate the importance of the various forcing mechanisms italicized in the previous paragraph. Some of them are intentionally designed to be similar to those of previous workers, and in those cases we compare respective solutions and conclusions. Solutions are also forced by idealizations of the observed alongshore wind field, and they develop systems of gyres and wedges that compare favorably with observations. Although the western boundary currents of solutions are highly nonlinear, several properties of the interior circulations can be explained with linear dynamics. Relevant linear solutions are reviewed in the Appendix, and we suggest that readers consult the Appendix before continuing on to the numerical solutions in Section 3. Some of our conclusions are the following. The Southern Gyre forms in May in response to the moderate alongshore winds near the equator, and is not likely to be significantly forced by the southern hemisphere trades. The Great Whirl forms later in response to the Findlater jet, but it is not a directly forced response to the negative wind curl associated with it. A double-gyre state is not a possible equilibrium response to the peak phase of the Southwest Monsoon; as a result, the Southern Gyre moves northward, and eventually coalesces with the Great Whirl. Whether the coalescence occurs soon (before October) is sensitive to the horizontal structure of the Findlater jet, and this sensitivity may explain why observed gyres do not always coalesce.

2. The model ocean a. Equations and boundary conditions. The model has two active layers, overlying a deep layer where horizontal gradients of pressure are assumed to vanish (a 21/rlayer 30 Journal of Marine Research [46, 1 model). Equations of motion in the upper layer, denoted by subscript 1, are

A -- Z (h1v.), + \1 • (vlhlvl) + fk x h]V1 + hl\1P. = 'T + WeVZ + Vh\1 (hlvl) - -yh.v\>

hit + \1 • (h1v.) = We + Kh\1zhl - -y(h] - HI)'

TIl + VI • \1T1 = Q/hl - We(TI - Tz)lhl + Kh\1zTI, (la) and the lower layer equations, denoted by subscript 2, are

A Z (hzvz), + \1 • (vzhzvz) + fk x hzvz + hZ\1P2 = - wevz +vh"V (hzvz) - -yhzvz,

hu + \1 • (hzvz) = - We + Kh\12h2 - -y(hz - Hz),

Tu = O. (I b)

In the above, V is the velocity of the fluid, h is the layer thickness, H is the initial layer thickness, T is the water temperature, Q is the heat input at the ocean surface, 'T is the wind stress, and k is the unit vector in the vertical direction. The equatorial ,B-plane is adopted throughout, so that f = ,By . There is Laplacian horizontal mixing with the coefficients Vhand Kh, and a damper with the x-dependent coefficient -y(x) is included near the eastern boundary of the model. The system entrains lower layer water into the upper layer at the rate w•• but detrainment (we < 0) is not allowed for reasons discussed in the next subsection. Pressure gradients in the two layers are given by

\1PI = ga\1[hl(T) - TJ) + hz(Tz - TJ)] + gaz\1T\>

\1pz = ga(Tz - T3) \1(h. + hz), (Ie) where g is the acceleration of gravity, a is the coefficient of thermal expansion (assumed constant), and TJ is the temperature of the deep ocean. Note that, because TI is not constant in our thermodynamic model, part of \1p] varies linearly with depth. To ensure that this part does not drive a depth-dependent current, we assume that the Reynolds stress v;w)' has a vertical structure such that the depth-dependent parts of (v; w;)z and \1PI cancel. A necessary condition for this cancellation is that the depth-independent part of the pressure gradient that appears in (la) is its average value in the layer, \1Pb evaluated by substituting z = -h1/2 in (Ie). The surface heat flux is parameterized by (2) a form similar to the one proposed by Haney (1971). The temperature To is the initial temperature of the upper layer, and th is a measure of the e-folding time for the upper layer to relax back to To. The inclusion of horizontal mixing in the h-equations is not a common feature in layer models. In the present model, hI can become small in upwelling regions near the western boundary, and sharp fronts are produced on the leading edge of northward- moving gyres. Laplacian smoothing of the h-field reduces the development of small-scale noise in these regions, and in some instances is necessary to ensure model stability. 1988] McCreary & Kundu: Model of the Somali Current 31

Boundary conditions are

(3) where the subscript n indicates a partial derivative in a direction normal to the boundary. The first three conditions represent zero slip and no heat flux. The zero normal gradients of the h-fields in (3) ensure that the mass of each layer is conserved (in the absence of entrainment and the damping term /,), as can be verified by integrating the h-equations in (ia) and (i b) over the area of flow. The northern, southern and eastern boundaries of the model basin do not coincide with any real boundaries of the western Indian Ocean, and it is important to minimize their influence. Toward this end, wind fields forcing the model are usually cut off smoothly near these boundaries. In addition, the damping parameter /', which is zero throughout most of the basin, is increased to a large value near the eastern boundary; this damper absorbs equatorial Kelvin and Yanai waves, and inhibits the propagation of coastal Kelvin waves along the boundary and Rossby waves offshore (Moore and McCreary, 1987). In effect, there is a "sponge layer" near the eastern boundary that simulates open boundary conditions there. b. Entrainment. An important process in the model is the entrainment of water from the second layer into the first. This process cools the upper layer and provides stress at its bottom. It also prevents the interface between the two layers from surfacing, a numerical necessity in a layer model like the present one. Entrainment in the model is completely determined by the choice of its rate We' One method for obtaining We involves the solution of a set of equations for turbulent quantities (see, for example, Kundu, 1980). This method, however, is only applicable in a vertically continuous model. Another method, used in bulk models, is to use the Kraus and Turner (1967) formulation, which drastically simplifies and parameterizes the various terms·of the turbulent kinetic-energy equation (see, for example, Schopf and Cane, 1983). A problem with this approach is that, for commonly accepted values of parameters, the interface deepens too much (-400 m) in regions of intense and prolonged wind (like the Somali Coast). Clearly, values of parameters in these formulations are neither universal nor precisely determined. It is also known that quite different models can be made to fit observed layer thicknesses and temperatures (Thompson, 1976). Because of these ambiguities, in this study we adopt the point of view that any method for obtaining We is acceptable if it makes good physical sense and prevents the interface from surfacing.

Our choice for We is the smooth function

(4) 32 Journal of Marine Research [46, I

According to (4), there is entrainment only when hi is less than a specified value He, and We increases parabolically toward a maximum value of He/te as hI approaches zero. [We did try other choices for We that were not as smooth, for example, We = (He/te)()(He - hd, where () is the Heaviside step function. Such functions, however, tended to generate grid-scale noise.]

The entrainment time scale te is chosen to ensure that the interface between layers does not surface. Consider the upwelling induced by the alongshore component of wind a a stress T • The offshore Ekman transport is T / f, and by mass balance an upper limit for a the rate of upward rise of the interface is T / (f6.x), where 6.x is the grid spacing. The maximum value of We must be larger than this value, so that

f6.xHe te~--a-' (5) T

Test runs showed that (5) is an accurate necessary condition for model stability. They also showed that solutions are not sensitive to the value of t•• provided that (5) is satisfied. Not allowing We to become less than zero in (4) is equivalent to omission of detrainment from the model. It is well known that turbulence in the surface layer cannot be sustained for sufficiently large mixed layer depths (caused by downwelling, for example) or for large heating rates, and in that event the interface between turbulent and non turbulent regions retreats. During these detrainment periods, additional layers containing "fossil" turbulence form below the actively turbulent surface layer, some distance above the main thermocline. In a 21klayer model like ours, one must decide how to treat these fossil layers. If the upper layer is viewed as being only the turbulent wind-mixed layer, then the proper choice is to mix the fossil layers into the lower layer, a procedure equivalent to allowing the model to detrain (Schopf and Cane, 1983). In contrast, we view the upper layer as being the entire layer above the thermocline (which should be able to deepen in downwelling regions, for example). In this case the correct procedure is to mix the fossil layers into the upper layer, a task automatically accomplished by neglecting detrainment. c. Finite-difference scheme. Solutions are found numerically on a staggered grid, with variables defined in rectangular grid boxes of dimension 6.x by 6.y. The hand T points are located at the center of grid boxes, and u and v points are located on meridional and zonal edges of the boxes, respectively. The slanted western boundary is passed through u and v points, so that its inclination with respect to the x-axis is tan-I (6.y/6.x). Equations of motion are forward differenced in time using the leap-frog scheme, and fields are averaged between two time levels every 41 time steps in order to control time-splitting instability. Diffusive terms are evaluated at the backward time level, and all other terms at the central time level. The grid step is 6.x = 6.y = 55 km, and the time step is either 6.t = 40,60 or 80 min, depending on the strength of the forcing. 1988] McCreary & Kundu: Model of the Somali Current 33

3. Results a. Parameter choices. The model ocean is forced by wind fields that are composed of one or more patches of the form

.,.= "'oX(x')Y(y')T(t), (6) where x' and y' are either x and y, or they are the coordinates ~ and fJdefined in (A2) with the fJ-axis parallel to a slanted western boundary. Values of the wind strength "'0 are specified below for each solution. The offshore and alongshore structures, X(x') and Y(y'), are also described for each solution and are illustrated schematically in many of the figures. Wind fields are cut off smoothly near northern and southern boundaries, as shown by profile Y(y) in Figures 6 and 7; with one exception (Fig. 6) they are also cut off just west of the damper at the eastern boundary. For the solutions in Sections 3b and 3c, T(t) increases linearly from 0 to 1 in 20 days and is constant thereafter, whereas for those in Section 3d, T(t) is described in Figure 10.

The initial values for layer thicknesses are HI = 75 m and H2 = 250 m.

Temperatures are To = 29°C, where Tois the initial and maximum possible value of TI,

T2 = 15°C and TJ = O°C. The value of the coefficient of thermal expansion is ex = .0002°C-I. The thickness HI is a typical value for the depth of the pycnocline in the

Arabian Sea, H2 is representative of the depth range of the strongest subsurface currents, and T2 and TJ are typical values of temperatures in their respective layers (Roffer et al., 1981; Bruce, 1979; Schott, 1983). With these parameters the character- istic speeds of the two baroclinic modes of the system are CI = 321 cmjs and C2 = 123 cm/s. 7 2 7 2 7 2 The coefficient Vh is 2 X 10 cm js and Kh is either 2 x 10 cm /s or 5 x 10 cm js, 2 2 depending on whether the maximum wind stress is 2 dyn/cm or 5 dyn/cm , respectively. The damping coefficient 'Yis zero everywhere except within 300 km of the eastern boundary layer, where it increases linearly to a maximum value of 1 day-I at a distance of 150 km and is constant thereafter. The thickness below which the upper layer starts entraining is He = HI = 75 m, and the thermodynamic time constants are th = 20 days and te = 0.8 or 0.5 days, the values for the latter depending on the wind strength through inequality (5). Test runs showed that grid-scale noise developed if He was made much less than HI (so that We was a more sharply varying function of hI)' and for this reason we used the maximum possible value for He. b. Response to southern hemisphere east~rlies. Figure 5 shows the model response when it is forced by an idealization of the zonal component of the southern hemisphere trades. The eastern boundary of the model is at x = 40°. The wind stress has a 2 minimum value of 1'(; = -1.5 dynjcm , and its horizontal structure is indicated by profiles X(x) and Y(y) in Figure 5; X(x) also decreases smoothly to zero from 31° to

36°, just outside the damper (not shown because Fig. 5 is only displayed up to x = 30°). 34 Journal of Marine Research [46, 1

x (xl ~ 30 Days 60 Days

120 Days 360 Days 10· i ~L 200 cll/.

- -10·

••• • • - -20· • . :~:.,"... o· 30· o· 30· X X Figure 5. Surface currents and SST in response to forcing by the southern hemisphere easterlies. The wind stress has a minimum value of -1.5 dyn/cm\ and profiles X(x) and Y(y) illustrate its zonal and meridional structures. The 28°C isotherm is indicated by a continuous line, and nowhere is temperature less than 24°. After 360 days the near-equatorial response is almost in equilibrium with the wind. A strong western boundary current overshoots to 1N, and there is a meandering eastward current just south of the equator. Note the absence of cold temperature along the western boundary, and the similarity with the observed flow pattern in Figure 2a. 1988] McCreary & Kundu: Model of the Somali Current 35

So, the model easterlies reach their minimum value at 12.5S and vanish at the equator, 25S, and the African coast, similar to the observed winds in Figure I. After 30 days southward Ekman drift is evident throughout most of the forcing region. There are also westward currents just north and south of the equator that are dynamically related to the two-dimensional, linear, Yoshida-jet solution discussed in Moore and Philander (1978). [The Yoshida jet owes its existence to the vanishing of Coriolis force at the equator, so that near the equator a zonal wind drives an accelerating zonal current. As usually defined, the Yoshida jet is forced by a wind field that is independent of y, whereas in Figure 5 the wind vanishes at the equator.] At later times the currents become more zonal and strengthen considerably, and after 360 days there is a strong eastward current just south of the equator and a westward current near 7.5S. These changes in the flow field occur because the interior ocean gradually adjusts toward Sverdrup balance as Rossby waves propagate across the basin. By 360 days the interior flow field north of lOS is quite similar to that predicted by Sverdrup theory [see the discussion of equation (A6)]. The hi field gradually shoals south of the equator, causing entrainment and a .decrease of TI' The cooling is significant, with T] decreasing by almost 4°C about 750 km from the eastern boundary. There is, however, no cooling anywhere along the coast, a consequence of the lack of upwelling favorable winds there. The region where hi shoals, and therefore the region where the model entrains, is also consistent with Sverdrup theory [equation (A6»). Although linear dynamics can account for some basic properties of the flow field, the solution has obvious features which are not linear. By day 90 the northward western boundary current becomes strong enough for nonlinear terms to affect its path. It overshoots the mean latitude of the eastward interior flow to IN, where it bends offshore and southward to join the eastward current. Meanders form on the current near the coast and then gradually spread out into the interior ocean. Note that as the eastward current increases in strength the wavelength of the meanders increases. Similar features (overshoots and meanders) also develop in other models of western boundary currents (Gill, 1982, P 519). Arguments using potential vorticity have often been invoked to explain overshoots as follows. In order to join with the eastward interior current farther north, water parcels from the southern ocean must acquire positive potential vorticity. Horizontal mixing in the northward, western boundary

current is a strong source of positive vorticity ~, since necessarily Vh~xx > 0 near the boundary; the parcel remains in the boundary current, overshooting if necessary, until it has acquired the necessary amount. The meanders are akin to stationary Rossby waves, for which the westward phase speed is balanced by an eastward current (see, for example, White and McCreary, 1976). The increase in meander wavelength with current strength is consistent with this interpretation. The development of the meanders away from the eastern boundary is also consistent, because stationary Rossby waves have eastward group velocity. The solution in Figure 5 is similar to the numerical solutions reported in Anderson 36 Journal of Marine Research [46, 1 and Moore (1979) with one important difference: the western boundary current in their solution separates from the coast considerably farther north near 8N. One reason for this difference is that the northern edge of their wind stress was located 2° farther north than ours. The primary reason, however, is that their western boundary was everywhere oriented meridionally. In a test run, we repeated the calculation in Figure 5 with a meridional boundary, and the western boundary current also separated much farther north. There are several reasons why the solution in Figure 5 is not a good representation of the observed Southern Gyre. One is that the location of the gyre in Figure 5 is too far to the south. Another is that the spin-up time for the gyre in F~ure 5 is far too long, since the observations show that the coastal currents are set up only days after the wind onset (Diiing and Schott, 1978; Schott, 1983). Finally, and perhaps most importantly, there is no cold wedge to the north of the separation point. On the other hand, the near-equilibrium solution in Figure 5 may account for the flow that already exists in late April/early May before the winds become southerly (Fig. 2a); consistent with the observations, the solution has a coastal eddy and a meandering eastward flow, all confined south of the equator. Thus, the circulation in April may be driven by the annual mean of the southern hemisphere trades, becoming visible during the transition period between the two monsoons when the locally forced circulation is weak or absent. c. Response to alongshore winds. In this subsection we describe solutions that are forced by alongshore wind fields with different horizontal structures in ocean basins with western boundaries that are either oriented meridionally or slanted at 45°. The structures of the western boundary currents differ markedly, and illustrate four distinctly different types of behavior.

(i) Zonally-independent wind. meridional boundary Figure 6 shows the model response forced by an x-independent northward wind in a rectangular basin with an eastern boundary at x =35°. The wind stress has a maximum value of T6 = 2 dyn/cm2"and its horizontal structure is indicated by the profiles X(x) and Y(y) in the figure. The eastern boundary of the model is at x = 35°, and the wind is not cut off near the boundary. Outside the equatorial Rossby radius (-3°), the interior flow field is a simple Ekman flow with zonal currents that are inversely porportional to f Inside the equatorial Rossby radius, the interior zonal currents weaken and vanish on the equator, so that they are strongest near ±3°, as in the two-dimensional, linear solution of Moore and Philander (1978). In contrast to the solution in Figure 5, the interior flow does not change significantly as time passes. The reason for this is that the wind does not have an eastern edge. Consequently, no Rossby waves are generated in the interior ocean, and the solution does not adjust toward Sverdrup balance. 1988] McCreary & Kundu: Model of the Somali Current 37

x Ixl < 20'l: 20' - 24'l: 24' - 2B'l: _.i'i.;,'i·'··-I __

30 Days 60 Days

-10'

120 Daya 270 Daya

-10' 20' 0' x 20' O' x

Figure 6. Surface currents and SST in response to forcing by a uniform northward wind. The wind stress has a maximum of 2 dynjcm2, and profiles X{x) and Y{y) illustrate its zonal and meridional structures. Light and dark shaded regions indicate the temperature ranges 20°C T, < 24°C and Tl < 20°C, respectively, and the 28°C temperature contour is shown. Note the constant formation of eddies that propagate north and decay. 38 Journal of Marine Research [46, I

After only 30 days, the coastal current is strong enough for the effects of the nonlinear terms to be apparent. The current overshoots the latitude of the strongest eastward interior flow (-3N), bends offshore near ION to form a semi-closed eddy, and finally returns southward in a coastal countercurrent to join the eastward interior current. Meanders later develop on this eastward current for the same dynamical reasons that they do in the solution of Figure 5. The semi-closed eddy moves northward slowly and weakens, and by day 180 has decayed to negligible strength. As the eddy propagates north, new ones develop in the south, which in turn propagate north and weaken (day 120). Thus, the solution never reaches a steady state in the 360 days of this calculation, but rather continues to shed eddies that propagate north and decay. There is a concentrated region of cold water at the northern edge of the eddies, particularly at times when there is a strong gyre (days 30 and 270). The wedge at day 30 forms as follows, and the others develop for similar reasons. Initially, entrainment due to offshore Ekman drift occurs relatively uniformly everywhere along the northern coast. Subsequently, cool upwelled water is advected offshore where the western boundary current leaves the coast. South of the eddy the boundary cuuent advects warm water and a thicker surface layer to the north, and thereby eliminates entrainment and cooling south of the eddy. The result of these two advective processes is the formation of a sharp temperature front on the northern flank of the gyre. It is noteworthy that the eddies never stopped propagating northward in any of our calculations with x-independent winds. Similar calculations have been performed in several previous studies, and eddies also continued to propagate northward in most of them. Hurlburt and Thompson (1976) forced a 2-layer model with a wind stress of amplitude I dyn/cmZ; their solution developed a single eddy that propagated north rapidly, moving out of their model basin wi~hin 50 days. Lin and Hurlburt (1981) 2 forced a I liz-layer model with a stronger wind stress of 2 dyn/cm ; the main eddy in their solution moved northward more slowly and tended to stall out after 90 days, but it did not completely stop its movement. Philander and Delecluse (1983) forced an oceanic general circulation model (GCM) with a northward wind stress of .5 dyn/cmz, and the cold wedge in their solution continued to move northward throughout the 50 days of their integration. In contrast, the cold wedge in the GCM calculation of Philander and Pacanowski (1981) remained near 7N even after 200 days. The reason for this stalling, however, is most likely due to their not using a sufficiently strong damper on the artificial northern boundary of their model basin. Their Figure 4 suggests that coastal Kelvin waves, generated along the eastern boundary, propagated around the basin and generated a southward flow along the northern portion of the western boundary; this southward flow very likely inhibited the northward movement of the wedge. (A similar difficulty was encountered by Lin and Hurlburt, 1981, when they used a closed, rather than open, northern boundary.) (ii) Alongshore-independent wind with curl, meridional boundary Figure 7 shows the model response to a meridional wind stress that weakens offshore, a situation more relevant to the forcing in the Somali Current region. The 1988] McCreary & Kundu: Model o/the Somali Current 39

x (x) ~ 30 Days 60 Days

- 20' ~L 100 ute

- \0' Y

.'" ...... Eq

-\0'

90 Days \60 Days

x x

Figure 7. Surface currents and SST in response to forcing by an alongshore wind with curl. The 2 wind stre~s has a maximum strength of 2 dyn/cm , and profiles X(x) and Y(y) illustrate its zonal and meridional structures. Shaded areas indicate regions of cold water, as described in Figure 6. Note the change of scale for eastward velocity in the different panels. Initially the circulation is very similar to that in Figure 6. At 180 days, however, the flow field is eddy-free and almost adjusted to a steady Sverdrup balance. An additional circulation, generated by entrainment south of the equator, flowsout of the basin along the equator. 40 Journal of Marine Research [46, 1 eastern boundary of the basin is at x = 35°. The wind stress has a maximum value of 2 rb = 2 dyn/ cm at the coast and decays to zero 1500 km offshore, as indicated by the profile X(x) in the figure. It is also cut off near the northern and southern boundaries with the profile Y(y). After 30 days the solution is quite similar to that in Figure 6, but thereafter the two solutions differ markedly. The initial gyre propagates northward and weakens more rapidly than in Figure 6, and virtually vanishes after 90 days. By day 180 the ocean has very nearly adjusted to an eddy-free, completely steady state. Initially, there is strong entrainment and cooling along the northern coast, but as time passes coastal upwelling decreases and by day 180 has almost vanished. In contrast, entrainment gradually develops over a broad region south of the equator, and Tl eventually dlecreases by nearly 4°C there. The extensive differences in circulation between Figures 6 and 7 demonstrate clearly how strongly remote forcing affects solutions. Because the wind has an eastern edge, Rossby waves are excited; they propagate westward and adjust the interior flow field toward Sverdrup balance. In this state there is a southward drift in the offshore curl region, eastward and westward flows at the northern and southern edges of the wind field, respectively, and a connecting northward western boundary current [see the discussion of Eq. (A 7)]. After 180 days one part of the circulation in Figure 7 is clearly a flow of this type. (Southward Sverdrup drift is not visible in Figure 7 because it is smaller than the threshold value for plotting arrows.) Another part of the circulation, the equatorial jet, is due to entrainment in the model, as discussed next. An effect of the adjustment of the interior ocean to Sverdrup balance is that hi is deeper than HI everywhere north of the equator and shallower than HI to the south [Eq. (A 7)]. This property accounts both for the vanishing of coastal upwelling along the northern coast as the model comes into equilibrium with the wind, and for the gradual development of entrainment and decrease of SST south of the equator. Another consequence of entrainment south of the ~quator is that there is a continuous flux of mass into the surface layer, and the system adjusts to eliminate this fluid. The entrained water flows west to the western boundary, north along the boundary to the equator, and finally out of the basin along the equator in an eastward jet established by equatorial Kelvin waves. Cox (1979, 1981) carried out a calculation similar to that in Figure 7 using an oceanic GCM. He integrated the model for a period of 90 days, and during that time the solution continued to shed eddies that propagated northward. Our solutions suggest that the eddies would have vanished had Cox integrated the model for a longer time. In support of this idea, the eddies in his solution were clearly weakening in the later stages of his calculation.

(iii) Alongshore-independent wind with curl, slanted boundary Figure 8 shows the response forced by an alongshore wind stress when the coast is inclined at 45°, similar to the real coast of Somalia. The wind is assumed alongshore 1988] McCreary & Kundu: Model of the Somali Current 41

20·

10· y

• .•...... •••••••44 -10· o· o· 10· o· 10· 20· 30· x Figure 8. Surface currents and SST in response to forcing by an alongshore wind with curl. The wind stress has a maximum value of 2 dyn/cm2. The profile X(~) illustrates the offshore structure of the wind stress, and its alongshore structure is uniform. Shaded areas indicate regions of cold water as described in Figure 6. At 180 days, the flow field is nearly adjusted to a quasi-steady state that is very different from that in Figure 7. A strong cross-equatorial current overshoots to 4N, and then bends offshore to form a meandering eastward flow along the equator. There is a stationary closed gyre, and two wedges of cold SST near 4N and 9N.

2 independent, has a maximum value of 76 = 2 dyn/cm at the coast, and decays to zero at an offshore distance of ~ = 1500 km as indicated by the profile Xm in the figure. In addition, the wind field is cut off near artificial boundaries as discussed previously. Thus, the horizontal structure of this wind field is equivalent to that in Figure 7, the difference in the two situations being only the orientation of the western boundary and the wind. At 30 days, an eddy forms near the equator with its northern branch near 3N, and there is a weak eastward flow along the equator. By 60 days the equatorial flow intensifies and develops a meandering pattern, and the southern eddy is now only semi-closed since much of its outflow joins with the equatorial jet. At the same time, a second eddy begins to develop between 3N and 9N. The patterns at 60 and 180 days are quite similar, except that a third, weak eddy appears near 13N after 180 days. The eddies remain stationary, and do not move along the coast or weaken with time. Note 42 Journal of Marine Research [46, 1 that neither the size nor the shape of the gyres resembles that of the wind curl, indicating that they are not a directly forced response to the Ekman pumping there. In contrast to the solution in Figure 7, coastal upwelling continues along the northern coast even after the ocean has adjusted to equilibrium with the wind, and there are wedge-shaped regions of cold water located on the northern flanks of eddies. As discussed before, the southern front of the wedges is caused by the offshore advection of cold water and by the advections of warm water and deep hI along the coast from the southwest. Their northern front is due to the onshore advections of warm water and deep hi by the southern branch of an eddy just to the north. Thus, cold wedges with two fronts are usually found between two eddies. If there is only one eddy present, then the region of cold water only has a sharp southern front, as in Figures 6 and 7. As in the solution in Figure 7, one component of the equilibrium, interior circulation is very nearly a Sverdrup flow confined to the edges of the wind (compare Fig. 8 with Fig. 15), and the other is due to entrainment mass flux, which ultimately flows out of the upper layer along the equator. As discussed next, entrainment is greater for the solution in Figure 8. Consequently, the western boundary current is stronger and overshoots the equator, and meanders form on the equatorial jet. The equilibrium, offshore structure of hI is also consistent with Sverdrup theory. Because the wind stress has a westerly component, hI shoals toward the coast in both hemispheres [due to the integral of F in Eq. (A3)]. As a result, hi is shallower everywhere than it is in the solution of Figure 7, and is less than HI along the northern coast [Fig. 16 and Eq. (A8)]. It follows that in Figure 8 there is an increased rate of entrainment in the southern hemisphere, and that upwelling exists along the northern coast. Cox (1979, 1981) found a solution similar to that in Figure 8 using an oceanic GCM. He noted the presence of stationary gyres and cold wedges in his solution, and pointed out that they were an effect of boundary slope. The solution in Figure 8 is in fact quite similar to Cox's (see Fig. 3 of Cox, 1979). The two solutions differ primarily in that his gyres are positioned 3° farther north than ours. The likely reason for this difference is the strong entrainment mass flux south of the equator in our model. As in the solution in Figure 7, the system adjusts to eliminate the entrained water along the equator, and so the boundary current bends offshore just north of the equator to feed this flow.

(iv) Wind patch. slanted boundary Figure 9 shows the response forced by a strong patch of alongshore wind stress confined in the northern hemisphere when the western boundary is slanted. The wind 2 stress has a maximum value of Til = 5 dyn/cm , and its horizontal structure is the same as that shown in Figure lOb. There is a region of strong negative wind curl not far from the coast. After 30 days a gyre has begun to spin-up in the southern half of the wind patch. By 1988] McCreary & Kundu: Model of the Somali Current 43

20·

10· y

-10· o· 10· o· 10· o· 10· 20· 30· x

20·

10· y

-10· x

'I6l> Figure 9. Surface currents and SST in response to forcing by a patch of strong alongshore wind. The wind has a maximum magnitude of 5 dyn/cm2 at the coast, and has the bell-shaped horizontal distribution shown in Figure lOb. The flow vacillates between single-gyre and double-gyre states with a period of about ISOdays. 44 Journal of Marine Research [46, I

90 days the gyre strengthens and a second gyre forms to the north. By 180 days there is a well-developed two-gyre system with two cold wedges, and the southernmost gyre has moved southward by 2°. Shortly thereafter the southern gyre reverses its movement and starts to move northward. After 210 days it begins to interact with the northern gyre, and by 240 days the two gyres have coalesced. The single, coalesced gyre then moves southward, and a new gyre spins-up to its north. On further integration this entire sequence repeats, and the system vacillates slowly between single-gyre and double-gyre states with a period of about 150 days. As in Figure 8, the structure of gyres does not at all resemble that of the wind curl. Moreover, gyres move southward completely out of the region of strong forcing. These properties indicate that the dynamics of gyres are not governed by simple Ekman pumping. As in the solutions of Figures 7 and 8, one part of the interior flow field resembles a Sverdrup flow (compare Figs. 9 and 16), whereas the other part resulting in an equatorial outflow is due to entrainment. Because the wind has an eastward component, hI shoals to the west and is less than HI near the coast (Fig. 6) so that entrainment occurs there. Several other calculations were carried out to test the sensitivity of this solution to parameter changes. In one of these, the strength of the wind stress was reduced from 5 2 to 2 dynjcm , while the other parameters were kept the same as in Figure 9. In this case, the resulting double-gyre system remained steady and did not vacillate. In another calculation, 'the western boundary was oriented meridionally and the wind 2 stress was directed northward with a strength of 5 dynjcm • A single eddy formed, moved north and weakened, and eventually the solution adjusted to an eddy-free steady state with no coastal upwelling, a state virtually the same as that given by linear theory [Eq. (A7)]. d. The model Somali Current. Here we discuss solutions that are forced by an idealized representation of the alongshore wind stress field near the Somali Coast during the Southwest Monsoon. The model wind field is shown in Figure 10, and has two components: a background field TB that represents the moderate, cross-equatorial and alongshore winds appearing in May (Fig. 1a), and a wind patch TF that represents the Findlater jet beginning in June (Fig. 1b). The background field TB has a maximum 2 strength of I dynjcm , is essentially independent of alongshore distance, and decays offshore in 1500 km (Fig. lOa). The wind patch TF has a maximum strength of 2 4 dynjcm , is centered at 12N, and decays offshore in a distance that increases linearly from 500 km in the south to 2500 km in the north (Fig. lOb). The horizontal structures of TB and TF are indicated by the profiles Xm and Y(17) in the two panels. The total wind stress field, TB + TF' which occurs during the peak phase of the monsoon, is shown in Figure 10c. The time variations of the maximum strengths of T Band T F are given in

Figure 10d, with t = 0 corresponding to May 1. Figure 11 shows the model response when the winds are not relaxed in September 1988] McCreary & Kundu: Model of the Somali Current 45

181 Ibl Ie)

20'

10' Y

-5 dyn/em . -10' 30' O' 10' X 20' X 20' ',30'

(dl -"""" rol(t) / / -...•...•~., ----~-~--~--~-----_., . II0 30 60 90 120 150 180 days t

Figure 10. Idealized representation of the observed wind field during the Southwest Monsoon that is used to force the model in Figures 11-15. Panel (a) shows the background wind field TB that represents the observed wind field in May (Fig. la); TB is composed of a patch of northward wind at low latitudes [with distributions X(x) and Y(y)], and a second patch of alongshore wind along the slanted coast [with distributions Xm and Y(I1)]. Panel (b) shows 2 the Findlater jet field TF' The wind stress has maximum values of I dyn/cm for each of the patches in panel (a) and a maximum value of 4 dyn/cm2 for the patch in panel (b). Panel (c) shows the sum TB + TF that represents the wind field in July at the peak of the Southwest 2 Monsoon (Fig. 1b), and the contour interval is .5 dyn/cm • The lower panel (d) indicates how TB (light line) and TF (heavy line) are imposed over time, with t = 0 corresponding to May 1. In most runs TB and TF are kept constant after day 60 (solid lines); in one case (Fig. 14) they are relaxed to zero from 130 to 150 days (dashed lines).

(solid lines in Fig. 10d). The model Southern Gyre quickly spins up in response to TD, and by 60 days (July 1) is well developed with its northern flank near 4N. The model

Great Whirl spins up later in response to Tp, and by 90 days (August 1) the system has a well-developed double-gyre state with associated cold wedges. At this time the Southern Gyre has already started to move north. By 120 days there is a partial coalescence of the two gyres, and a third gyre, the model Socotra Eddy, starts to develop north of ION. Complete coalescence has occurred by 150 days. Subsequently, the single coalesced gyre moves southward, and the Socotra Eddy strengthens to become a new Great Whirl. After 270 days the flow field has returned to a double-gyre state, very similar to that on day 90. These two gyres collapse again by 330 days, and the process continues. As in Figure 9, then, the system slowly vacillates between single-gyre and double-gyre states. Thus, the motion of gyres along the coast, and their 20'

'0'

20'

'0'

Figure 11. Surface currents and SST in response to the wind field of Figure 10, up to 330 days. Shaded areas indicate regions of cold water as described in Figure 6. The Southern Gyre spins up initially in response to Te, and the Great Whirl spins up later in response to TF' After 90 days there is a well-developed two-gyre system with two associated cold wedges near 4N and ION. Subsequently, the Southern Gyre moves northward and coalesces with the Great Whirl. On continued integration, the flowfield vacillates between single-gyre and double-gyre states. 1988] McCreary & Kundu: Model of the Somali Current 47 coalescence, is part of the model's response to the peak monsoon wind field, and is not due to the monsoon relaxation or any other change in the wind. Figure 12 shows details of the initial coalescence in Figure 11, focussing on the velocity and temperature fields at 100, 110, 120 and 130 days. The temperature fields clearly show the double-wedge pattern at 100 days, the northward propagation of the southern wedge at 110 and 120 days, and its eventual coalescence with the northern wedge at 130 days (September 10). Note that the final collapse is quite rapid, since two distinct cold wedges are stilI visible at 120 days.

Figure 13 shows the upper layer thickness hI and the second-layer velocity field V2 for the calculation of Figure 11 at 130 days. The line drawn parallel to the coast through the hi field is a "model tanker track", which corresponds to the real tanker track of Figure 3. The hi field along the model tanker track reaches a maximum value of 168 m at the center of the gyre, similar to the observed value of 200 m for the 20°C isotherm in Figure 3. The hi field also deepens in a location corresponding to that of the Socotra Eddy and is relatively flat south of the main gyre, again consistent with the shape of the

20°C isotherm in Figure 3. The V2 field shows that the coalesced eddy spins in the same direction in the second layer as in the first, and that there is no coastal undercurrent. Observations, however, indicate that subsurface flow is southward at several places along the Somali Coast (for example, Figs. 12 and 13 of Schott, 1983). It is unclear to us why the model fails to produce any subsurface southward flow. A possible cause is that the wind field forcing the model is too simple, both temporally and spatially. Another possibility is that the model entrainment along the coast is too strong, thereby requiring a continuous source of lower-layer water; this water can only be supplied in a northward boundary current that is fed by a westward equatorial jet in the lower layer. Such a source would not be necessary in a different model, which allows isopycnals to surface, for example. The model response near and after the end of the monsoon is shown in Figure 14. The forcing for this case is the same as in Figure 11, except that the forcing is turned off from 130-150 days (dashed lines in Fig. lOd). The coalesced eddy weakens and breaks up, and coastal SST warms up due to lack of upwelling favorable winds. Several other calculations were performed to test the sensitivity of the model to various changes in the wind field. In one calculation, both TO and TF were applied simulataneously; no Southern Gyre developed during the first months of the integration, indicating that the Southern Gyre is forced by TO alone. In a second calculation, 2 the maximum magnitude of TO was decreased to 0.75 dyn/cm while that of TF was 2 increased to 4.25 dyn/cm • In this case the coalescence of the Southern Gyre and the Great Whirl occurred after only 100 days, one month sooner than in Figure II. In a third calculation the alongshore extent of TF was increased slightly. (The structure of the wind was similar to that in Fig. lOb, except that it extended from 2.5N to 22.5N, instead of from 3N to 21 N.) In this case, the Southern Gyre and the Great Whirl moved very little during the first 180 days of integration, and no coalescence occurred. 48 Journal of Marine Research [46, 1

20·

10·

-10·

20·

10·

Figure 12. Surface currents and SST during the coalescing period of Figure 11. Cool SST is indicated by contour plots with a contour interval of 1°C. The panels clearly show the coalescence of the two gyres and cold wedges at day 130. ] 988] McCreary & Kundu: Model of the Somali Current 49

20·

10·

-10· o· 10· o· 10· x 20· 30· Figure 13. Second layer velocity and upper layer thickness hi at 130 days for the flow field of Figure 12. Regions where hi is shallower than 75 m are shaded. The line parallel to the coast corresponds to the tanker lane of Figure 3. Note the similarity between hi along this line and the depth of the 20°C isotherm in Figure 3. A model Socotra Eddy is beginning to develop.

The solutions in the previous paragraph suggest that the model response is quite sensitive to the forcing. When the runs a're continued past 180 days, however, all of them begin to vacillate between single-gyre and double-gyre states with a period of about 180 days, and only the phase of the vacillation cycle differs among them. Thus, the final behavior of the model is not sensitive to the structure of the wind. It is only the initial development, which determines the phase of the vacillation, that is sensitive. A final calculation, inspired by Experiment 10 of Cox (1979), was carried out to test the model's sensitivity to the numerical scheme, particularly to the orientation of the grid. In this run the ocean basin was a rectangular domain rotated clockwise by 45°, with the left edge of the domain corresponding to the slanted Somali Coast. In addition, f)"x and f)"y were reduced to 39 km in order to make the resolution of the Somali Current comparable in the rotated and original grids; since the model Somali Current flows diagonally across grid boxes in the original grid, the effective grid size is f)"x/ fi = f)"y/ fi = 39 km rather than 55 km. The model was forced by the wind stress shown in Figure 10, except for minor modifications south of the equator, and all other 50 Journal of Marine Research [46, I

20·

10· y

-10· 10· o· 10· 10· 20· 30· o· o· x

Figure 14. Surface currents and SST near and after the relaxation of the monsoon winds. In this run TB and TF are gradually turned off from 130 to 150 days, as indicated by the dashed lines in Figure 10d. The wind relaxation causes the gyres to weaken and coastal upwelling to cease. parameters were kept the same as for the solution in Figure 11. During the first 150 days, the solution followed a time development much like that in Figure 11, the primary difference being that the two gyres coalesced somewhat prior to day 120 instead of near day 130. Subsequently, however, the solution did not vacillate; instead, the coalesced gyre moved slowly southward until its center was positioned near 5N, and then oscillated about this mean position with a period of about 60 days and an amplitude of .5°. Cox (1979) also noted a sensitivity to grid orientation, and suggested that it was due to the effective change in the finite-difference formulation of the advection terms between the two grids. Luther and O'Brien (1985) and Luther et al. (1985) have recently carried out a numerical simulation of the Somali Current system throughout the year. They used a 11/2-layer model without entrainment, and forced it with monthly mean observed winds. The thickness of their layer was large (HI = 300 m), presumably to prevent the model interface from surfacing near the coast, and as a consequence their solution developed rather weak (-50 cm/s) currents. Nevertheless, their solutions compared favorably with observations during the Southwest Monsoon, including the generation and coalescence of eddies. Because of the differences between their modell and ours, however, it is not clear whether eddies form and move in the two systems for the same dynamical reasons. 1988] McCreary & Kundu: Model of the Somali Current 51

4. Summary and discussion The dynamics of the Somali Current system during the Southwest Monsoon are studied using a 2lj2-layer numerical model that includes entrainment of water into the upper layer. Entrainment generates cool SST, provides interfacial friction, and prevents the interface from surfacing in regions of strong coastal upwelling. The entrainment velocity is given by the simple formulation (4), which makes good physical sense in regions of strong upwelling like the Somali Coast. Solutions are forced by a variety of simple wind stress fields in ocean basins with western boundaries oriented either meridionally or at a 45° angle (Sections 3b and 3c); these solutions isolate some basic processes at work in the model, and allow our results to be compared with those of previous workers. Other solutions are forced by an idealized representation of the real wind field off Somalia (Section 3d), and they compare favorably with observations. Solutions forced by southern hemisphere easterlies slowly adjust to equilibrium with the wind. After 360 days there is a strong western boundary current south of the equator that bends offshore at the equator and meanders back into the ocean interior; SST cools south of the equator in the interior ocean, but no cold wedge forms on the Somali Coast (Fig. 5). It is unlikely that the easterlies are important for generating the major features of the Somali Current circulation, especially the Southern Gyre which turns off at 4N. On the other hand, the observed flow just south of the equator at the end of April before the monsoon begins (Fig. 1a) could very well be forced by the annual mean component of the easterlies. Equilibrium solutions forced by alongshore winds vary considerably depending on the orientation of the western boundary and the horizontal structure of the wind, and illustrate four distinctly different types of western boundary current response. When the western boundary is meridional and the wind is x-independent (curl-free), the solution does not reach a steady state but constantly forms new eddies that propagate northward and decay (Fig. 6). In contrast, if the boundary is meridional and the winds weaken offshore, the solution reaches a completely steady, eddy-free state, with no coastal upwelling (Fig. 7). A comparison of these two solutions (Figs. 6 and 7) demonstrates how strongly remote forcing affects solutions. When the western 2 boundary is slanted and the alongshore wind stress is moderate (~2 dynjcm ), solutions adjust to a steady state that contains stationary gyres and cold wedges (Fig. 8), a result first reported by Cox (1979,1981). If the boundary is slanted and the 2 wind stress is strong (~5 dynjcm ) and confined north of the equator, then the response slowly vacillates between single-gyre and double-gyre states (Fig. 9). The latter two solutions (Figs. 8 and 9) show that gyres are not directly forced by negative wind curl. The structures of the offshore flow field and the upper-layer thickness (and hence the regions where entrainment occurs) in the solutions are to a large extent determined by linear dynamics, with the interior ocean adjusting toward Sverdrup balance via the radiation of Rossby waves (see the Appendix). One interesting conclusion of linear 52 Journal of Marine Research [46, 1 theory is that steady coastal upwelling forced by an alongshore wind with an eastern edge is possible only when the western boundary is slanted [Eq. (A8)), a property consistent with our nonlinear solutions. Other features of the offshore flow field are not determined by linear dynamics. For example, there is an additional circulation due to entrainment mass flux into the upper layer, which eventually flows out of the system along the equator. In addition, stationary meanders form on sufficiently strong, eastward interior jets. Meanders occur whenever the western boundary current that feeds a jet inertially overshoots the mean latitude of the jet. Their dynamics are similar to those of stationary Rossby waves. Our representation of the monsoon wind field consists of two components: a moderate background wind stress field TB turned on in May, and a strong wind patch TF turned on gradually in June (Fig. 10). Figure II shows the model response to this wind field. A single gyre, the Southern Gyre, initially develops south of 4N in response to TB' and a second gyre, the Great Whirl, develops later between 4N-9N in response to 7'F' Cold wedges form on the northern flanks of both gyres, and by the end of July the model flow field resembles the observed two-gyre system (Fig. 2). The Southern Gyre subsequently moves northward, and eventually coalesces with the Great Whirl in September before the monsoon begins to weaken, consistent with the observations (compare Fig. 13 and Fig. 4). If the monsoon wind field is not relaxed, the solution in Figure 11 slowly vacillates between single-gyre and double-gyre states. Although most solutions forced by monsoon winds, 7'8 + TF, eventually do vacillate, the time at which the vacillation cycle begins is sensitive to both the spatial and temporal structure of the forcing; for example, when TF is slightly increased in areal extent, the initial coalescence of the two gyres does not take place until after 180 days. This sensitivity may explain why observed gyres do not always coalesce. If the solution is evaluated in a rectangular basin rotated clockwise by 45°, the coalescence happens two weeks earlier than it does in Figure 11 and a long-period vacillation does not occur. Thus, the existence of vacillating solutions is also sensitive to the numerical scheme. The good agreement between our model Somali Current simulation and the major features of the observed circulation is encouraging, indicating that the present model contains much of the fundamental dynamics involved. On the other hand, contrary to the observations, the model fails to reproduce a southward coastal undercurrent, suggesting that some important processes are neglected or not well represented. In addition, there are unexplained questions concerning the dynamics of the gyres. For example, we do not yet clearly understand why the slope of the western boundary is so critical for the generation of either steady or vacillating systems of gyres. We are currently continuing this research in an effort to provide a more thorough understand- ing of the fundamental processes involved.

Acknowledgments. This work was supported by ONR Contract No. NOOOI4-85-K-OOI9,and NSF Grant No. OCE-85-09752. We thank Dennis Moore, Mark Luther and Bob Molinari for 1988] McCreary & Kundu: Model of the Somali Current 53

helpful discussions, Kevin Kohler for computer programming, and Kathy Maxson for drafting and typing.

APPENDIX Steady linear solutions Equilibrium solutions to the present model have basic properties that are to a large extent determined by linear dynamics. Notably, when the wind stress has an eastern edge the model interior ocean adjusts toward Sverdrup balance, and this adjustment sets the structures of the interior flow field and the upper-layer thickness hi' The structure of hi is particularly important, since entrainment in the model occurs only in regions where hi is less than He = HI [see Eq. (4)]. A simple model that illustrates these properties is a linearized, 11/2-layer model with linear drag (Stommel, 1948), for which the steady-state equations of motion are

-fv + g'hx = F - vu,

fu + g'hy = G - vv, (AI)

X Y where F = T / H, G = T / H, g' = (top / p)g, H is the initial thickness of the layer, and v is a drag coefficient. Since the velocity field is nondivergent, it is useful to introduce a stream function defined by t/lx = v and t/ly = - u. Here we find solutions to (AI) when there is a western boundary along the line x = - y tan 8. It is convenient to introduce the rotated coordinate system

~ = x cos 8 + y sin 8, 7] = -x sin 8 + y cos 8, (A2) so that the 7]-axis is coincident with the boundary. Any function q(x, y) expressed in terms of ~ and 7/ is designated below by primes, that is, q'(t 7]) = q(x, y). For example, in the rotated coordinate system the Coriolis parameter is!, = (3(~sin fJ + 17 cos fJ). Provided the horizontal scale of the wind is sufficiently large, mixing in the interior ocean is negligible and the flow field adjusts to Sverdrup balance. The streamfunction t/ls(x,y) and layer thickness hs(x,y) for Sverdrup flow are

(A3) hs = H + ?~t/ls + 1:FdX).

The assumption that the wind field has an eastern edge is implicit in (A3); otherwise the integrals are not well defined. A boundary layer is required along the western boundary to ensure that there is no flow through the boundary. Equations for the boundary streamfunction t/I~(~, 7/) and layer thickness h~(~,7])are

(A4)

where the boundary-layer assumption that t/I~ varies slowly in the alongshore direction 54 Journal of Marine Research [46, I has been adopted. The solutions to (A4), subject to the boundary condition 1/;~(0,'11) = -1/;~(0, '11), are

1 h~ = -; (f' + v tan O)1/;~. (AS) g

The complete solution is the sum of the solutions in (A3) and (AS). When the wind stress is zonal, the interior solution is

I 1 1/;s = - R JX Fydx, hs = H + -; JX (F - yFy) dx. (A6) /.l +~ g +~

For a westward wind field like that in Figure 5, it follows that there is a westward current in the middle of the wind band where Fyy > 0, and there are eastward countercurrents near the northern and southern edges of the wind where Fyy < O. In addition, h is shallower than H in a latitude band south of the equator, reaching its minimum value at 6.25S where Fyy = O. After 360 days the circulation in the interior ocean in Figure 5 is beginning to look very much like that described by (A6). For example, there is a strong eastward countercurrent near the equator. In addition, the hI field is shallower than HI in the broad region south of the equator, as indicated by the presence of cool SST due to entrainment there. When the wind field and the western boundary are meridional, the complete solution IS

I 1/; = - [G(x, y) - G(O, y)e-tlx/pJ, (A7) ~

For a northward wind field like that in Figure 7, there is eastward flow at the northern edge where Gy < 0, southward flow throughout the ocean interior where Gx < 0, westward flow at the southern edge where Gy > 0, and a northward western boundary current that connects the eastward- and westward-flowing branches. The layer thickness h is shallower than H only south of the equator where y1/; < O. Note that h = H everywhere along the western boundary, even in regions where the winds are upwelling favorable. After 360 days, the solution in Figure 7 closely resembles this linear response, with one component of the circulation flowing around the edges of the wind. The hI field is shallower than HI only offshore and south of the equator, and so entrainment and cooling are confined to the interior, southern ocean. An extra component to the circulation in Figure 6, the equatorial jet, provides an exit for the water entrained south of the equator; this current is not present in (A 7) because of the lack of entrainment in (AI). For an alongshore wind and a slanted western boundary, the value of the layer 1988] McCreary & Kundu: Model of the Somali Current 55

Figure 15. Surface currents and layer thickness h in a linear, reduced gravity model forced by 2 an alongshore wind field. The wind stress has a maximum value of 2 dynJcm , and profiles X(x) and Y(y) illustrate its zonal and meridional structures. The contour interval for h is 20 m, and regions where h is less than 75 m are shaded. Compare this solution to that in Figure 8. The interior flowfieldsare similar, except there is an additional circulation in Figure 8 due to entrainment mass flux. Regions where h is shallower than H correspond to regions of cool SST in Figure 8.

thickness at the coast is

h'(O,11) = h( - y tan 8, y) = H + --;1 [l-YtanO Fdx - v tan 81/;s( - y tan 8, y) ] . (A8) g +~ The last term within the square brackets of (A8) is almost always negligible with respect to first term. It follows that when the alongshore winds have an eastward component (that is, F> 0), h will be shallower than H everywhere along the western boundary. Therefore, in a model that includes entrainment for h < H cold coastal temperatures will remain as part of the equilibrium response to the wind. Figures 15 and 16 show v and h for two different alongshore wind fields when the western boundary is slanted at the angle 0 = - 45°. Values of parameters are H = 75 m, 1 g = gOi (T1 - T2)/p = 2.8 cm/s2, and v = 2 X 1O-6s- • In Figure 15 the wind has a 2 2 maximum strength of 2 dyn/cm , whereas in Figure 16 its strength is 5 dyn/cm , their horizontal structures are indicated in the figure by the profiles X(~) and Y(7). The wind fields are very similar to those forcing the solutions in Figures 8 and 9. In both solutions there is southwestward flow in the region of wind curl offshore where G~< 0; 56 Journal of Marine Research [46, I

Figure 16. Surface currents and layer thickness in a linear, reduced-gravity model forced by a wind stress patch with a maximum value of 5 dynjcm2 confined north of the equator. The structure of the wind field is the same as that in Figure lab. Regions where h is less than 75 m are shaded, and h is negative at the coast because the model has no entrainment. Compare this solution to the one in Figure 9. The interior flow fields are similar, except there is an additional circulation in Figure 9 due to entrainment mass flux. Regions where h is shallower than H correspond to regions of cool SST in Figure 9. Also compare the structure of h to that of hI in Figure 13. this flow forces eastward and westward currents at the northern and southern edges of the wind-curl region, respectively, and a northeastward return flow along the western boundary. The layer thickness h is shallower than H everywhere near the coast in both cases, and also in a broad region south of the equator in Figure 15. The interior circulations and the regions where hI is less than HI are consistent with those in Figures 8 and 9. Also note the similarities between the h fields in Figures] 3 and ]6.

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Received: 15 May, 1987; revised: 23 November, 1987.