A Theory of the Cromwell Current (the Equatorial Undercurrent)

and of the Equatorial Upwelling

An Interpretation in a Similarity to •\ a Costal Circulation*•\

Kozo YOSHIDA**

Abstract: A theory is given to account for the CROMWELL Current-the Equatorial Undercurrent. The equatorial upwelling is closely related to the Current, and a remark- able similarity between the equatorial circulation and the circulation in the coastal upwell- ing regions. The widths of the equatorial upwelling as well as of the CROMWELL Current the maximum speeds of the upwelling and of the CROMWELL Current, the depth of the core and the thickness of the CROMWELL Current, are all found to be explained quantita- tively. The rate of change in the CORIOLIS parameter with latitude and the mean vertical stability of the waters are essential to determine those length scales of the phenomena. The easterly wind stress over the equatorial region is responsible for the processes.

1. Introduction In 1952, Townsend CROMWELLet al. (CRom- WELL et al., 1954) discovered an excitingly strong current flowing eastward just below the west-going surface equatorial current. This was the current which had not been known to us before and has been established by later investigation. Particularly, recent direct measurements of the current by John KNAUSS (1958) have revealed striking features of the current. This subsurface current which had hitherto been entirely unknown and has now become convinced to exist is named the CROMWELLCurrent or the Equatorial Undercurrent. Fig. 1. Sigma-t. Northbound section along We are so curious about this current not 140•‹W longitude, 7•‹S to 8•‹N, Stations 17- only because it is new to us, having entirely 31, June 3-8, 1952 (Hugh M. SMITH been overlooked by the world oceano- cruise 15). Sigma-t, in grams per liter, isopleth inter- graphers, but also because the discovery val 0.2 gr/1, (according to T. S. AUSTIN, seems to provide us with an extremely Mid-Pacific oceanography V, U.S. Fish and interesting phenomenon in the ocean. As Wildlife Serv., Spec. Sci. Rep.: Fish. No. KNAUSS has reported. the current is narrow, 136, Fig. 9) thin, deep and strong, the core of the cur- The temperature and density sections in rent sticking to the equator, with a strik- the meridional plane across the equator ing symmetry about the equator. All other reveal the outstanding features of "vertical ocean currents as far as we know do reveal divergence" of isotherms and isopycnals certain variations in their axes, mostly in responses to those in large-scale wind (Fig. 1), between 50 and 500 meter depths. Most of those sections to the east of about system. 180° longitude reveal this feature but not *Received Dec . 19, 1959 usually to the west. This feature looks **Geophysical Institute , Tokyo University, Tokyo very similar, at least apparently, to that

( 1 ) 160 Journ. Oceanogr. Soc. Japan, Vol.15, No.4 (1959)

encountered in the regions where pronounced sponds to that of characteristic density- coastal upwelling take places, such as off divergent features as described before. California. Two different mechanism will be considered The CROMWELL Current appears to be for maintaining such subsurface conver- present right in the layer of such charac- gence: one is through the equatorward flow teristic density feature or at least to be with longitudinally uniform eastward flow, closely related to this density structure. and the other is through the eastward cur- In fact, it is apparent from the density rent decreasing its speed toward eastern distributions that the Undercurrent is nearly boundary. The former model would apply in geostrophic balance with the pressure to the regions in the central portion of the field. The question is then how such pres- equatorial oceans where the undercurrent sure field can be produced and maintained. exists with relatively uniform velocity longi- It will be attemped in this paper to give a tudinally. Although observations seem to possible dynamical explanation for the oc- show that the core velocity of the Current curence of the CROMWELL Current as so far does not vary appreciably between the observed. Galapagos Island and 140•‹W and disappears Of course, foregoing observations of the rather abruptly near the Island, the depth Current have been somewhat limited in the of the core seems to decrease toward the conditions. We have very little or no in- east, so that the latter model may be sug- formations as to the pressure of similar gested to apply for eastern regions. equatorial undercurrents in the Atlantic, It will be found from the following analy- in the and even in the western sis that the principal features as observed portion of the Pacific. Weak meridional may be explained quantitatively by those components of flow have not been measured. dynamical models which are highly simpli- It is uncertain whether the current might fied. The similarity of the equatorial circu- reveal certain fluctuation from season to lation to the coastal circulation will also season. Such a situation may still allow be considered to be real, and the narrow for various different possibilities of theore- coastal undercurrent in certain regions of tical accounts for what have so far been coastal upwelling may be suspected. observed. Therefore, the present attempt may only provide one of those possible 2. The observed facts to be accounted for models. will be those as follows: (1) The CROMWELL The model considered in this paper is Current exists at and very near the equator, that within the framework of a linear between 2•‹S and 2•‹N approximately and is system. The CORIOLIS change with latitudes symmetrical about the equator: (2) The is the most important factor, and the den- core of the current is at about 100 meters; sity stratification is essential to the process (3) The thickness of the current is about as well. The equatorial upwelling which is 400 meters between the depth of 50 and 500 confined near the equator is considered to meters; (4) The maximum velocities of the be closely related to the Undercurrent. Current (at the core) are about 100- The easterly winds over the equatorial re- 500 cm-sec-1; (5) The core of the current gions will be responsible for the upwelling is likely to be fixed at the equator and to and consequently for the Undercurrent. be quite steady; (6) The temperature and The Undercurrent will be present in the density profiles on the meridional section layer below the surface layer within which across equator indicate striking features the wind-induced horizontal divergence is of the vertical stretching of the layer near assumed to be limited. This lower layer is the which appear to be charac- thus a layer of convergence compensating teristic to the CROMWELL Current. the surface divergence layer and corre- Of course, it would be quite probable that

( 2 ) Kozo Yoshida: A Theory of the Cromwell Current and of the Equatorial Upwelling 161 nonlinear terms are comparable with other intensity at the longitudes nearly in the half terms in the dynamic balances* very near way between the 180th meridiam and the the equator, especially around the core of eastern coast, that is, around 130° to 135° W the undercurrent. The significances of the in all seasons (HIDAKA, 1958) . The surface use of vertical mixing without these non- current charts (such as CROMWELL et al., liner effects might be doubtful, so that it 1959; the Oceans) seem to show that the would not be justified to go much in details westward surface drift has the maximum of the Undercurrent at the very equator, speed at some longitudes between 110° and such as the depth of the core and the 140°W, nearly in consistence with the wind thickness of the Current witnin the frame- distributions. work of the linear system considered. Such distributionsin the westward surface Highly concentrated activities within the drifts will tend to give the surface divergence narrow equatorial zone are not the direct in the east and convergence in the west. consequence of the external forces such as However, the equatorial upwelling may seem winds having similar concentration. Instead, to be indicated to occur at least in the the winds have rather much more uniform eastern half of the equator, to the east of distribution over larger areas. The physical 180•‹ meridian. Hence the principal factor factors which may cause such a concentrated which may be responsible for the equato- pattern in the ocean must therefore be rial upwelling in wide range of the equator seeked for in dynamical mechanism within will be considered to be the horizontal the interior of the ocean system. divergence due to the distribution of the As far as the surface winds over the meridional component of flow. equatorial regions are relatively uniform, The mechanism may then be similar to the distributions of the upwelling centered for the coastal upwelling and may be close at the equator will be nearly symmetrical to that described qualitatively by CROMWELL about the equator. The width of the upwell- ing zone may not essentially depend upon (1952). The following analysis will give the quantitative explanation for the latitudinal wind conditions but only on characteristics width of the equatorial upwelling, the speed of density stratification and on a rate of of the upwelling, and so forth in terms of change in the CORIOLIS parameter. It will the measurable quantities. be shown that if the horizontal divergence Taking x eastward, y northward (from the associated with the wind-induced upwelling equator), and z downward (from the sea sur- is limited within the surface layer, the con- face), the equations for the layer above are vergence to maintain the surface divergence would require the eastward corrent in the layer just below the surface layer. (3.1)

3. Equatorial upwelling (3.2) Alike the processes along the coast (SVERD- RUP et al., 1942), the easterly winds along where f is the CORIOLIS parameter, p is the the equator appear to be essentially res- pressure, u and v are the eastward and ponsible for the equatorial processes under northward components of the horizontal consideration. We may note that the easterly currents respectively, and A is the eddy component of the average winds along the viscosity (vertical mixing coefficient) . equator of the Pacific has the maximum ∂2v/ The term A in (3.2) can be ignored as ∂z2 *The order of magnitudes is attempted in the it can seen unimportant essentially. recent preprint manuscript by Dr. R.S. ARTHUR For this surface layer, we may put ap- (1959). proximately

( 3 ) 162 Journ. Oceanogr. Soc. Japan, Vol.15, No.4 (1959)

where (3.11) (3.3) The equation (3.10) can be written where T. is the eastwest component of the (3.12) surface wind stress. Then (3.1) becomes where P and e are dimensionless quantities defined by (3.4) (3.13) Let us assume for the whole layers,

(3.5) and (3.15) where p is the density of sea water and w is the vertical component of velocity. werhe ƒÀ=df/•Ýy=2•~10-13 cm-1 sec-1, and Then from (1.2) and (1.4), quantity LƒÀ is a characteristic length which is essential to the lengths involved in the (3.6) process. ∂ρ/ It would be desirable to obtain the solution where s= ∂z of (3.12) which tends to ƒÌ-1 for sufficiently It may be assumed that the vertical velo- large values of E. Instead of this, we may city having the maximum value at z=H and assume P=0 for ƒÌ=0 and P=ƒÌ-1 for suffi- vanishing at the sea surface would be ex- ciently large values of pressed, to the first approximation, by Although the numerical solutions** under these conditions give some small departures (3.7) from ƒÌ-1. for very large values of they near the depth z=H. are sufficiently accurate for the range of In this case, from (3.6) ξwhich is of interest. Assuming P=0 for ξ=0 and P=ƒÌ-1 for ƒÌ=4, the solution is (3.8) obtained as illustrated in Fig. 2A. consider- so that (3.4) becomes

(3.9)

If we follow the CROMWELL'S model for the upwelling, we could ignore •Ýu/•Ýx and ∂p/∂x. On the other hand, we might have somewhat better approximation, if we retain ∂p/∂x and assume it to be equal to 2/5 Tx/H according to the REID's density model. In this case, •Ýv/•Ýy=-wH/H and (3.9) become Fig. 2A. Latitudinal distribution of the meri- (3.10) dional velocity: expressed by the dimen- sionless parameters.

*Although A may differ from the eddy viscosity defined in (3.1), we have little knowledge as to the difference and will simply disregard the difference under this crude model. **The solution of (1.11) is given by

( 4 ) Kozo Yoshida: A Theory of the Cromwell Current and of the Equatorial Upwelling 163 ing that (3.10) is rather crude equation 3/ Tx/ and ws=- ×0.14 with Tx constant and that obtained values 5 βLβ2 of P approach to ƒÌ-1 well for these large The actual density data in the equatorial values of concerned, this approximation region of the Pacific indicate that the mean may practically be good enough. vertical stability •ÝƒÏ/•Ýz over the upper 500 meters is about 6 to 8•~10-8. As the values of those physical quantities are relatively insensitive to the changes in the values of the stability chosen for this range, the values of 6•~10-8 will be employed. Putting H=104 cm and Tx=-0.5 dynes cm-2, we obtain gH1ƒ¢ƒÏ=2.5•~103cm2•Esec-2 and LƒÀ=1.57•~107cm. With these values,

(i) ym=2.3•~107 cm (latitudes: 2.3•‹N and S) (ii) vm=4.9 cm•Esec-1 (poleward) (iii) WH0=3.0•~10-3cm•Esec-1 (upwelling) Fig. 2B. Latitudinal distribution of the ver- (iv) ys=3.6•~107cm tical velocity: expressed by the dimension- less parameters. (latitudes: 3.6•‹N and S) ws=0.7•~10-3 cm•Esec-1 (sinking) Important numerical values thus deter- All of these values look very reasonable in mined are of the following quantities: comparison with the average values so far (i) Initial slope of P, observed. It should be noted that these dP/ = 0.60 values depend only upon the average vertical dξ ξ= 0 stability as far T. and H are given as (ii) ƒÌ for the maximum value of P, observed. ξM=1.45 (iii) The maximum value of P, 4. Equatorial Undercurrent (CROMWELL Pmax=0.51 Current) (iv) The inflection point of P, and the Let us now deal with the layers below slope of P at this point, z=H with the same equations (3.1), (3.2) dP/ = -0 and (3.5). The approximation (3.3) and ξt=2.3, and .14 dξ ξi hence (3.4) are not valid for the layers With these values, the physical quantities now concerned. From (3.1) and (3.2), are given as follows: eliminating the pressure terms, (i) The half meridional width of the upwelling region, (4.1) yM=1.45Lβ As (3.6) is valid, (4.1) becomes (ii) The maximum value of v, (4.2) 0.60 5/ Tx/ vM=- ( /βLβ 3 H ) Then if we assume •Ýv/•Ýy=-•Ýw/•Ýz, (4.2) (iii) The upwelling velocity at the equa- yields tor, (4.3) 5 Tx/ WH K= 0.60 y=0 (/ 3 βLβ2 ) If we further assume,

(iv) The value of y for maximum sinking w(y,z)=wH(y)F(z) and the maximum velocity, where wH(y) satisfies (3.10) with

ys=2.3 LƒÀ, wH=-H•Ýv/•Ýy

( 5 ) 164 Journ. Oceanogr. Soc. Japan, Vol.15, No.4 (1959)

we can readily see from (4.3) and (3.10) Mx42= × 1012cm2・sec-1= 42×106m3・sec-1 which are very close to the observed values. (4.4) Although we assume in the above calcula-

s tions that the eddy viscosity is equal to the Thus F (z) F 0 cos √ (z-H), / H1Δ ρ eddy diffusivity, the value A=20 cm2•Esec-1 so that may be considered quite acceptable. The thickness of the Undercurrent is given (4.5) by (4.10) where (4.6) and the depth of the core of the Undercur- in virtue of (1.10) rent is, measuring from the bottom of the Having now (4.5) for w (y, z), we can upper layer now put (4.11)

(4.7) As far as these of the depth and thickness in which um(y) can be determined from of the Undercurrent are concerned, the obtained values, (4.10) and (4.11), may only (3.6) and (4.5), to be give the rough order of magnitudes. The core of the Undercurrent as observed is shallower and the thickness is somewhat (4.8) greater. Although it may be difficult to find the source of such discrepancies, the For f=0, greater vertical stability in the layer be- (4.9) tween 100 and 200 meter depths as seen from actual density data might possibly Using (4.7), and (4.8), the total transport is make the core much shallower and the thickness greater.

To derive (3.5), the assumption was made that the magnitude of the vertical velocity has the maximum at z=H for all latitudes (4.9) concerned. Even though this assumption is accepted, the distribution of wH(y) de- since ƒÌi=2.3. rived above may not be valid at the lati- The ratio of Mz to 141(10 does not depend on tudes higher than 4 or 5 degrees, because A, but only on H and Lo, as given by the wind stress curl due to the northward increase in the easterly wind velocities may be as much effective to the distribution of wH as the vorticity due to the latitudinal The observed values are Mx=40•~1012 cm3• change in the CORIOLIS parameter. sec-4 and uu|0=102 cm• sec1, so that Thus, we may have upwelling at latitudes Mx =4.0×1011cm2. as high as 7°, if we consider ƒÑx. in (3.10) as /uM|0 a function of y as observed. In such more Hence the computed value is fairly close to realistic cases, the solution wH(y) may the observed one. resemble something like wH(o) cos ly, where The values of uM|0 and M. depend upon the l=2π/Ly= 2π/8×107=0.8×10-7cm-1. values of A which is less certain than any In this case,** for larger values of y, other observable quantities involved. How- ever, if we assume A=20 cm2•Esec-1, ** The equation (4.3) can also be written uM|0= 96 cm•Esec-1 and

( 6 ) Kozo Yoshida: A Theory of the Cromwell Current and of the Equatorial Upwelling 165

(4.12) Hence ∂2w/ - gsl2 w=0 ∂z2 / f2 so that

(4.13) For the smaller values of y,

(4.14) Hence

Fig. 2C. Latitudinal distribution of the east- west component of velocity: expressed by of which the solution will be the dimensionless parameters.

(4.15) Undercurrent, respectively. Hence, the undercurrent exists in the region where Putting gs=6•~10-5 sec-2.l=0.8•~10-7, (A•Ýu/•Ýz)H has a significant magnitude com- in (4.13), we have w(z)/w(0)=e-1 pared with the surface wind stress. The f/ computed curve for is given in Fig. for z= cm. At latitude 6•‹, 2C, and the computed values of the core 6.4•~10-10 velocity of the Undercurrent are 96cm•Esec-1 z=190m; and at 10•‹, z=315m. at the equator, 75 cm•Esec-1 at 1•‹N and S, 2π/ Putting w=wMcos LƒÑ(z-H) in (4.15) 36cm•Esec-1 at 2•‹N and S, 8cm•Esec-1 at 3•‹N and S and 2cm•Esec-1 westward at 4•‹N and Lτ=2π ×104cm=628meters S. Thus, the vertical velocity does not change The meridional circulation will be ob- its sign with depths at higher latitudes, tained by the solution of (3.10) as well as whereas it does so very near the equator, (4.3). provided that is given by something like For z>H, WH(o) cos ly. As seen from (3.1), the width of the (4.17) Equatorial Undercurrent is somewhat where vo (y) denotes the average meridional broader than the width of the surface velocity in the surface layer given by (3.10). upwelling. Thus, there is equatorward flow beneath The half width of the Undercurrent is the surface layer and this flow leads to the the distance between the equator and the subsurface convergence at latitudes lower maximum sinking which occurs at 3.6•‹. than 2.3•‹ and to the divergence beyond the From (1.7), latitude of 2.3 (4.16) 5. A model in which •Ýu/•Ýx is important As the solution must approach very close- ly to PƒÌ•¨1 for large values of shearing It is again assumed that the vertical stress (A•Ýu/•Ýz) H becomes negligible at lati- velocity has the maximum at z=H. The tudes well apart from the equator. Prac- presence of the equatorward flow in the tically the stress is quite small beyond layer below z=H would be consistent with ξ=ξM～1.45 and is negligible beyond ƒÌ=ƒÌi•` the occurrence of subsurface convergence, 2.3, corresponding to the outer boundaries only if the relative vorticity decreases as of the surface upwelling region and the the water moves southward either through

( 7 ) 166 Journ. Oceanogr. Soc. Japan, Vol.15, No.4 (1959) diffusion or advection of the vorticity. In the absence of such effects of friction or (5.2) accelerations, on the other hand, the longi- At the equator, tudinal variation in the zonal component of ∂u ∂u =-2 current could maintain the subsurface con- /∂x /∂z vergence. This could be the case when If we put eastward current decreases its speed toward the eastern boundary of the ocean. The meridional component of flow directs pole- ward in this case and the divergence due to this component of flow on and very near ∂u then =-1×10-7sec-1 the equator could be overcompensated by /∂X the eastward current. It should be noticed Assuming u=0 at the eastern boundary, that the equator is an exceptional place as u(x) ～-1×10-7x to the relation between the geostrophic With x=5•~108, horizontal divergence and the meridional u(x) ～5°cm・sec-1 flow. Except for the lowest latitudes, the As u (x) refers to the average eastward poleward flow may produce the geostrophic velocity at the equator, the obtained value convergence and hence maintain the up- ward motion of water above (STOMMEL1956 will be reasonable. YOSHIDA and MAO, 1957). The idea given above could in fact be This can immediately be seen from the explained by a small modification from the following equation derived by differentiating MUNK'S masstransport theory (1950). Based (4.1) with y: on the simple vorticity equation as Munk assumes for the central and eastern por- (5.1), tions of the oceans; in which (5.3) ∂v =-∂u/ -∂w/ /∂y ∂x ∂z we may now devide the ocean into two is used. layers of which the interface refers to the Put depth of no horizontal divergence. 2β=2×10-13,ω=10-3,|∂/∂z|～10-4, The upper layer (with the subscript 1) may u=102, |∂/∂x|～(5×108)-1 correspond to the upper mixed layer in and then which the wind mixing is effective, and the ∂u/ |2β |=4×10-13×10-7=4×10-20 lower layer (with the subscript 2) is assumed ∂z to be frictionless. ∂u 1 β |=2×10-13×102× ×10-8=4ｘ10-20. Vertical integration of (5.3) for each of | /∂x /5 the upper and the lower layer gives For the scales of motions corresponding (5.4) to the Undercurrent, it will be seen that the friction term in the right hand side of (5.5) where w (0) w (D) =0, (5.1) is quite comparable with these two terms, provided that A is of the order ot 10 in its magnitude (C.G.S.). However, in this model, we may assume that the model Differentiating (5.4) and (5.5) with y, and is nearly geostrophic in this layer below putting f=0, we obtain z=H, in contrast to the model given in the (5.6) preceding sections. Anyhow, from (5.1) ignoring the mixing (5.7) term,

( 8 ) Kozo Yoshida: A Theory of the Cromwell Current and of the Equatorial Upwelling 167

∂H/ ∂H If we use wH obtained in the section 3, Considering that wH=uH + vH , we ∂x /∂y it is shown that the outer boundary of the must have divH/M1=divH/M2=0 Undercurrent is nearly at =0.95 which (5.6) and (5.7) can be written corresponds to 1.5•‹ N and S approximately. (5.13) can be written (5.8)

(5.9) If we put Tx=-0.5, 5•~108, D0=3•~104, The integration with the boundary condition that Mx1=Mx2=0 at the eastern edge of the ocean x=xe yields

(5.10) (5.11) The equations (5.9) and (5.11) represent nearly the same things as (5.3). In the annual mean, the term

•Ý curlzT ∫ dx xe x /∂y is positive, so that the zonal component of the total transport along the equator is On this model, the Undercurrent is much eastward in MUNK'S result. REID'S result narrower than obtained on preceding model. (1948) shows, on the other hand, the west- The observed width of the Current may ward transport at the equator, since he appear to be closer to this present model. deals with the conditions during October to November when his wind data gives a curl,T 6. Similarity to the costal upwelling negative values of •ÝcurlzT/•Ýy. The eastward Some analogy can be seen between the transport at the equator in MUNK'S result equatorial upwelling and the coastal up- might suggest the presence of the Equa- welling. Let us assume the similar equa- torial Undercurrent rather than that tions and the coastal boundary on one edge of the surface Equatorial Countercurrent of the ocean. extending down to a little south of the The equations are equator. From (5.2), if we simply put (6.1)

(6.2)

(6.3) (5.12) Hence where all symbols denote the quantities which are the same as in preceding sec- (5.13) tions, and the coast is assumed to be at It is seen that the eastward flow (u>0) x=L. occurs in the regions very near the equator From (6.2) and the width of the eastward current is in this case somewhat narrower than that (6.4) of the surface upwelling.

( 9 ) 168 Journ. Oceanogr. Soc. Japan, Vol,15, No.4 (1959)

From (6.1) and (6.3), (6.10) (6.5) For τy=-0.5 Assuming π w=wHsin z /2H (6.11) π Assuming A=50, and v=vocos z 2H (6.12) (6.4) becomes For instance, off the California coast, the undercurrents of such speeds have not been observed. Hence The width of the upwelling and hence the undercurrent will be very small, less than 50 km as seen from (6.10), so that the cur-

Assuming ∂u/∂x=-wH/H,and∂p/∂y=0, rent is difficult to be detected by ordinary (4.4) becomes observations. Furthermore, the shallow depths adjacent to the coast may prevent the development of such undercurrent. where Even though this might really exist, future direct measurements of the current could (6.7) only detect it. The presence of the geo- This is the equation analogous to (3.10) for strophic northward current (opposite to the equatorial upwelling. the surface wind direction) below the The main difference is that the CORIOLIS thermocline has been reported in the up- welling region off California coasts (SVERD- parameter f can be regarded constant in the case of coastal upwelling. RUP et al., 1942; YOSHIDAand MAO, 1957). The characteristic length in this case is The analogy may essentially be in the deep penetration of the vertical mixing in √ gHiΔP/f which is something like the radius of deformation for the baroclinic motions. the narrow boundary zone along the equator In this case, we must have u=0 for x=0 and along the coast. The occurrence of such deep mixing may be due to the es- τ-y and u→ forx→-∞. / fH sential balance between this mixing and Then, the solution is pressure gradient in the direction of the dominant current at the boundary, where (6.8) the component of the must vanish. At some distances from the bound- in case when Ty= constant. aries, the pressure gradient would rather balance the CORIOLISforce, approaching the Then (6.9) geostrophic balance. Along the coast, assuming The undercurrents in both cases may occur 2π v=vMsin (z-H), /4H *From one obtains

2H τy vM=- ( /π ) /A Putting gs=10-4 and H=5x103, we have

gH1Δ ρ=103cm2・sec-2 1 For f= ×10-4, /2

( 10 ) Kozo Yoshida A Theory of the Cromwell Current and of the Equatorial Upwelling 169 within the zones where such deep mixing at the core is found to be 100cm•Esec-1 is considerable. and the total eastward transport becomes 40•~106m3•Esec-4, provided that the eddy viscosity as well as the eddy diffusivity is Concluding Remarks assumed to be about 20. These seems to be in the oceans no such The present model may suggest that well-fixed current like the CROMWELL Cur- vertical mixing extends down to the layers rent which is fixed on the equator and below thermocline near the equator. confined within only one to two degrees The eastward current exists in the regions from the equator with a beautiful symmetry where vertical mixing penetrates deep. The about the equator! For instance, the Equa- Undercurrent may thus be interpreted to be torial Counter Current is relatively narrow maintained by the vertical shearing stress current, but this is found to reveal con- exerting over the surface z=H near the siderable degree of seasonal fluctuation in equator. its position as well as in the intensity. The As far as we have seen, the characteristic position is fixed only in a statistical mean density features across the equator may be within a certain latitudinal range, principal- considered as indicative of the Undercur- ly depending on large-scale wind stress rent. The Undercurrent is contained over distributions. As far as we can refer to the layer of convergence. The broad easter- current ever observed, it is likely to suppose ly winds over the equatorial region must be that the phenomenon of the Cromwell Cur- responsible for the Undercurrent. If this rent is that characteristic to the equator may only be the essential conditions for itself. It is quite impressive that the waters the Undercurrent, it will be very likely near the equator, particularly in the sub- that the Current may exist also in the surface layer, seem to "feel the equator Altantic. It is very curious that an obser- very accurately". Why should they be able vational data taken by the Japanese in the to do this? The answer is simply that the eastern portion of the equatorial Indian equator has a singularity of vanishing Ocean indicates very clearly the similar vorticity due to the Earth's rotation ! It thermal feature across the equator as seen may be of interest to see that the width in the eastern Pacific. (YAMANAKA, 1958) . of the equatorial upwelling as well as the The observations were taken during Undercurrent is determined essentialy by the characteristic factor related to the January. Although the wind conditions are not reported, the usual conditions over density stratification or by the mean vertical stability. With the reasonable value for the these regions seem to differ largely from mean vertical stability, the width of the those in other oceans upwelling is computed to be between 2.3•‹S The similarity between the density distri- and 2.3•‹N. Under certain assumption, the butions in the equatorial region and the latitudinal distributions of w and v are coastal region seems to be a manifestation found reasonable. It is found that the layer of real similarity in dynamical processes of convergence will have a thickness of involved. Owing to the shallow depths about 200 meters below the depth of ther- adjacent to the coast, the coastal undercur- mocline. rent may not develop as the equatorial

The eastward current is present within undercurrent, so that such striking pheno- this layer of convergence, and the core of mena of the strong undercurrent may not the current is at the mid-depth of the layer exist in actuality. However, as pointed out along the equtor. Of course, the theoretical by the present author before, the density model may be too crude to obtain the distributions seem to indicate that the

vertical distributions of the eastward cur- geostrophic northward flow does occur along rent. The magnitude of the Undercurrent the coast of California during upwelling.

( 11 ) 170 Journ. Oceanogr. Soc. Japan, Vol.15, No.4 (1959)

Direct current measurements must be made current. Nature, 182, 601-602. to detect such narrow subsurface counter- YAMANAKA, Hajime, 1958: current. Conditions of the ocean in relevant to fishing conditions for tunas in the eastern indian ocean. I. Several informations in regard to the structure References of the ocean during the period from January to March. ARTHUR, R. S., 1959: Report of Nankai Regional Fisheries Research A review of the calculation of current velocity Laboratory, No.9: 117-124. at the equator. (preprint manuscript), 21pp. STOMMEL, Henry, 1956: CROMWELL, T., MONTGOMERY, R. B., and STROUP, On the determination of the depth of no meri- E. C., 1954: dional motion. Deep-Sea Res., 3 (4): 273-278. Equatorial undercurrent in Pacific Ocean reveal- SVERDRUP, H.U., M. W. JOHNSON and R. H. FLEM- ed by new methods. Science, 119, 648-649. ING, 1942: CROMWELL, T., 1953: The oceans. Prentice Hall, Inc., New York, Circulation in a meridional plane in the central 1087 pp. equatorial Pacific. J. Mar. Res. 12 (2): 196-213. REID, R. O., 1948: CROMWELL, T., E. B. BENETT, 1959: A model of the vertical structure of mass in Surface drift chart's for the eastern tropical equatorial wind-driven currents of a baroclinic Pacific Ocean. Bull. Inter-American Tropical ocean. J. Mar. Res. 7 (3): 304-312. Tuna Commission, 3 (5): 217-237. YOSHIDA, Kozo, 1955: HIDAKA, Koji, 1958: Coastal upwelling off the California coast. Rec. Computation of the wind stresses over the oceans, Oceanogr. Works Japan, 2 (2): 1-13. Rec. Oceanogr. Works. Japan, 4 (2): 77-123. YOSHIDA, Kozo, and Han-Lee MAO, 1957: KNAUSS, J. A., and J. E. KING, 1958: A theory of upwelling of large horizontal extent. Observations of the Pacific Equatorial Under- J. Mar. Res. 16 (1): 40-54.

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