## 1. Introduction

Understanding the climatological general circulation has been a major challenge in large-scale atmospheric dynamics. In recent years, a combination of axisymmetric circulation theories (Schneider 1977; Held and Hou 1980; Lindzen and Hou 1988) and theories and observations of midlatitude wave activity (Simmons and Hoskins 1978; Held and Phillips 1987; Edmon et al. 1980, among others) have formed a basic paradigm for understanding elements of the climatological zonal mean general circulation. Namely, axisymmetric circulations establish Hadley cells and subtropical jets, and meridional propagation of midlatitude eddies, generated by baroclinic instability and stationary wave sources, accelerates the midlatitude zonal mean zonal winds and decelerates the zonal mean zonal winds on the equatorward flank of the subtropical jets, as the waves are absorbed near their critical latitudes (e.g., Held and Phillips 1987; Feldstein and Held 1989). It appears that a general understanding of the tropical upper-tropospheric easterlies is built on both Hide’s theorem (Hide 1969; Held and Hou 1980) in the context of axisymmetric circulations and the absorption of midlatitude wave activity on the equatorward side of subtropical jets (Suarez and Duffy 1992).

*uυ*

*uυ*

*u*′

*υ*′

*u*

*υ*

*u*

*υ*

*u*′

*υ*′

*u*′*

*υ*′*

*u*]′[

*υ*]′

*ϕ*< 0° above 500 mb, where

*ϕ*is the latitude, [

*u*′

*υ*′

*u*]′[

*υ*]′

*u*′

*υ*′

*u*′*

*υ*′*

*u*′

*υ*′

*u*]′[

*υ*]′

*u*′*

*υ*′*

By performing such an analysis, this study will show that the above presumption is incorrect. For the transient eddy momentum flux, we will show that it is not the midlatitude-generated eddies, but the eddies associated with the Madden–Julian oscillation (MJO) (Madden and Julian 1971, 1972), intraannual,^{2} and interannual timescales that dominate in the deep Tropics. In fact, it will be shown that the transient eddies associated with the MJO, intraannual, and interannual timescales *accelerate* the tropical zonal mean zonal winds. Also, in the Tropics, the transient meridional circulation is far from being negligible; instead, we will show that the transient meridional circulation associated with the seasonal cycle plays a crucial role in the deceleration of the zonal mean zonal winds, contributing toward the maintenance of the tropical upper-tropospheric easterlies. The above role of the transient eddy fluxes is particularly intriguing given that an atmosphere with an equatorial superrotation (i.e., westerlies over the equator) can be obtained in a two-layer GCM, if there is a zonally asymmetric equatorial heat source above a certain threshold value (Suarez and Duffy 1992; Saravanan 1993).

Data and analysis methods are described in section 2, followed by results in section 3. Section 4 presents results from an idealized GCM that complement the findings in section 3. The conclusions are presented in section 5.

## 2. Data and analyses

The data used in this study are the daily National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis covering 1980–95. We chose to analyze the 200-mb horizontal winds because the momentum fluxes reach their maxima close to this level in the Tropics. The original data are converted to rhomboidal spectral truncation at wavenumber 30. A detailed description of this dataset can be found in Kalnay et al. (1996).

The main results of this study can be succinctly presented by space–time cross-spectral analyses. Because this analysis method has been described and applied to the momentum flux in previous studies (e.g., Hayashi 1982; Zhangvil and Yanai 1980; Randel and Held 1991), only a brief description is given here. First, in order to identify robust characteristics in our analysis, the 16 yr of data are divided into two 8-yr periods, 1980–87 and 1988–95, giving a 2922-day time series for each period. For each latitude, the zonal and meridional winds, *u* and *υ,* are decomposed into both frequency and zonal wavenumber space by a Fourier transform. Then the covariance spectra of [*uυ**ω,* where Δ*ω* is the unit frequency interval of 2*π*/2922 days. Once these covariance spectra are obtained, it is straightforward to calculate *u*]′[*υ*]′*u*′**υ*′*

As will be shown below, the seasonal cycle plays a dominant role in the transient meridional momentum flux (*u*]′[*υ*]′

## 3. Results from the reanalysis data

### a. Horizontal momentum flux

Figures 1a and 1b show the four components of the momentum flux ([*u**υ**u**υ**u*]′[*υ*]′*u*′**υ*′**convergences* for 23.5°S ⩽ *ϕ* 23.5°N at 200 mb. First, one notes that [*u**υ**u*′**υ*′**ϕ* ⩽ 8°N (see Fig. 1b). The maximum value of this acceleration is comparable to that due to the convergence of [*u**υ**u**υ**u*]′[*υ*]′*u*′**υ*′**net* effect of the transient meridional circulation and transient eddies is to decelerate the zonal winds at the equator, consistent with the results of Oort and Peixoto (1983). On the other hand, it should be noted that in the subtropics the transient eddies do decelerate the zonal mean zonal winds, and the effect of the transient eddies is greater than that of the transient meridional circulation. Noting that the focus of this paper is on the deep Tropics, however, this subtropical feature will not again be discussed in this paper.

The simple analysis, presented in Fig. 1, clearly demonstrates that in order to understand the climatological zonal mean zonal winds in the Tropics, both the transient eddies and transient meridional circulation should be better appreciated. For this purpose, we examine covariance spectra of [*u*′**υ*′**u*]′[*υ*]′

Figure 2a shows the PSD of [*u*′**υ*′**k*) 1 and 2. The PSD, integrated over all zonal wavenumbers, displayed as a function of period and latitude, is shown in Fig. 2b. Because there is no well-organized, strong transient eddy momentum flux for periods less than 25 days or so, we only show the PSD for frequencies corresponding to a period that is greater than 20 days. Zhangvil and Yanai (1980) also showed that for periods less than 30 days, which is the longest timescale they considered, there is no well-organized momentum flux in the deep Tropics. In both hemispheres, there are two distinct periods for which equatorward transient eddy momentum fluxes are prominent; one greater than 100 days, another ≈ 50 days. We also note that the intraseasonal timescale disturbance shows clear eastward propagation.

Because *k* = 1 and 2 are mainly responsible for the equatorward momentum flux, in order to identify phenomena that account for this direction of the momentum flux, the PSDs are constructed for *k* = 1 and 2 separately and are shown in Figs. 2c and 2d, respectively. For *k* = 1, centered around 12°N and 10°S, equatorward momentum fluxes can be seen at periods between approximately 30 and 70 days, associated with an eastward-propagating feature. These characteristics are consistent with velocity potential spatial scale, period, and direction of propagation of the MJO (Knutson and Weickmann 1987), suggesting that in the time and zonal mean, the MJO pumps westerly momentum into the deep Tropics. If one accepts that zonally asymmetric heating associated with the MJO can act as a wave source, the above finding may not be too surprising. This is because one expects wave energy to propagate away from a source region, hence a divergence of group velocity from the source region; provided that the meridional potential vorticity gradient is positive, the direction of the eddy momentum flux is opposite to that of the group velocity. Thus, in a region where the group velocity diverges, the eddy momentum flux is expected to converge, accelerating the zonal mean zonal wind.

For both *k* = 1 and 2, two main centers of prominent equatorward transient eddy momentum flux exist at 6°N and 8°S, both with a period of ≈2–4 yr, and propagate eastward. Based on its period and direction of propagation, we speculate that this interannual timescale eddy momentum flux is associated with changes in the geographical distribution of diabatic heating during ENSO events. Precipitation composites by Kiladis and Diaz (1989) show that in the Tropics, during June, July, and August (JJA) of the year that precedes an ENSO event, precipitation maxima occur over Indonesia and the western Pacific, and over the Amazon Basin and western Africa. As the ENSO event progresses, the positive precipitation anomaly over Indonesia and the western Pacific propagates eastward. By JJA of the following year, during which the ENSO signal reaches its maximum, the anomalous precipitation maximum appears in the central Pacific. However, eastward propagation of the other precipitation center, that is, over the Amazon Basin and western Africa, is rather unclear. It is possible that the anomalous heating associated with ENSO events project onto both zonal wavenumbers 1 and 2, producing the equatorward transient eddy momentum flux found for both *k* = 1 and 2.

Figure 3 shows the PSD of the momentum flux due to the transient meridional circulation (*u*]′[*υ*]′^{−7} m s^{−2}. This value accounts for only 3% of the deceleration due to the total transient meridional circulation (see Fig. 1b).

Figures 4a and 4b show *u*]′[*υ*]′*u*′**υ*′**convergences* due to the seasonal cycle. Between the equator and 15°S the transient eddies due to the seasonal cycle accelerate the zonal wind. However, they play only a secondary role in the acceleration of the zonal winds in the deep Tropics (cf. Figs. 1b and 4b).

Both *u*]′[*υ*]′*u*]′[*υ*]′*u*]′[*υ*]′

The key findings for the 1980–87 period, described above, are confirmed by analyses of data for the 1988–95 period. The PSD of [*u*′**υ*′**k* = 1 and 2 and to eastward-propagating intraseasonal and interannual fluctuations. Again, as for the 1980–87 period, in the PSD of [*u*′**υ*′**k* = 1 (Fig. 5c), the signature of an equatorward momentum flux by the MJO is prominent. However, there is one noticeable difference between the two time periods in that equatorward momentum flux at the MJO timescale appears in *k* = 2 for the 1988–95 period but not for the 1980–87 period. This difference may be explained by the possibility that zonally localized heating might project more strongly onto *k* = 2 during the latter half than during the former half of the analyzed period. As for the 1980–87 period, the momentum flux by the transient meridional circulation is poleward except between the equator and 5°N, with essentially all the power being concentrated in periods greater than 100 days (not shown). In addition, transient momentum fluxes due to the seasonal cycle during this latter 8-yr period (not shown) are found to be essentially identical to those for the 1980–87 period.

Given the robustness of the equatorward momentum flux by the MJO, intraannual, and interannual timescale fluctuations, the transient eddy momentum flux and its convergence are separately calculated for *k* = 1 and 30–70 days, and *k* = 1 and 2, for periods greater than 100 days. In the latter calculation the seasonal cycle is included because the seasonal cycle cannot be neglected in the transient momentum fluxes for *k* = 1 and 2. For reference, however, the transient eddy momentum flux and its convergence for *k* = 1 and 2, arising from the seasonal cycle, is also calculated (Fig. 6). At the equator,^{3} the transient eddy momentum flux convergence by all zonal scales and periods is 3 × 10^{−6} m s^{−2} (see Fig. 1b), while that by the MJO and fluctuations with periods greater than 100 days is 0.6 × 10^{−6} m s^{−2} and 2.5 × 10^{−6} m s^{−2}, respectively. This indicates that the sum of the momentum flux convergence associated with these two fluctuations can, by and large, explain the acceleration of the equatorial [*u*

### b. Zonal momentum budget

*u*′*

*υ*′*

*u*]′[

*υ*]′

*ω*= −

*ρgw*is assumed. The vertical convergence of zonal momentum, −∂[

*uω*

*p,*at 200 mb, is obtained by finite differencing [

*uω*

*uω*

*p*is negative over the entire domain (not shown), but its magnitude is at least an order of magnitude smaller than that of the horizontal momentum flux convergence, −∂([

*uυ*

*ϕ*)/

*a*cos

*ϕ*∂

*ϕ.*In addition, the amplitude of all four components—MMC, transient meridional circulation, stationary eddies, and transient eddies—of the vertical momentum flux convergence is at least an order of magnitude smaller than the corresponding components of the horizontal momentum flux convergence.

The sum of the terms on the rhs of (2) that account for a steady, axisymmetric circulation (i.e., the sum of the MMC component of the first four terms and the Coriolis torques) yields 10^{−6} m s^{−2} over the equator. Although this number should be taken with caution due to sparsity of observed data in this region, this result suggests that the observed climatological easterlies in the equatorial upper troposphere should not be interpreted on the basis of Hide’s theorem.

## 4. Results from idealized GCMs

The results from the NCEP–NCAR reanalysis data indicate that in the deep Tropics, the transient meridional circulation due to the seasonal cycle is crucial for maintaining the easterly upper-tropospheric climatological zonal mean zonal wind. On the other hand, transient eddies associated with the MJO and intraannual/interannual timescales can exert an acceleration on the climatological zonal mean zonal wind. Therefore, in an atmosphere where the seasonal cycle is suppressed, while zonally asymmetric heating, such as the MJO, is retained, one might expect to find climatological zonal mean westerlies over the equator. As will be shown below, such a solution is indeed found in an idealized Geophysical Fluid Dynamics Laboratory GCM for which the lower boundary is all ocean, with a prescribed sea surface temperature (SST). In this GCM, the insolation and ozone are fixed at annual mean values. In spite of these idealizations, this GCM contains a full hydrological cycle, including predicted clouds.

*ϕ*is the latitude, SST

_{eq}the SST at the equator, and Δ

*T*the SST difference between the equator and the poles. Two GCM runs are analyzed here; one will be referred to as the control case, and the other as the uniform warming (hereafter UW) case. For both the control and UW cases, the value of Δ

*T*is fixed at 40 K, while SST

_{eq}equals 300 and 303 K for the control and UW cases, respectively. Thus, the SST of the UW case is everywhere 3 K higher than that of the control case.

Figure 7a shows [*u**u**u**u*^{−1}. Inspection of the momentum flux convergence (Fig. 8b) indicates that these westerlies over the equator owe their existence to the equatorward momentum flux by the transient eddies (Fig. 8a). The momentum flux convergence by the MMC decelerates [*u*

In this GCM, the acceleration over the equator is almost entirely due to the model’s MJO. For the control case, the PSD of the transient eddy momentum flux indicates that in the Tropics, the equatorward transient eddy momentum flux is completely dominated by disturbances with *k* = 1 (see Fig. 9a) and a peak period of 42 days (Fig. 9b). The PSD, as a function of period and latitude for *k* = 1, clearly captures the signal of this 42-day disturbance (Fig. 9c). As will be shown below, this scale and periodicity are consistent with the model’s MJO, diagnosed by an empirical orthogonal function (EOF) analysis of the velocity potential. The momentum flux and momentum flux convergence (see thick dashed lines in Figs. 8a and 8b, respectively) for *k* = 1 and a 30–70-day period indicate that the equatorward momentum flux in the Tropics and the acceleration over the deep Tropics are indeed due to the model’s MJO. However, it should also be noted that the momentum flux convergence by the MJO in this idealized model is unrealistically strong (cf. Figs. 6b and 8b). Evidently, the climatological westerlies over the equator in this idealized GCM owe their existence to the absence of the seasonal cycle of the Hadley cells and to the unrealistically strong momentum flux convergence associated with the MJO.

As stated earlier, in order to confirm that the zonal wavenumber 1 and 42-day period in the transient eddy momentum flux are indeed associated with the model’s MJO, an EOF analysis of the velocity potential is performed. Verification of this relationship between the transient eddy momentum flux and the MJO requires that the velocity potential be dominated by the same zonal wavenumber and period. Figures 10a and 10b show the first and second EOFs of the velocity potential, respectively. The first and the second EOFs explain 39.3% and 38.5% of the total variance, respectively; both EOFs are dominated by zonal wavenumber 1; and the principal component of the first EOF lags that of the second EOF by 10 days, with a correlation coefficient of 0.85. Given that the first two velocity potential EOFs are in spatial quadrature, the period of this feature, captured by the first two EOFs, is 40 days. Not only is this result consistent with the spectral analysis of the eddy transient momentum flux, but it is also very close to the MJO period in the atmosphere (Madden and Julian 1971, 1972).

In the UW case, where the prescribed SST is raised by 3 K everywhere, the amplitude of the model’s MJO becomes stronger. Consistent with this change, the westerlies over the Tropics also intensify. The deviation of [*u**u*^{−1}. As for the control case, Figs. 11a–c indicate that the transient eddy momentum flux for the UW case is also dominated by zonal wavenumber 1 and a range of periods approximately between 30 and 70 days, except that the peak period is now 38 days, perhaps due to the increased Doppler shift by the strengthened tropical westerlies. Comparing Figs. 11a–c with 9a–c, one notes for the UW case that the amplitude of the eddy momentum flux by the MJO is increased by a factor of 1.6. Consistent with this result, the velocity potential EOF analysis indicates that sum of the variance of the first two EOFs is 5.66 × 10^{16} m^{4} s^{−2} and 7.61 × 10^{16} m^{4} s^{−2} for the control and UW cases, respectively. In light of climate change and global warming, to the extent that the basic mechanism of the MJO is faithfully represented in this GCM, it is interesting to note that strength of the MJO and the equatorial westerlies increase as the SST increases.

## 5. Concluding remarks

The aim of this study was to examine whether eddies generated in midlatitudes are a major factor in maintaining the tropical upper-tropospheric easterlies. This is accomplished by examining the decomposition of the transient momentum flux into its eddy and meridional components. It is found that the midlatitude-generated transient eddies do not play an important role in the zonal mean zonal wind budget of the deep Tropics. Instead, this study shows that the intraseasonal (MJO) and intraannual/interannual timescales dominate the transient eddy momentum flux in the deep Tropics. For the interannual timescale transient eddy momentum flux, we suspect that ENSO plays an important role. More importantly, the intraseasonal (MJO), intraannual, and interannual timescale transient eddies each contribute to the acceleration of the equatorial zonal mean zonal wind.

In contrast to the role of the transient eddy momentum fluxes, the momentum flux convergence due to the transient meridional circulation exerts a deceleration of the zonal mean zonal wind in the equatorial upper troposphere. In fact, the zonal momentum budget suggests that it is the transient meridional momentum flux convergence that is the most important factor in maintaining the climatological zonal mean upper-tropospheric easterlies in the Tropics. Because the transient meridional momentum fluxes are almost entirely due to the seasonal cycle of the Hadley cells, this result implies that a nonzero obliquity of the earth is crucial for maintaining the present climate’s equatorial easterlies.

In summary, for the intraseasonal, intraannual, and interannual timescales, the transient eddy momentum fluxes dominate the transient meridional momentum fluxes, accelerating the zonal mean zonal winds in the equatorial upper troposphere. However, this acceleration is weaker than the deceleration of the zonal winds due to the seasonal cycle contribution to the transient meridional momentum fluxes. Therefore, the net effect of the all transients is to decelerate the zonal mean zonal winds in the equatorial upper troposphere.

The role of the MJO for the equatorial acceleration is also illuminated with two idealized GCM runs. Because the SST distributions and the value of the insolation are fixed in these GCM runs, the amplitude of transients whose time scale is greater than a season is very small, at least in the Tropics. Therefore, in the Tropics, the momentum flux by the transient meridional circulation is essentially nonexistent, and the transient eddy momentum flux is dominated by the intraseasonal timescale MJO, rather than seasonal and interannual timescale fluctuations. Recalling that in the observations the primary contributor to the maintenance of the tropical upper-tropospheric easterlies is the transient meridional momentum flux convergence due to the seasonal cycle of the Hadley cells, consistent with the fact that this quantity is essentially absent in these GCM runs, the zonal winds in the tropical upper troposphere are westerly. When the prescribed value of the SST field is uniformly raised in one of the GCM runs, the model’s MJO is stronger and accompanies a greater transient eddy momentum flux convergence, resulting in stronger westerlies over the equator.

The analyses in this study shed new light on our understanding of the earth’s general circulation in that equatorial westerlies may be *possible* if the MJO becomes stronger and/or if the obliquity of the earth were to decrease by a sufficient amount. The results of this study also imply a potentially serious limitation in the ability of perpetual GCM runs to faithfully represent the atmospheric circulation in the Tropics, as such models are lacking a seasonal cycle of the meridional circulation, which is crucial for maintaining easterlies over the tropical upper troposphere.

## Acknowledgments

The author thanks Dr. Steven Feldstein for useful comments on this manuscript. This manuscript has also greatly benefited from constructive comments by anonymous reviewers. The NCEP/NCAR reanalysis data is provided by the Climate Diagnostic Center, and the GCM integrations were performed by Peter Phillipps of GFDL. This research was supported by the National Science Foundation through Grant ATM-9416701.

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The PSD of the transient eddy momentum flux for the period of 1980–87, as a function of (a) zonal wavenumber and latitude, integrated over all periods; (b) period and latitude, integrated over all entire zonal wavenumbers; (c) period and latitude, for zonal wavenumber 1; and (d) period and latitude, for zonal wavenumber 2. Solid contours are positive, dashed contour negative, and the zero contour is omitted. Contour interval is (a) 0.3 m^{2} s^{−2}, (b)–(d) 10^{−2} m^{2} s^{−2}.

Citation: Journal of the Atmospheric Sciences 56, 10; 10.1175/1520-0469(1999)056<1353:WATCZW>2.0.CO;2

The PSD of the transient eddy momentum flux for the period of 1980–87, as a function of (a) zonal wavenumber and latitude, integrated over all periods; (b) period and latitude, integrated over all entire zonal wavenumbers; (c) period and latitude, for zonal wavenumber 1; and (d) period and latitude, for zonal wavenumber 2. Solid contours are positive, dashed contour negative, and the zero contour is omitted. Contour interval is (a) 0.3 m^{2} s^{−2}, (b)–(d) 10^{−2} m^{2} s^{−2}.

Citation: Journal of the Atmospheric Sciences 56, 10; 10.1175/1520-0469(1999)056<1353:WATCZW>2.0.CO;2

The PSD of the transient eddy momentum flux for the period of 1980–87, as a function of (a) zonal wavenumber and latitude, integrated over all periods; (b) period and latitude, integrated over all entire zonal wavenumbers; (c) period and latitude, for zonal wavenumber 1; and (d) period and latitude, for zonal wavenumber 2. Solid contours are positive, dashed contour negative, and the zero contour is omitted. Contour interval is (a) 0.3 m^{2} s^{−2}, (b)–(d) 10^{−2} m^{2} s^{−2}.

Citation: Journal of the Atmospheric Sciences 56, 10; 10.1175/1520-0469(1999)056<1353:WATCZW>2.0.CO;2

The PSD of the transient meridional circulation as a function of period and latitude for the period of 1980–87. Solid contours are positive, dashed negative, and the zero contour is omitted. Contour interval is 2 × 10^{−2} m^{2} s^{−2}.

The PSD of the transient meridional circulation as a function of period and latitude for the period of 1980–87. Solid contours are positive, dashed negative, and the zero contour is omitted. Contour interval is 2 × 10^{−2} m^{2} s^{−2}.

The PSD of the transient meridional circulation as a function of period and latitude for the period of 1980–87. Solid contours are positive, dashed negative, and the zero contour is omitted. Contour interval is 2 × 10^{−2} m^{2} s^{−2}.

(a) Momentum fluxes and (b) momentum flux convergences by transient eddies (solid line) and the transient meridional circulation (dashed line) due to the seasonal cycle, for the period 1980–87.

(a) Momentum fluxes and (b) momentum flux convergences by transient eddies (solid line) and the transient meridional circulation (dashed line) due to the seasonal cycle, for the period 1980–87.

(a) Momentum fluxes and (b) momentum flux convergences by transient eddies (solid line) and the transient meridional circulation (dashed line) due to the seasonal cycle, for the period 1980–87.

As in Fig. 2, except for the period 1988–95.

As in Fig. 2, except for the period 1988–95.

As in Fig. 2, except for the period 1988–95.

(a) Momentum fluxes and (b) momentum flux convergences by transient eddies with periods of 30–70 days and *k* = 1 (thick solid line), by transient eddies with periods greater than 100 days and *k* = 1 and 2 (thick dashed line), and by transient eddies due to the seasonal cycle for *k* = 1 and 2 (thin dashed line), for the period 1980–95.

(a) Momentum fluxes and (b) momentum flux convergences by transient eddies with periods of 30–70 days and *k* = 1 (thick solid line), by transient eddies with periods greater than 100 days and *k* = 1 and 2 (thick dashed line), and by transient eddies due to the seasonal cycle for *k* = 1 and 2 (thin dashed line), for the period 1980–95.

(a) Momentum fluxes and (b) momentum flux convergences by transient eddies with periods of 30–70 days and *k* = 1 (thick solid line), by transient eddies with periods greater than 100 days and *k* = 1 and 2 (thick dashed line), and by transient eddies due to the seasonal cycle for *k* = 1 and 2 (thin dashed line), for the period 1980–95.

Fig 7. (a) *u*]*u*]*u*]^{−1}.

Fig 7. (a) *u*]*u*]*u*]^{−1}.

Fig 7. (a) *u*]*u*]*u*]^{−1}.

(a) Momentum fluxes and (b) momentum flux convergences by all transient eddies (thick solid line), transient eddies with periods of 30–70 days (thick dashed line), and mean meridional circulation (thin solid line) for the control case.

(a) Momentum fluxes and (b) momentum flux convergences by all transient eddies (thick solid line), transient eddies with periods of 30–70 days (thick dashed line), and mean meridional circulation (thin solid line) for the control case.

(a) Momentum fluxes and (b) momentum flux convergences by all transient eddies (thick solid line), transient eddies with periods of 30–70 days (thick dashed line), and mean meridional circulation (thin solid line) for the control case.

The PSD of the transient eddy momentum flux for the control case, as a function of (a) zonal wavenumber and latitude, integrated over all periods; (b) period and latitude, integrated over all zonal wavenumbers; and (c) period and latitude, for zonal wavenumber 1. Solid contours are positive, dashed contours negative, and the zero contour is omitted. Contour interval is (a) 0.3 m^{2} s^{−2}, (b) 10^{−2} m^{2} s^{−2}, and (c) 10^{−2} m^{2} s^{−2}.

The PSD of the transient eddy momentum flux for the control case, as a function of (a) zonal wavenumber and latitude, integrated over all periods; (b) period and latitude, integrated over all zonal wavenumbers; and (c) period and latitude, for zonal wavenumber 1. Solid contours are positive, dashed contours negative, and the zero contour is omitted. Contour interval is (a) 0.3 m^{2} s^{−2}, (b) 10^{−2} m^{2} s^{−2}, and (c) 10^{−2} m^{2} s^{−2}.

The PSD of the transient eddy momentum flux for the control case, as a function of (a) zonal wavenumber and latitude, integrated over all periods; (b) period and latitude, integrated over all zonal wavenumbers; and (c) period and latitude, for zonal wavenumber 1. Solid contours are positive, dashed contours negative, and the zero contour is omitted. Contour interval is (a) 0.3 m^{2} s^{−2}, (b) 10^{−2} m^{2} s^{−2}, and (c) 10^{−2} m^{2} s^{−2}.

(a) First and (b) second EOFs of velocity potential for the control case. Solid contours are positive, dashed are negative, and zero contour is omitted. Contour interval is 10^{6} m^{2} s^{−1}.

(a) First and (b) second EOFs of velocity potential for the control case. Solid contours are positive, dashed are negative, and zero contour is omitted. Contour interval is 10^{6} m^{2} s^{−1}.

(a) First and (b) second EOFs of velocity potential for the control case. Solid contours are positive, dashed are negative, and zero contour is omitted. Contour interval is 10^{6} m^{2} s^{−1}.

As in Fig. 9, except for the UW case.

As in Fig. 9, except for the UW case.

As in Fig. 9, except for the UW case.

^{1}

In this study, the term acceleration (deceleration) refers to an eastward (westward) acceleration.

^{2}

We use the term *intraannual* to denote timescales greater than one season and less than one year. Therefore, the intraannual timescale does *not* include the seasonal cycle.

^{3}

Because there is no grid point on the equator, the equatorial value is estimated by averaging the values at 1.12°S and 1.12°N.