Model results of flow instabilities in the tropical Pacific Ocean

A two-and-a-half-layer model of the tropical Pacific Ocean is used to investigate the energy source for the intraseasonal dynamic-height variability observed near 6øN. A simulation of equatorial circulation is produced by forcing the model with mean-monthly wind-stress climatology. Two westward-propagating waves appear in the upper layer in the central and eastern portion of the model basin. These two waves are distinguished by period and meridional structure. An offequatorial wave with period of 30 days and wavelength of 1100 km has a meridional sea-level maximum near 6øN similar to that of the 30-50 day intraseasonal wave observed in the ocean. The meridional velocity signal also is asymmetric with respect to the equator, with'maximum near 4øN. The second wave with period of 15 days has a strong meridional velocity signal centered on the equator. The sealevel and zonal velocity signals associated with this equatorial wave have maxima near 1.5øN and 1.5øS. The eddy-energy budget reveals strong conversions from the mean-flow to eddy field through baroclinic and upper-layer barotropic conversion terms. Conversion terms north of the equator exhibit a bimodal structure: one maximum between the equator and 3øN is dominated by upper-layer barotropic conversion spatially coincident with the cyclonic shear along the equatorward edge of the South Equatorial Current (SEC), and a second smaller maximum between 3øN and 5øN is a combination of upper-layer barotropic conversion along the poleward edge of the SEC (anticyclonic shear) and baroclinic conversion ear the core of the SEC. The two peaks in the conversion terms, combined with similar structure in the flux-divergence terms in the model eddy-energy budget, provide evidence that two wave processes are generated at the different source regions: one near the equator and a second between 2øN and 5øN.


Introduction
The parallel shear flows that characterize the equatorial circulation are potential sites for instabilities.Observations of the equatorial Pacific Ocean reveal annual bursts of synoptic-scale motions (zonal wavelengths of order 1000 km and periods of order 1 month) strong in boreal summer, fall, and winter, except during E1 Nifio events when they are absent [e.g., Philander et al., 1985].These motions, presumably the result of instabilities within the wind-driven near-surface currents, play an important role in the heat, momentum, and energy balances of the tropical Pacific.At first, researchers attempted to link all annually modulated synoptic motions to a single dynamical process; more recent ments from two different systems (in situ and satellite) and in the results from a numerical model of the re-gion, the global version of the Navy layered ocean model [Wallcraft, 1991].In particular, synoptic-scale oscillations appear at 6øN, and are strongest around the end of each non-E1 Nifio calendar year.Since location, timing, wavelength, and period of the instability in the numerical model and in the observations are in good agreement, this model is used in the current study to analyze this instability and hence help us understand its dynamics.

Model
The folowing equations are solved by the isopycnal two-and-a-half-layer ocean model used in this study [Wallcraft, 1991].The subscript i indicates the layer.

Analysis of model output highlights possible generation mechanisms for instability waves.
Aside from basic limitations inherent in any primitive equation numerical model (i.e., grid resolution, parameterization of mixing, etc.), the three most severe limitations in this study are low vertical resolution, absence of explicit thermodynamic processes, and artificial poleward boundaries.Slab-like flow within layers poorly resolves the vertical shears that exist in the ocean, for example, above and below the core of the EUC.Artificial poleward boundaries in this model sever communication with midlatitudes and allow artificial Kelvin-wave propagation along the boundaries.We accept these shortcomings because the fundamental goal of this modeling study is to reproduce and examine the instability-wave processes in the simplest framework possible.

Mean Conditions
The structure of the mean currents provides a useful foundation for further analysis of the model output.
chosen as representative for the region, and the densities of these layers are based on suitable averages of Levitus [1982] oceanic climatology.The value of each h/+ is chosen so that the EUC has realistic behavior [Hurlburr et al., 1992].The model is integrated forward in time from an initial state of no motion, using mean-monthly wind-stress values from Hellerman and Rosenstein [1983].The coastline is the 500 m isobath from the ETOP05 database of world bathymetry.After 10 years the fluctuations in total layer potential and kinetic energies are consistent from year to year, indicating the initial transients have died away.The model output is subsampled at intervals of 3 days over the entire model grid.The following discussion is based on analysis of 4 years of model integration (years 11-14).

Figure 3 .Figure 7 .
Figure 2. Upper-layer (top panels) and lower-layer (bottom panels) zonal velocity, at 155øW (left panels), 140øW (middle panels), and 125øW (right panels) contoured as a function of latitude and time.Zonal velocities have been low-pass filtered with a 90-day filter.Contour interval is 20 cm s -1.Shaded areas represent westward flow.

Figure 9 .
Figure 8. Same as Figure 7 but for the winter (December through March).
Totals represent sums of positive contributions only, for the longitude ranges specified and latitudes between 10øN and 10øS.pied during the TIWE experiment, are confined to narrow period and wavelength ranges around at 21 days and 1060 km, respectively, that is, westward phase speed of 51 cm s -z [Qiao and Weisberg, 1995-energy budget reveals strong conversions from mean-flow to eddy field through upper-layer barotropic and baroclinic conversion terms.Conversion terms north of the equator exhibit a bimodal structure.One maximum between the equator and 3øN has conversions dominated by upper-layer barotropic conversion spatially coincident with the cyclonic shear along the equatorward edge of the SEC.The other is a second, smaller maximum between 3øN and 5øN, where conversion terms are a combination of upper-layer barotropic conversion along the poleward edge of the SEC (anticyclonic shear) and baroclinic conversion embedded in the SEC.The energetics budget determined by Hansen and Paul [1984] shows the same structure: bar-otropic conversion along the cyclonic and anticyclonic SEC shear regions and baroclinic conversion within the SEC.This double-peak conversion term, combined with similar structure in the flux-divergence terms in the model eddy-energy budget, provides evidence that two distinct instabilities are generated at the different source regions, one near the equator and a second between 2øN and 5øN.A temporal and longitudinal dependence exists in the eddy-energy budget.The westward progression of upper-layer current intensification is evident in the energy budget.During boreal summer and fall, energy conversions are largest east of 140øW, while during winter, conversion terms are largest west of 140øW.In the western and eastern instability regions, 150øW to 140øW and 130øW to 120øW, respectively, the partitioning of conversion between baroclinic and barotropic changes during the year.At 150øW-140øW, there is a transition from barotropic conversion along the SEC shear zones during summer and fall to baroclinic conversion within the SEC during winter, similar to the results of Luther and Johnson [1990].To the east, at 130 ø-120øW, the early stages of instability are almost entirely dominated by barotropic conversion.Proehl [1996] recently readdressed the utility of using energy conversion terms in the classification of flow instabilities, stressing the importance of the geometry of the flow.He showed that the partitioning of baroclinic and barotropic conversion in the linear instability analysis of a westward jet changed as the core moved from 2 ø to 6 ø latitude, although the unstable wave structure changed little.As the geostrophically balanced jet moves further north, baroclinic conversion dominates, reflecting the increase in isopycnal slopes.Using the insight of Proehl [1996], we can interpret the model simulation in the following way.The SEC becomes unstable during boreal summer through boreal winter.The instability is manifested in two wave processes.Because the background flow field is constantly changing as a function of time and longitude, the available energy that the instabilites can extract is also changing.We do not expect the results from this modeling effort to duplicate the real ocean in detail, because the model physics are highly simplified.For example, the role of the surface density front near 1.5øN cannot be addressed with our model configuration, and McCreary and Yu [1992] and Yu et al. [1995] have suggested that instability of this front provides an additional source of eddy energy.However, the similarities of the meridional structures of the observed and modeled tropical instability waves and the conversion terms suggest that our model has captured much of the essential physics.The results emphasize the importance of the meridional structure of the tropical instability waves and the temporal and longitudinal variations in eddy-energy conversion terms, which depend on the local current and density fields.Future modeling efforts incorporating more realistic tropical physics should address the im-pact of both near-equatorial and off-equatorial variability on the regional heat and momentum budgets.A.3.Eddy Energy Equation An equation describing the rate of change of the energy associated with the eddy field is obtained by subtracting (A19) from the mean of the total energy equathe Navy layered ocean model and gave many helpful suggestions.Special thanks to E. Joseph Metzger and Allan Wallcraft for assistance during the model setup and subsequent runs.Comments from two anonymous reviewers have greatly improved the paper.

Table 1 . Model Parameters Implemented in the Model Simulation Parameter Value Layers Interfacial friction coetficient Layer density pi Resting layer thickness Hi Mixing velocity 5•i Mixing depth h/+
CoastlineForcingHorizontal eddy viscosity A