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Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Ocean Models
  5. 3. Results
  6. 4. Discussion
  7. Acknowledgments
  8. References

[1] The spatial and temporal properties of zonally coherent jet-like structures found in high resolution ocean models is examined. We focus on the Pacific Ocean. We find the properties of the jets are not very sensitive to the model configuration. Distinct differences are found in the persistence and vertical structure of the jets poleward of 30°N and S compared with those in the tropics. We make a quantitative comparison between the meridional scale of the jets and the Rhines scale. We find a local scaling applies in that the horizontal variation of the meridional scale of the jets is consistent with horizontal variations in the Rhines scale.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Ocean Models
  5. 3. Results
  6. 4. Discussion
  7. Acknowledgments
  8. References

[2] The classical view of the circulation of the ocean at mid-latitudes above the thermocline and away from western boundaries is one of broad sweeping flows of the sub-tropical and sub-polar gyres. Recognition that the ocean is populated by mesoscale eddies complicates the picture, although it is still assumed that in the interior there is a clear distinction in scales between the eddying flow and the long time-mean flow of the circulation. Recent results from numerical models and data analysis suggest there is likely to be a class of flow structures that is intermediate in both spatial and temporal scale between mesoscale eddies and the long time-mean flow, and of sufficient intensity that they can dominate the circulation. Nakano and Hasumi [2005], who performed numerical experiments with a relatively high resolution ocean model of the North Pacific with low dissipation, find the model sub-surface flow averaged over a few years to be populated by a series of jets that are oriented approximately zonally and have a meridional scale of 3–5°. Galperin et al [2004] argue that the jets found in the model of Nakano and Hasumi [2005] are similar in character to those found in the atmospheric circulation of the giant planets and that the energy spectra of the oceanic and planetary jets obey the same power law.

[3] Direct observations of jets in the ocean are hampered by sampling issues relating to sufficient horizontal and temporal sampling. (Alternating jets have been observed in the deep ocean using float data [Hogg and Owens, 1999].) Indirect evidence comes from satellite altimetry. Maximenko et al. [2005] find alternating zonal jets in the anomaly of geostrophic velocity, derived from gridded sea surface height fields, when averaged over a few weeks. Both the amplitude and meridional scale of these jets are very similar to those found at depth in high resolution numerical ocean models. Analyzing the output from one such model Maximenko et al. [2005] find the model jets have a strong signature in sea level height.

[4] The formation of jets in rotating flows has received considerable attention. Free and forced geostrophic turbulence has a tendency to produce alternating zonal jets on a beta-plane or sphere, a necessary condition being the meridional gradient in planetary vorticity [cf. Rhines, 1975; Panetta, 1993; Vallis and Maltrud, 1993; Chekhlov et al., 1996; Huang and Robinson, 1998; Sinha and Richards, 1999]. The meridional scale of the jets is found to be proportional to the Rhines scale, LR = equation image, where u′ is the r.m.s. eddy velocity and β the meridional gradient of the Coriolis parameter.

[5] Much of the work referred to above assumes a zonal symmetry to the long-time mean of the flow. In the case of an ocean basin, such as the Pacific, in which the eddy activity and flow is spatially variable, it is not obvious that a local scaling applies. (Nonlinear interactions of resonant basin modes can also produce zonal jets [Berloff, 2005] which have a non-local scaling). Here we analyze the results from a number of runs of two high-resolution ocean models with low dissipation, with a focus on the intermediate scale of flow and its spatial and temporal variation. We find a local scaling does indeed seem to apply in the horizontal variation of the jet structures. This is not the case in the vertical. The implications of our findings are discussed in the final section.

2. Ocean Models

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Ocean Models
  5. 3. Results
  6. 4. Discussion
  7. Acknowledgments
  8. References

[6] We present the results from two ocean general circulation models. The configuration of the two is essentially the same for our purposes. The first (which we refer to as POP) is a fully global implementation of the Parallel Ocean Program at a 1/10° horizontal resolution (at the equator) with 40 levels in the vertical (and very similar to that described by Maltrud and McClean [2005]). The second (referred to as OFES) is based on MOM3, again at 1/10° horizontal resolution (but with the North Pole excluded), and with 54 levels in the vertical [Masumoto et al., 2004]. Both models were run on the Japanese Earth Simulator. The general characteristics of the zonal jets found in the results from the two models are very similar.

[7] The reason for analyzing two sets of model runs is that different experiments were done with each. POP was run for a relatively short time (order 15 model years) with a climatology from the NCEP/NCAR reanalysis but for a number of different values for the lateral mixing coefficients, different lateral mixing parameterizations, and with smooth and rough topography. The particular run of OFES we employ here is a run from 1950 to 2003 using 6 hourly forcing from the NCEP/NCAR reanalysis. The 50 year spin-up phase of this experiment was used in the analysis of Maximenko et al. [2005]. We therefore can examine the robustness of our results in respect to the imposed dissipation and forcing.

3. Results

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Ocean Models
  5. 3. Results
  6. 4. Discussion
  7. Acknowledgments
  8. References

[8] The zonal component of velocity, u, from the climatological run of the POP model, at 400 m depth and averaged over 3 years is shown in Figure 1. The striking thing about this figure is the zonal coherence of structures that have a relatively fine meridional scale and which appear to dominate the time-averaged flow. Such structures are a robust feature of ocean models with relatively high resolution and low imposed dissipation [Galperin et al., 2004; Nakano and Hasumi, 2005]. Here we find the properties of the fine scale structure, as analyzed below, are not sensitive to the form or magnitude of the imposed dissipation in the model. For the case shown the coefficients for the biharmonic momentum and tracer dissipation are set to be 2.7 and 0.9 × 10−9 m4 s−1, respectively. Varying these by a factor of 3, including a harmonic parameterization for tracer transport suggested by Gent and McWilliams [1990] (GM), or smoothing the topography, does not unduly affect the amplitude or meridional scales of the flow structures (see below). (We have not investigated how large the dissipation has to be before there is a significant impact.)

image

Figure 1. Zonal component of velocity at 400 m depth averaged over 3 years from the climatological run of the POP model. Color saturates at −0.06 m s−1 (blue) and 0.06 m s−1 (red).

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[9] Alternating jet-like structures are clearly seen, most notably between 30–55°N and in the tropics. The model Antarctic Circumpolar Current (ACC) also has a marked multiple-jet character which is masked by the color saturation in Figure 1. These regions also have high levels of eddy activity. We will analyze the structure of jets in these three regions in more detail. Jets are also associated with some islands such as the SW sub-tropical Pacific [cf. Webb, 2000] and the Hawaiian Lee Counter Current [cf. Xie et al., 2001].

[10] The vertical structure of the jets is shown in Figure 2. There is a jet-like structure throughout the entire depth of the ocean, but the structure is markedly different in the tropics compared with that further north. Between 30–50°N the jets are coherent throughout the entire depth of the ocean, with a surface intensification. (The most prominent jet is the extension of the Kuroshio at around 35°N.) Close to the equator, between 10°S–10°N, the vertical coherency of individual jets is much reduced.

image

Figure 2. Zonal component of velocity along 180°E averaged over 3 years from the climatological run of the POP model as a function of latitude and depth. Model run the same as in Figure 1. Color saturates at −0.06 m s−1 (blue) and 0.08 m s−1 (red). Zero contour given by black line.

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[11] The temporal coherency of the jets is shown in Figure 3 which shows a two-year running average of u at 400 m depth from OFES forced with NCEP/NCAR reanalysis, and averaged between 140–150°W. Poleward of 30°N and S there are features that are persistent in time. Between 30°N–55°N we see individual jets are persistent with time with their latitudinal position slowly varying with time. Jets merge and bifurcate on a timescale of O(3–5) years, with some jets persisting for much longer. The temporal evolution of the jets is very similar to that found by Panetta [1993] for forced geostrophic turbulence on a β-plane. In the ACC at this longitude the position of the jets is constrained by topography.

image

Figure 3. Two year running average of the zonal component of velocity at 400m depth averaged between 140–150°W, as a function of latitude and time, from OFES. Color saturates at −0.2 m s−1 (blue) and 0.2 m s−1 (red). Zero contour given by black line.

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[12] In the tropics at any particular time the two-year averaged flow does show a multiple jet structure. However the persistence of individual jets away from the equator is very variable. In the 1960's we see jets persisting for most of the decade, in particular between 5–20°N. In the 1980's there is very little persistence in this region.

[13] The flow in the sub-tropics, between 20–30°N and S, shows a very different behavior. Here the flow is dominated by features propagating toward the equator with a phase speed of approximately 0.045 m s−1 and a period of approximately 4 years (the two-year averaging partially obscures these features in Figure 3). The zonal and meridional wavelengths are approximately 4000 km and 500 km respectively. The westward phase speed is consistent with what we would expect for a long (in the zonal sense) Rossby wave at approximately 30° latitude [Killworth and Blundell, 2003]. The reason for the production of these waves in the model is unclear (radiation of energy away from the equator being a possibility). Further analysis will be given in a subsequent paper.

[14] In order to provide a quantitative measure of the meridional scale of the jets we have performed a wavelet analysis on the time-averaged u-field from POP. The wavelet power spectrum of the zonal component of velocity as a function of meridional wavelength and longitude is shown in Figure 4 (corresponding to the field shown in Figure 1). The wavelet power spectrum has been averaged over three latitudinal bands, corresponding to the ACC, the tropics and between 30°N and 50°N. In all three regions there is a distinct maximum in power at a meridional wavelength that varies with longitude. In the northern region the maximum is at approximately 6° of latitude at 150°E reducing to 3° by 160°W. In the tropics the maximum is approximately 3° in the west with a broader band at 100°W, whilst in the ACC the maximum is generally around 4–5°.

image

Figure 4. Wavelet power spectrum (normalized with respect to the variance) in the meridional direction of the zonal component of velocity shown in Figure 1 as a function of the meridional wavelength and longitude, averaged between (a) 70°S and 50°S, (b) 6°S and 6°N, and (c) 30°N and 50°N. Contours are at log2 intervals.

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[15] We compare the meridional scale of the jets with the Rhines scale. The Rhines scale, LR is shown in Figure 5 averaged over the same three regions as in Figure 4. The Rhines scale has been multiplied by a factor 2π to put it in terms of a wavelength. The correspondence in the spatial variations of LR and the meridional scale of the jets is remarkably good in the northern and tropical regions, with a tendency for LR to be slightly larger. In the ACC LR is significantly larger than the scale of the jets. Here the jets extend throughout the water column. Taking the large scale slope into account, and using an effective topographic β brings the value of LR much closer to the scale of the jets in the model ACC [Sinha and Richards, 1999]. However we also note that smaller scale topography may well impact on the jet structure in this region [see Treguier and Panetta, 1994].

image

Figure 5. The Rhines scale (2π LR) calculated for the climatological run of the POP model at 400 m depth averaged between 70°S and 50°S (thin line), 6°S and 6°N (thick solid line), and 30°N and 50°N (thick dashed line).

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[16] Reducing the biharmonic friction coefficients by a factor of 3 from the case shown in Figure 1 does produce a slight increase in the level of eddy energy. In terms of the Rhines scale as shown in Figure 5 the change is greatest in the ACC and the NE Pacific with a 10% increase in these regions. There is a commensurate increase in the meridional scale of the jets. Similar order changes are found by including harmonic GM mixing with a coefficient of 600 m2 s−1 and a moderate smoothing of the topography, respectively.

4. Discussion

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Ocean Models
  5. 3. Results
  6. 4. Discussion
  7. Acknowledgments
  8. References

[17] The existence of intermediate scale features with a meridional scale of O(300–500 km) and persistent for a few years in the circulation of the ocean is found to be a robust feature of high resolution/low dissipation ocean models, with the characteristics of these features not particularly sensitive to the model configuration. The features take the form of jets and propagating long crested Rossby waves. Such features are found in the sea surface height field as measured by satellite altimetry. A major conclusion from this work is the horizontal variation of the meridional scale of the jets is consistent with horizontal variations in the Rhines scale, LR.

[18] In the vertical the wavelength with maximum power in the wavelet spectrum is remarkably constant with depth, extending over almost the full water depth in all three regions. On the other hand the r.m.s. eddy velocity, u′, falls off with depth, suggesting the scaling of the jets in the vertical is non-local. Over the top 500 m LR varies by approximately 20%. At 2000 m depth LR is approximately halved. It does beg the question as to what sets the scale of the jets in a baroclinic ocean where the eddy energy varies with depth. One possibility is that the scale is set by the more energetic flow in the upper ocean and the deeper jets are formed through a barotropization process, at least at higher latitudes, but this needs to be tested by numerical experimentation. In the tropics the individual jets have a reduced vertical coherency of individual jets. Theiss [2004] suggests that baroclinic jets will form through a rectification process only if the Rhines scale is less than the baroclinic Rossby radius. For the first baroclinic mode this criterion is satisfied equatorward of ∼20°N and S. The different vertical structure of the jets found between the tropics and higher latitudes (see Figure 2) is consistent with this view, but further work is required.

[19] In the upper ocean of the tropics, equatorial dynamics produce a number of zonal flows. We have chosen to produce maps of properties at 400 m so as to be beneath the Equatorial Under Current. However flow features such as the subsurface countercurrents (SCCs, also known as Tsuchiya jets) do penetrate this deep [see, e.g., Rowe et al., 2000]. Individual meridional sections do suggest a multiple jet structure at around 400 m in addition to the SCCs [e.g., Rowe et al., 2000], but there is not enough observational evidence to deduce their zonal and temporal coherence. The fact that the model results show the off-equator jets in the tropics to be somewhat ephemeral compounds the problem. The relationship between these jets and the upper ocean currents requires careful numerical experimentation to elucidate.

[20] So what are the implications for the existence of intermediate scale flow features? We present two. The first relates to the ultimate fate of energy in the ocean. If the eddying action in the ocean tends toward zonal jets, then we need to rethink the way unresolved motions are parameterized in coarser resolution ocean models used in climate studies. The second concerns tracer transport and dispersion. The presence of high horizontal shear, and large scale structures in the flow will significantly alter the dispersion characteristics at long times through shear dispersion [Bartello and Holloway, 1991]. We therefore may expect a fundamentally different behavior for tracer transport and dispersion in the flows considered here as compared to that in coarser more diffuse ocean models (even in the case where such models are eddy permitting). A study to investigate the dynamical and Lagrangian properties of the intermediate flow structures is planned for the near future.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Ocean Models
  5. 3. Results
  6. 4. Discussion
  7. Acknowledgments
  8. References

[21] The POP and OFES model runs were performed on the Earth Simulator of Japan. This research was supported in part by JAMSTEC through its sponsorship of the IPRC. KJR gratefully acknowledges support from the visitors program of NCAR. IPRC/SOEST contribution 363/6712.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Ocean Models
  5. 3. Results
  6. 4. Discussion
  7. Acknowledgments
  8. References