the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 04 Aug 2026
Observed Yanai wave trajectories in the Western Equatorial Atlantic
Abstract. The western equatorial Atlantic Ocean features a variety of dynamical processes. The upper-ocean circulation is characterized by both western boundary currents and the equatorial current system, which are important pathways of the upper branch of the Atlantic Meridional Overturning Circulation. On subseasonal to seasonal timescales, equatorial waves such as Yanai waves further influence local ocean dynamics. Yanai waves, also referred to as mixed Rossby-gravity waves, exist in all tropical ocean basins predominantly on timescales of 10 to 30 days. They are associated with meridional velocities at the equator, setting them apart from other equatorial waves. While Yanai waves have been thoroughly analyzed regarding their energy dissipation, generation mechanisms, and propagation characteristics, little observational evidence has been provided regarding their surface trajectories. This study investigates the trajectories of Lagrangian surface drifters with respect to the presence of Yanai waves in the western equatorial Atlantic. Only few surface drifters remain long enough at or close to the equator to offer insights into equatorial phenomena since the prevailing poleward Ekman flow near the equator typically drives drifters to higher latitudes fairly quickly, which makes measurements sparse but particularly valuable. During a research cruise in May 2023, eight surface drifters were deployed into the western boundary current system off Brazil along 35 °W between the equator and 2.25 °S. Three of these drifters got trapped within circling surface movements centered around the equator. Our analysis suggests that this circular movement can be attributed to a Yanai wave. First, we find that the drifter oscillations coincided with cross-equatorial fluctuations of the meridional velocity component of the wind, a commonly accepted generation mechanism of Yanai waves. Additionally, we could reproduce the observed trajectories by conducting a series of numerical experiments with artificial drifters, combining the mean background flow of the area with theoretical Yanai wave-induced surface velocities. The observed Yanai wave is characterized by a 14-day period and velocity amplitudes of approximately 0.6 to 0.7 m s-1.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-4390', Anonymous Referee #1, 28 Aug 2026
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RC2: 'Comment on egusphere-2026-4390', Anonymous Referee #2, 25 Sep 2026
Review of "Observed Yanai wave trajectories in the Western Equatorial Atlantic" (Ocean Science) by Alexandra Andrae, Peter Brandt, Franz Philip Tuchen, Rebecca Hummels, and Joke F. Lübbecke
This paper interprets trajectories from 8 surface drifters deployed in the equatorial Atlantic near 35W. Some of the drifter trajectories made circular loops, which are interpreted as being due to Yanai waves with a period of about 14 days, superimposed on a background current. The paper is clearly written, and the analysis generally is sound. However, the paper is close to being a "least publishable unit". There is some information here that may be useful and interesting to other researchers, so I think the paper has (barely) enough new science to be publishable. It is a straightforward interpretation of some limited new observations. The main insight is that linear Yanai waves can produce looping trajectories, something that I think many people know (e.g., see Figure 6b of the original paper on equatorial waves, Matsuno, 1966), but that may not be widely appreciated and may not have been demonstrated with data. I am ambivalent about whether the paper is worth publishing.Major points:
1. I think the main result is that linear Yanai waves can produce looping trajectories. I cannot think of a paper that has made this point very explicitly, but the vortical nature of Yanai wave flow has come up in some papers (Neduhal et al., 2024, JGR Atmospheres, Fig. 11, showing that atmospheric Yanai waves have more vorticity than divergence; discussion of Dutrieux et al., 2008, JPO, noting that linear equatorial waves can have vortex-like velocity fields). However, it seems clear from the velocity field of linear Yanai waves (Figure 6b of Matsuno, 1966) that they could drive circular drifter trajectories. (Other equatorial waves can have vortex-like velocity fields, like in Matsuno, 1966, Figs. 4b, 4c, 5c. Linear surface gravity waves also drive looping Lagrangian trajectories, of course.)
2. The interpretation that the looping drifter trajectories are due to a linear superposition of a linear mixed Rossby-gravity wave (or Yanai wave) and a background current derived from a monthly climatology requires the unstated assumption that there is no nonlinear interaction between the Yanai wave and the mean flow. This should be discussed and justified. I don't think it is very hard to justify because the Yanai waves propagate very fast compared to the mean flow speeds. This is discussed in Farrar and Durland (2012) and McPhaden and Taft (1979).
3. I fail to understand the point of the histograms in Figures 6 and 7 and all of the associated text (Lines 205-245). This strikes me as something that could make sense to an LLM agent. I think maps of trajectories might be more informative. Or, you might consider not including that at all and instead discussing Major Point 1 above.
4. There is an apparent major discrepancy between the linear model and the observed trajectories in Figure 5: the observed trajectory appears to have "looped" several times, but the simulated trajectories looped at most once. Could the drifter have been caught in an eddy?
Minor points:
a. Line 8 and many other places (e.g., line 261): the term "surface trajectories" is used in reference to waves, and this does not seem like the right phrase. The "trajectory of a wave" is not the same thing as the trajectory of a drifter in a wave field.
b. Line 26: First of all, it is a trivial statement to say that Yanai waves exhibit westward phase propagation at negative wavenumbers -- that is what it means to have negative wavenumbers. Second, Yanai waves do not resemble Kelvin waves, even at positive wavenumbers. The classical statement, which does not need to be repeated here, is that mixed Rossby-gravity waves resemble Rossby waves at large negative wavenumbers and gravity waves at large positive wavenumbers.
c. I find it preferable to call these waves mixed Rossby-gravity waves, which tells us something about their dynamics, instead of Yanai waves, but fine. (I think it is generally clearer and better for scientific terms to describe the phenomena they label rather than to be named after someone.)
b. Section 2.2.3: It would be clearer to first describe the spectrum and then describe the filtering in another paragraph.
c. Section 2.2.4: It would be clearer to first explain why you need this and then describe it. Moreover, there is not a clear statement of what reanalysis you are talking about. GLORYS is mentioned in the fourth sentence.
d. Section 2.2.4: The validation of GLORYS velocities against PIRATA velocities is weak for the following reasons: (i) correlation does not tell us what time scales are well represented (the spectral coherence would do that), (ii) it appears (from the caption of Figure 1) that a 10-day running mean was applied to the velocities before calculating the correlation -- that seems like a poor choice, since a 10-day average is not sufficient to look at a 14-day signal.
e. Lines 195-205: The wording in these two paragraphs needs work.
f. Line 232: "reality-close" is not an adjective I am familiar with.Citation: https://doi.org/10.5194/egusphere-2026-4390-RC2
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- 1
Review of "Observed Yanai wave trajectories in the Western Equatorial Atlantic" by Alexandra Andrae et al. (egusphere-2026-4390)
This study describes the trajectories of surface drifters in the equatorial western Atlantic Ocean and discusses surface velocity associated with the mean current (NBC) and Yanai waves. The results are interesting and worth reporting in my evaluation, but I wonder whether the manuscript could be improved by adding one view: the Stokes drift of Yanai waves. I also suggest additional analyses of the statistical significance of correlation coefficients and those of spectra of surface velocity and winds. These points are detailed below.
1) The authors examined the trajectories of surface drifters, which represent Lagrangian-mean horizontal velocity. Lagrangian-mean velocity is the sum of Eulerian-mean velocity and Stokes drift. Eulerian-mean velocity is the flow field averaged at a fixed point. Stokes drift is wave-induced transport. Stokes drift is a wave property and can be computed from the linear solution. (Section 10.1 in Bühler (2014) describes Stokes drift in general.) Smyth et al. (2015) computed the Stokes drift of a vertically propagating Yanai wave (their Eq. (10)). Its zonal component on the equator is (|m|/N) v0^2/2, which is always positive. (m is vertical wavenumber, N is buoyancy frequency, and v0 is a parameter of wave amplitude.) Note that N/|m| can be replaced with c, where c is the horizontal phase speed of inertial gravity waves in a shallow water system (see Section 4b in McCreary 1984). I think this is consistent with the eastward movement of an artificial drifter in the right panel of Fig. 4. The meridional component of the Stokes drift is 0 (Smyth et al. 2015). This also seems consistent with the right panel of Fig. 4, because Stokes drift represents the transport averaged over one wave cycle. This is worth mentioning.
Bühler, O., 2014: Waves and Mean Flows, Cambridge University Press.
McCreary, J. P., 1984: Equatorial beams. J. Mar. Res., 42, 395-430.
Smyth, W. D., T. S. Durland, and J. N. Moum (2015), Energy and heat fluxes due to vertically propagating Yanai waves observed in the equatorial Indian Ocean, J. Geophys. Res. Oceans, 120, 1–15, doi:10.1002/2014JC010152.
2) Smyth et al. (2015) theoretically predicted that Yanai waves would be accompanied by zonal Stokes drift, but, to my knowledge, observational evidence for this has never been reported so far. Since Stokes drift contributes to material transport, it may also have climatic significance. This point further highlights the significance of the present study.
3) Smyth et al. (2015) estimated the Stokes drift for a vertically propagating wave, and it is unclear whether their result applies directly to the current case. I wonder if it is feasible to analytically compute the horizontal Stokes drift from Eqs. (2) and (3) in the manuscript, and compare it with the numerical estimate in the right panel of Fig. 4. The following papers may help. Weber et al. (2014) computed the Stokes drift of equatorial Kelvin waves. Weber (2017) calculated the Stokes drift of equatorial Rossby waves. Alternatively, please look for a study that computes the Stokes drift of Yanai waves in a shallow-water system and cite it if one exists.
Weber, J. E. H., Christensen, K. H., & Broström, G. (2014). Stokes drift in internal equatorial Kelvin waves: Continuous stratification versus two-layer models. Journal of Physical Oceanography, 44(2), 591-599.
Weber, J. E. H. (2017), Equatorial Stokes drift and Rossby rip currents, J. Geophys. Res. Oceans, 122, 4819–4828, doi:10.1002/2016JC012653.
4) The authors reported that the trajectories of some of the drifters are circular in shape. I wonder whether a circular trajectory occurs when the eastward Stokes drift of Yanai waves balances the mean westward current. The lower panel of Fig. 7 shows that floats make a circular trajectory when they are deployed south of the equator along 35°W. This might be due to westward NBC south of the equator at this longitude. This point can be checked by generating an artificial flow field that includes Yanai waves and a spatially uniform westward mean current, then deploying an artificial drifter.
5) Line 156 and Figure 1. Please discuss the statistical significance of the correlation coefficients. It can be computed following Section 3.14.1 in Thomson and Emery (2014). The effective degree of freedom can be computed following Section 3.15 in Thomson and Emery (2014) or the appendix in Metz (1991).
Metz, W. (1991). Optimal relationship of large-scale flow patterns and the barotropic feedback due to high-frequency eddies. Journal of Atmospheric Sciences, 48(9), 1141-1159.
Thomson, R.E., and W.J. Emery, 2014: Data Analysis Methods in Physical Oceanography. Elsevier.
6) The authors show meridional winds and oceanic current velocity bandpassed for the periods from 11 to 20 days in Figure 3. I suggest showing the spectrum of these variables to justify focusing on these specific periods.
7) Line 26: It is more straightforward to say "they resemble eastward-propagating inertia gravity waves.", because it is the "gravity" part of mixed Rossby gravity waves.