| 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.
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.