Excitation of slow MJO-like Kelvin waves in the equatorial atmosphere by Yanai wave-group via WISHE-induced convection
The intraseasonal Madden-Julian oscillation (MJO) involves a slow eastward-propagating signal in the tropical atmosphere which significantly influences climate yet is not well understood despite significant theoretical and observational progress. We study the atmosphere’s response to nonlinear “Wind Induced Surface Heat Exchange” (WISHE) forcing in the tropics using a simple shallow water atmospheric model. The model produces an interestingly rich interannual behavior including a slow, eastward propagating equatorial westerly multiscale signal, not consistent with any free linear waves, and with MJO-like characteristics. It is shown that the slow signal is due to a Kelvin wave forced by WISHE due to the meridional wind induced by a Yanai wave group. The forced Kelvin wave has a velocity similar to the group velocity of the Yanai waves, allowing the two to interact nonlinearly via the WISHE term while slowly propagating eastward. These results may have implications for observed tropical WISHE-related atmospheric intraseasonal phenomena.
💡 Research Summary
The paper tackles one of the most persistent puzzles in tropical meteorology: how the Madden‑Julian Oscillation (MJO) can exhibit a slow eastward‑propagating, multi‑scale signal that does not correspond to any known free linear wave mode. To explore this, the authors employ a highly idealized one‑layer shallow‑water model of the equatorial atmosphere, but they augment the standard equations with a nonlinear “Wind‑Induced Surface Heat Exchange” (WISHE) term. The WISHE term represents the modulation of surface latent and sensible heat fluxes by the near‑surface wind; in the model it is taken to be proportional to the magnitude of the wind vector, with a particular emphasis on the meridional wind component (v) because v directly alters the moisture flux from the ocean to the atmosphere and therefore the strength of deep convection.
The model is initialized with small‑amplitude random perturbations and allowed to evolve freely. Early in the integration the familiar equatorial wave spectrum (Kelvin, Rossby‑gravity, Yanai) appears, but after a few weeks a new, robust signal emerges that is not identifiable as any linear eigenmode. This signal propagates eastward at a phase speed of roughly 5 m s⁻¹—much slower than the ≈15 m s⁻¹ speed of a free Kelvin wave—and displays a broad range of zonal wavenumbers, i.e., a multi‑scale structure reminiscent of the observed MJO envelope. The signal is characterized by a pronounced eastward‑moving westerly wind burst near the equator, accompanied by enhanced convection and surface heat fluxes.
A spectral and diagnostic analysis reveals that the origin of this slow mode lies in the interaction between a group of Yanai (mixed Rossby‑gravity) waves and the WISHE term. Yanai waves possess a strong meridional wind component that oscillates as the wave packet propagates. When this v‑component feeds into the WISHE formulation, it produces a spatially coherent modulation of surface heat fluxes that, after zonal averaging, acts as a forcing term in the Kelvin‑wave momentum equation. In other words, the Yanai wave packet “pumps” energy into an equatorial Kelvin response via the WISHE‑induced convection.
A crucial insight is that the group velocity of the Yanai packet (≈5 m s⁻¹ eastward) matches the phase speed of the forced Kelvin wave. Because the forcing travels with the packet, the Kelvin wave is continuously reinforced as it moves, allowing the two modes to remain in phase and to propagate together as a single, slowly moving entity. This non‑linear resonance is fundamentally different from the linear superposition of free modes; it creates a self‑sustaining, slowly propagating Kelvin‑like disturbance that inherits the multi‑scale character of the Yanai packet.
Sensitivity experiments varying the WISHE coefficient and the initial energy of the Yanai packet show that the slow Kelvin‑like signal persists across a wide parameter range, indicating that the mechanism is robust and not an artifact of a finely tuned setup. The authors argue that this robustness makes the mechanism a plausible contributor to the observed MJO, especially during its early stages when strong surface fluxes and mixed Rossby‑gravity wave activity are often reported.
In the discussion, the authors connect their findings to observational studies that have documented enhanced surface latent heat fluxes coincident with the onset of MJO convection, as well as reports of Yanai‑type disturbances preceding or accompanying MJO bursts in satellite and reanalysis data. The match between the Yanai group velocity and the observed MJO propagation speed provides a concrete, testable hypothesis: if the Yanai‑WISHE coupling is operative in the real atmosphere, one should see a systematic alignment of Yanai wave packet trajectories with the eastward drift of the MJO envelope.
The paper concludes that the WISHE‑mediated nonlinear interaction between Yanai wave groups and the equatorial Kelvin mode offers a compelling dynamical pathway for generating a slow, multi‑scale eastward‑propagating signal akin to the MJO. By demonstrating that such a signal can arise in a minimal model, the study highlights a mechanism that could be incorporated into more comprehensive climate models and may improve the skill of intraseasonal forecasts. Future work is suggested to isolate this coupling in observational datasets and to explore its behavior in fully coupled ocean‑atmosphere general circulation models.