This work stands apart: its closest neighbors study the solar corona, the solar wind, fast radio bursts, and invisible ocean waves. But all of them, like this paper, investigate wave processes in rotating or stratified media. Classical two-dimensional Rossby waves in the atmosphere have periods of no more than 100 days, which does not explain the observed multi-year oscillations of the Southern Oscillation. The authors propose three-dimensional slow Rossby waves that arise only in stratified convection.
The authors consider a spherical rotating layer with density stratification in the limit of very small Mach numbers (the anelastic approximation). The equations are linearized, and the solution is sought in a basis of spherical vector functions that are eigenfunctions of the curl operator. A dispersion equation is derived that describes three modes: convective, inertial waves, and three-dimensional Rossby waves. To interpret the SOI periods, atmospheric parameters are used: density scale height 8.3 km, Earth's radius 6400 km, and angular rotation rate 2.27×10³ rad/yr.
An expression is obtained for the frequency of three-dimensional slow Rossby waves, depending on the vertical scale and the azimuthal number m. For m=1 and vertical scales from 7.3 to 16.3 km, the theoretical periods range from 3.96 to 13.88 years, which matches the observed SOI periods (13.88, 6.61, 4.96, 3.96, 3.08, 2.57 years). For m=2, periods of 3.96 and 2.57 years are obtained for vertical scales of 9.69 and 12.1 km. The vertical scales are on the order of the tropopause height. It is shown that the instability that excites the waves has a characteristic time exceeding the wave period and is powered by the thermal energy of convective motions.
This work differs from its neighbors in that it is the first to link three-dimensional slow Rossby waves in stratified convection to the observed periods of the Southern Oscillation. Neighboring studies examine waves in the solar corona, the ocean, or astrophysical objects, but do not apply the theory to climate oscillations. This paper offers a physical mechanism to explain the multi-year variability of the SOI, which may improve understanding of El Niño and the Southern Oscillation.
The topic could develop toward accounting for turbulence, which causes wave dissipation. In the atmosphere, the strongest turbulence is concentrated in the boundary layer with a height of about 1 km. It is also possible to investigate nonlinear wave interactions and their role in shaping zonal flows. Applying the theory to other planets and stars with convective envelopes could yield new predictions.
The results are important for geophysical fluid dynamics, climatology, and El Niño forecasting. They may also be useful in astrophysics for describing wave processes in stellar convection zones.
The next step could be to include turbulent viscosity and compare with more detailed climate models. It is also important to test the theory on data from other planets, such as Jupiter or Saturn.
The work connects the unresolved problem of the origin of multi-year periods in the Southern Oscillation with the wave dynamics of stratified rotating convection. This clarifies the mechanisms responsible for climate variability in the tropical Pacific.
The periods of slow Rossby waves are comparable to the time spent in school: from 2.5 to 14 years. The Southern Oscillation Index is measured by the pressure difference between Tahiti and Darwin, and its fluctuations are visible even after smoothing over 5 months.