Three-dimensional slow Rossby waves in rotating spherical density-stratified convection

Abstract

We develop a theory of three-dimensional slow Rossby waves in rotating spherical density stratified convection. The Rossby waves with frequencies which are much smaller than the rotating frequency, are excited by a non-axisymmetric instability from the equilibrium based on the developed convection. These waves interact with the inertial waves and the density stratified convection. The density stratification is taken into account using the anelastic approximation for very low-Machnumber flows. We study long-term planetary Rossby waves with periods which are larger than two years. We suggest that these waves are related to the Southern Oscillation and El Niño. The El Niño is an irregularly periodical variation in winds and sea surface temperatures over the tropical Pacific Ocean, while the Southern Oscillation is an oscillation in surface air pressure between the tropical eastern and the western Pacific Ocean. The strength of the Southern Oscillation is characterised by the Southern Oscillation Index (SOI). The developed theory is applied for the interpretation of the observed periods of the SOI. This study demonstrates a good agreement between the theoretical predictions and the observations.

Generation of large-scale vorticity in rotating stratified turbulence with inhomogeneous helicity: mean-field theory

“…In the absence of rotation and density stratification, the expression (4.5) for the growth rate of the large-scale instability coincides with that obtained by Elperin et al (2003). Equation (4.6) describes three-dimensional slow Rossby waves in rotating density stratified flows which are similar to those studied by Elperin, Kleeorin & Rogachevskii (2017), see equation (28). We remind that the system considered in this study is a three-dimensional one, where the angular velocity, Ω = (0, Ω, 0), stratification, λ = (λ, 0, 0) and the wavenumber, K = (0, 0, K z ), are perpendicular each other.…”

“…(2003). Equation (4.6) describes three-dimensional slow Rossby waves in rotating density stratified flows which are similar to those studied by Elperin, Kleeorin & Rogachevskii (2017), see equation (28). We remind that the system considered in this study is a three-dimensional one, where the angular velocity, , stratification, and the wavenumber, , are perpendicular each other.…”