The Compressional Beta-Effect: Analytical Solution, Numerical Benchmark, and Data Analysis

Abstract:

This study derives a complete set of equatorially confined wave solutions from an anelastic equation set with the complete Coriolis terms, which include both the vertical and meridional planetary vorticity. The propagation mechanism can change with the effective static stability. When the effective static stability reduces to neutral, buoyancy ceases, but the role of buoyancy as an eastward-propagation mechanism is replaced by the compressional beta-effect, i.e., vertical density-weighted advection of the meridional planetary vorticity. For example, the Kelvin mode becomes a compressional Rossby mode. Compressional Rossby waves are meridional vorticity disturbances that propagate eastward owing to the compressional beta-effect. The compressional Rossby wave solutions can serve as a benchmark to validate the implementation of the nontraditional Coriolis terms (NCTs); with an effectively neutral condition and initial large-scale disturbances given a half vertical wavelength spanning the troposphere on Earth, compressional Rossby waves are expected to propagate eastward at a phase speed of 0.24 m s^–1. The phase speed increases with the planetary rotation rate and the vertical wavelength and also changes with the density scale height. Besides, the compressional beta-effect and the meridional vorticity tendency are reconstructed using reanalysis data and regressed upon tropical precipitation filtered for the Madden–Julian oscillation (MJO). The results suggest that the compressional beta-effect contributes 10.8% of the meridional vorticity budget associated with the MJO in terms of the ratio of the minimum values. Ongoing study will correct the implementation of NCTs in the System for Atmospheric Modeling (SAM) and use it to simulate radiative-convective equilibrium on a generalized equatorial f-plane. We hypothesize that convective clusters prefer eastward propagation because of the compressional beta-effect.