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Abstract Linearized wave solutions on the equatorial beta plane are examined in the presence of a background meridional moisture gradient. Of interest is a slow, eastward-propagating n = 1 mode that is unstable at planetary scales and only exists for a small range of zonal wavenumbers ( ). The mode dispersion curve appears as an eastward extension of the westward-propagating equatorial Rossby wave solution. This mode is therefore termed the eastward-propagating equatorial Rossby wave (ERW). The zonal wavenumber-2 ERW horizontal structure consists of a low-level equatorial convergence center flanked by quadrupole off-equatorial gyres, and resembles the horizontal structure of the observed MJO. An analytic, leading-order dispersion relationship for the ERW shows that meridional moisture advection imparts eastward propagation, and that the smallness of a gross moist stability–like parameter contributes to the slow phase speed. The ERW is unstable near planetary scales when low-level easterlies moisten the column. This moistening could come from either zonal moisture advection or surface fluxes or a combination thereof. When westerlies instead moisten the column, the ERW is damped and the westward-propagating long Rossby wave is unstable. The ERW does not exist when the meridional moisture gradient is too weak. A moist static energy budget analysis shows that the ERW scale selection is partly due to finite-time-scale convective adjustment and less effective zonal wind–induced moistening at smaller scales. Similarities in the phase speed, preferred scale, and horizontal structure suggest that the ERW is a beta-plane analog of the MJO.
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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) in numerical models; 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 tendency associated with the MJO in terms of the ratio of the minimum values.
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- Award ID(s):
- 1757342
- PAR ID:
- 10226602
- Date Published:
- Journal Name:
- Journal of the Atmospheric Sciences
- Volume:
- 77
- Issue:
- 11
- ISSN:
- 0022-4928
- Page Range / eLocation ID:
- 3721 to 3732
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1175/JAS-D-20-0124.1
