The compressional beta-effect: Analytical solution, numerical benchmark, and data analysis. (arXiv:2004.15017v2 [physics.ao-ph] UPDATED)
<a href="http://arxiv.org/find/physics/1/au:+Ong_H/0/1/0/all/0/1">Hing Ong</a>, <a href="http://arxiv.org/find/physics/1/au:+Roundy_P/0/1/0/all/0/1">Paul E. Roundy</a>
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.
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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