Classification of eastward propagating waves on the spherical Earth

Area of Science:

• Atmospheric dynamics
• Geophysical fluid dynamics

Background:

• Observational evidence supports an equatorial non-dispersive wave mode propagating at gravity wave speeds.
• Previous spherical theories struggled to identify this mode outside specific asymptotic limits.

Purpose of the Study:

• Develop a novel solution for the linearized rotating shallow-water equations (LRSWE) on a sphere.
• Clarify the physical interpretation and classification of this equatorial wave mode.

Main Methods:

• Developed an ad hoc solution for the LRSWE on a sphere.
• Employed numerical calculations and eigenvalue analysis of an approximate Schrödinger equation.
• Compared results with gravity modes on a non-rotating sphere and existing wave theories.

Main Results:

• The new solution propagates eastward at nearly gravity wave speeds for all zonal wave numbers.
• The mode is identified as a rotation-modified counterpart of non-rotating sphere gravity modes at high wave numbers.
• The dispersion relation matches the n=0 eastward propagating inertia-gravity (EIG0) wave, suggesting a dual classification as Kelvin and EIG0 waves.

Conclusions:

• The developed solution accurately describes the observed equatorial non-dispersive mode.
• This work unifies the understanding of Kelvin waves and EIG0 waves on a sphere, resolving discrepancies with Cartesian coordinate treatments.
• Highlights limitations of asymptotic expansions for specific wave regimes like Kelvin waves.