Table 2.
Description of the viscous modes discussed in this paper for the case where Ω = Ω0 + Ω2cos2θ.
| Modes | Basic properties (all modes are retrograde, ωr < 0) |
|---|---|
| Rossby | Modes restored by the Coriolis force with frequencies near ω ≈ −2mΩ0/ℓ(ℓ + 1), where ℓ = m for the |
| equatorial R mode, ℓ = m + 1 for R1, and ℓ = m + 2 for R2. | |
| High-latitude | Modes whose eigenfunctions have largest amplitudes in the polar regions. Their frequencies are the most |
| negative in the rotating frame. The least damped mode at fixed m has frequency ω ≈ mΩ2. | |
| Critical-latitude | Modes whose eigenfunctions have the largest amplitudes at mid or low latitudes, between their critical |
| latitudes. Their frequencies are the smallest in absolute value, with Re[ω] ≈ Im[ω]. | |
| Strongly damped | Modes with very large attenuation (|Im[ω]| ≥ |Re[ω]|), whose eigenfunctions are highly oscillatory around their |
| critical latitudes and frequencies satisfy Re[ω] ≈ mΩ2/2 (for the β-plane analogy, see Grosch & Salwen 1968). | |
Notes. The high-latitude, critical-latitude, and strongly damped modes owe their existence to the presence of viscous critical layers. Rossby modes would exist even in the case of vanishing differential rotation (i.e., without critical layers).
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