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Table 2

Summary of analytical results at each critical level when the box is inclined or not with respect to the rotation axis, in the [0, π∕2] quadrant, and for positive wavenumbers.

Box Critical level Attenuation Amplification
yes for waves No
Inclined box Yes for waves No
       
σ = 0 No No

Pole (θ0 = 0) σ = 0 Yes if

Equator (θ0 = π∕2) σ = ± 1 \ \
σ = 0 No No

Notes. The table indicates whether each critical level can cause attenuation or amplification of the (upward and downward ) travelling wave in the y direction, which depends, notably at the pole, on and on the wave action flux above the critical level . The symbol \ indicates that no wave action flux is carried across the critical level. Moreover, the results are analogous in the otherquadrants of the spherical body (with the direction of the attenuated wave through varying according to sign(kzf)).

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