Table 2.
Dispersion relations of the modes of the model with uniform rotation (Ω = Ω0), ν = κ = 0, and δ = 0.
m | ℜ[ω]/Ω0 |
|||||
---|---|---|---|---|---|---|
Equatorial Rossby modes | Columnar convective modes | High-latitude modes | ||||
n = 0 | n = 1 | ζz sym. | ζz antisym. | ζz sym. | ζz antisym. | |
0 | – | −0.629 | – | 0.629 | – | – |
1 | −0.999 | −0.527 | 0.151 | 0.694 | −0.303 | −0.173 |
2 | −0.666 | −0.447 | 0.290 | 0.758 | −0.293 | −0.172 |
3 | −0.499 | −0.380 | 0.410 | 0.824 | −0.258 | −0.166 |
4 | −0.399 | −0.328 | 0.518 | 0.883 | −0.216 | −0.157 |
5 | −0.333 | −0.286 | 0.612 | 0.938 | −0.181 | −0.149 |
6 | −0.285 | −0.253 | 0.682 | 0.990 | −0.161 | −0.141 |
7 | −0.249 | −0.226 | 0.743 | 1.029 | −0.144 | −0.133 |
8 | −0.222 | −0.204 | 0.792 | 1.053 | −0.131 | −0.126 |
9 | −0.199 | −0.185 | 0.822 | 1.061 | −0.121 | −0.120 |
10 | −0.181 | −0.170 | 0.846 | 1.056 | −0.111 | −0.114 |
11 | −0.166 | −0.156 | 0.863 | 1.049 | −0.103 | −0.109 |
12 | −0.153 | −0.145 | 0.873 | 1.041 | −0.096 | −0.104 |
13 | −0.142 | −0.135 | 0.881 | 1.033 | −0.092 | −0.099 |
14 | −0.133 | −0.126 | 0.887 | 1.024 | −0.089 | −0.095 |
15 | −0.124 | −0.119 | 0.889 | 1.015 | −0.085 | −0.091 |
16 | −0.117 | −0.112 | 0.889 | 1.006 | −0.083 | −0.087 |
Notes. All the frequencies are measured in the corotating frame. For the equatorial Rossby modes, n denotes the number of radial nodes for vθ at the equator. For the other two types modes, at fixed m, there are both modes with north-south symmetric and and antisymmetric z-vorticity ζz where z denotes the rotational axis. These different dispersion relations and their connections are plotted in Fig. 10.
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