Fig. 4.

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Dispersion relation and eigenfunctions of the equatorial Rossby modes without radial nodes in the case of uniform rotation, no viscosity, and adiabatic stratification. (a) Dispersion relation from the calculated modes (red). Overplotted black dashed line represents the theoretical dispersion relation of the sectoral (l = m) Rossby modes ω = 2Ω0/(m + 1). (b) Schematic illustration of flow structure of the mode with m = 6. The red and blue volume rendering shows the structure of ℜ[ζr(r, θ)exp(imϕ − iωt)]. The black solid curve shows the meridional plane at ϕ = 0 and at t = 0 where vr and vθ are purely real and vϕ, p1, and ζr are purely imaginary. The black dashed line denotes the meridional plane at ϕ = −π/2m where vϕ, p1 and ζr are real. (c) Meridional cuts of the m = 2 eigenfunctions for the velocity v(r, θ)exp[i(mϕ − ωt)], the pressure p1(r, θ)exp[i(mϕ − ωt)], and the radial vorticity ζr(r, θ)exp[i(mϕ − ωt)]. The solutions are shown in the meridional plane at ϕ = 0 and t = 0. The units of the color bars are m s−1 for the three velocity components, 105 dyn cm−2 for the pressure, and 10−8 s−1 for the vorticity. The eigenfunctions are normalized such that the maximum of |vθ| is 2 m s−1. (d) The same as panel c but for m = 8.
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