(a) Growth rate σ of the inflectional instability as a function of the streamwise wavenumber k_x for k_z = 0, N = 1, Pr = 1, , f = 0 (i.e., Ω = 1 and θ = 90°) for Re = ∞ (black), Re = 50 (blue), and Re = 10 (red). The gray dash-dot line denotes the inviscid growth rate of the inflectional instability under the traditional approximation (i.e., ). (b,c) Growth rate σ of the inertial instability as a function of the vertical wavenumber k_z for k_x = 0, N = 1, , and f = 0.5 (i.e., Ω = 2.02 and θ = 82.9°) for (b) Pr = 1 and Re = ∞ (black), Re = 1000 (blue), and Re = 500 (red), and (c) Pr = 10⁻⁶ and Re = 10⁴ (black), Re = 5000 (blue), and Re = 1000 (red). Solid lines are numerical results, and dashed lines in (b) and (c) are asymptotic predictions from Eqs. (86) and (89), respectively.