The Small-Amplitude Dynamics of Spontaneous Tropical Cyclogenesis. Part II: Linear Stability Analysis

This two-paper series studies the tropical cyclone (TC) precursor vortices spontaneously generated in an idealized setup with uniform sea surface temperature and no background wind. We focus on the small-amplitude stage, where vortices appear in an orderly pattern, and what controls the vortex size remains unclear. In Part I, Fourier analysis shows that the vortex size is constrained by a short-wavelength cutoff and a long-wavelength cutoff. The short-wavelength cutoff is explained as a convective spreading length due to cold pools and anvil clouds. In Part II, we study the long- wavelength cutoff. Diagnostic analysis shows that a TC precursor vortex has a shallow overturning cell in the lower troposphere and a deep overturning cell in the upper troposphere, driven by different convective types. A four-layer quasigeostrophic system is established to understand how the shallow and deep cells couple. Their dynamic coupling via midlevel buoyancy is negligible due to a midlevel high-speed waveguide that maintains a weak horizontal buoyancy gradient. Their thermodynamic coupling via the cooperative moistening of the air column is dominant. Linear stability analysis shows that the long-wavelength cutoff is controlled by an effective Rossby deformation radius L e , which is a mixture of the local Rossby deformation radii of the shallow and deep cells. The most unstable wavelength corresponds to the TC precursor vortex size, which is proportional to the geometric average of Le and the convective spreading length. The theoretical predictions generally agree with cloud-permitting simulations using varying Coriolis parameters and longwave radiative feedback strengths.