Hao Fu, Morgan O'Neill

Cloud-permitting simulations have shown that tropical cyclones can form spontaneously in a quiescent environment with uniform sea surface temperature. While the moisture-radiation instability is known as the main mechanism for early-stage growth, two key questions remain unresolved: First, how does the noisy cumulus cloud field organize into a mesoscale perturbation? Second, what determines the length scale of the growing perturbation? This paper develops a theoretical framework in the spectral space to understand the mesoscale perturbation produced by homogeneous random convection and its amplification with mesoscale instability. The theory assumes that the random stretching of planetary vorticity by homogeneous random convection produces the initial vorticity perturbation. The theory predicts that the magnitude of its mesoscale component is universally proportional to the square root of the domain-averaged accumulated rainfall, in agreement with cloud-permitting simulations. The perturbation then kicks off a mesoscale instability that features exponential growth. The instability has a most unstable wavelength. Linear stability analysis shows that the most unstable wavelength is proportional to the geometric mean of the effective Rossby deformation radius of the convectively coupled gravity wave and a $\sim10$ km convective spreading length scale. Mechanism-denial numerical experiments show that the convective spreading length scale depends on the spread of convective activity by cold pools and the nonlocal longwave radiative heating induced by anvil clouds.