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Abstract Azimuthally asymmetric perturbations are important to hurricanes because they can influence the track, structure, and intensity of a hurricane. In this work, we applied space‐time spectral analysis on both dynamic and thermodynamic fields of these perturbations and found two distinct power peaks in most of the fields. We obtained the structure of each mode by first filtering the fields through a frequency‐wavenumber spectral window selected for each mode and then regressing these fields on an index based on the filtered radar reflectivity. We found that the fast‐propagating wave is dominated by perturbations near the eyewall, and its structure is similar to that of the unstable mixed vortex Rossby inertia gravity wave. The other peak corresponds to a slow‐propagating wave that has comparable perturbations in and beyond the eyewall. The slow wave has a retrograde intrinsic propagating speed and has a vertical structure that resembles that of convectively coupled waves. 

Abstract Collisions between cold pools are generally acknowledged to be important processes through which new convective cells are triggered. Yet relatively little has been done to characterize these processes in detail, quantify their impact on the life cycle of cold pools, and include them in convective parameterizations. We use a combination of Eulerian and Lagrangian models to investigate how much cold pools are affected by collisions. Results from simulations in radiative‐convective equilibrium suggest that collisions represent a first‐order process in the dynamics of cold pools, the median time of first collision being under 10 min since cold pool birth. Through a Lagrangian tracking algorithm, it is also shown that cold pools are significantly deformed by collisions and lose the circular shapes they would have if in isolation only a few minutes after birth. Finally, it is suggested that cold pools happen in clusters, and associated spatial and temporal scales are presented. 

Abstract A Lagrangian Particle Dispersion Model is embedded into large eddy simulations to diagnose the responses of shallow cumulus convection to a small‐amplitude large‐scale temperature perturbation. The Lagrangian framework allows for a decomposition of the vertical momentum budget and diagnosis of the forces that regulate cloudy updrafts. The results are used to shed light on the parameterization of vertical velocity in convective schemes, where the treatment of the effects of entrainment as well as buoyancy‐induced and mechanically induced pressure gradients remains highly uncertain. We show that both buoyancy‐induced and mechanically induced pressure gradients are important for the vertical momentum budget of cloudy updrafts, whereas the entrainment dilution term is relatively less important. Based on the analysis of the dominant force balance, we propose a simple model to derive the perturbation pressure gradient forces. We further illustrate that the effective buoyancy and dynamic perturbation pressure can be approximated to a good extent using a simple cylindrical updraft model given the cloud radius. This finding has the potential for improving the parameterization of vertical velocity in convective schemes and the development of a unified scheme for cumulus convection.