Development of an idealised downstream cyclone: Eulerian and Lagrangian perspective on the kinetic energy

In this idealised modelling study, the development of a downstream cyclone, which closely follows the life-cycle of a Shapiro-Keyser cyclone, is addressed from a quasi-geostrophic kinetic energy perspective. To this end a simulation of a dry, highly idealised, dispersive baroclinic wave, developing a primary and a downstream cyclone, is performed. Kinetic energy and processes contributing to its tendency – in particular baroclinic conversion and ageostrophic geopotential fluxes – are investigated in three dimensions both in an Eulerian and a Lagrangian framework from the genesis of the downstream cyclone as an upper-level kinetic energy centre, over frontal fracture to the fully developed cyclone showing the characteristic T-bone surface frontal structure, with a strong low-level jet along the bent-back front. Initially the downstream cyclone grows by the convergence of ageostrophic geopotential fluxes from the primary cyclone, but as vertical motions intensify this process is replaced by baroclinic conversion in the warm sector. We show that kinetic energy released in the warm sector is radiated away at all levels by ageostrophic geopotential fluxes: in the upper troposphere they are directed downstream, while in the lower troposphere they radiate kinetic energy to the rear of the cyclone. Thereby, vertical ageostrophic geopotential fluxes, their location and divergence, are identified to play a major role in the intensification of the cyclone in the lower troposphere and for the formation of the low-level jet. Low-level rearward ageostrophic geopotential fluxes converging along the bent-back front are shown to be a general characteristic of an eastward propagating baroclinic wave.