The Diabatic Rossby Vortex: Growth Rate, Length Scale, and the Wave–Vortex Transition

Abstract

<jats:title>Abstract</jats:title> <jats:p>In idealized simulations of moist baroclinic instability on a sphere, the most unstable mode transitions from a periodic wave to an isolated vortex in sufficiently warm climates. The vortex mode is maintained through latent heating and shows the principal characteristics of a diabatic Rossby vortex (DRV) that has been found in a range of different simulations and observations of the current climate. Currently, there is no analytical theory for DRVs or understanding of the wave–vortex transition that has been found in warmer climates. Here, we introduce a minimal moist two-layer quasigeostrophic model with tilted boundaries capable of producing a DRV mode, and we derive growth rates and length scales for this DRV mode. In the limit of a convectively neutral stratification, the length scale of ascent of the DRV is the same as that of a periodic moist baroclinic wave, but the growth rate of the DRV is 54% faster. We explain the isolated structure of the DRV using a simple potential vorticity (PV) argument, and we create a phase diagram for when the most unstable solution is a periodic wave versus a DRV, with the DRV emerging when the moist static stability and meridional PV gradients are weak. Last, we compare the structure of the DRV mode with DRV storms found in reanalysis and with a DRV storm in a warm-climate simulation.</jats:p> <jats:sec> <jats:title>Significance Statement</jats:title> <jats:p>Past research has identified a special class of midlatitude storm, dubbed the diabatic Rossby vortex (DRV), which derives its energy from the release of latent heat associated with condensation of water vapor and as such goes beyond the traditional understanding of midlatitude storm formation. DRVs have been implicated in extreme and poorly predicted forms of cyclogenesis along the east coast of the United States and the west coast of Europe with significant damage to property and human life. The purpose of this study is to develop a mathematical theory for the intensification rate and length scale of DRVs to gain a deeper understanding of the dynamics of these storms in current and future climates.</jats:p></jats:sec>