An investigation into convectively generated potential‐vorticity anomalies using a mass‐forcing model

A mass‐forcing model is used to investigate how the potential‐vorticity (PV) anomalies, formed as a response to changes in the mass field due to convection in a rotating, stratified fluid, are dependent upon the horizontal distribution of the vertical mass transfer. It is found that when the mass is concentrated within a single convective plume a stronger PV anomaly results than when an equivalent total mass is distributed about an ensemble of plumes. When the ensemble is well separated the resultant balanced energy is approximately proportional to the sum of each plume's convected mass to the five‐thirds. As the separation of the ensemble is reduced below that of a Rossby radius the ensemble behaves more like a single system. However, as the PV anomalies interact they coalesce and energy lost in this coalescence process, plus the entrainment of environmental PV, results in less balanced energy than predicted from the above quantitative relationship. Further experiments show that the final PV anomalies show only a little sensitivity to the horizontal scale of the mass transfer, and it is argued that the final balanced energy is primarily a function of the convected mass. However, when the local intensity of the mass transfer is high, such as when the mass is forced through smaller scales, there is a much stronger fast manifold response in the form of inertia‐gravity waves. This complements other studies which argue that convective heating on scales less than a Rossby radius will mostly excite inertia‐gravity waves, whilst when on scales greater than a Rossby radius will strengthen the balanced flow.