AbstractThe transformed Eulerian‐mean mass stream function gives an estimate of the mass flux across isentropic surfaces in terms of eddy fluxes evaluated on pressure surfaces. This is convenient both for data analysis and for the interpretation of theoretical results which are sometimes more easily expressed in pressure coordinates. A generalization is derived which describes the mass flux across an arbitrary iso‐surface, provided that the quantity defining the iso‐surface has a clear vertical gradient. The generalization is applied to iso‐surfaces of Ertel's potential vorticity, including the dynamical tro