In theoretical treatments of turbulent fountains, the entrainment of ambient fluid into the top of the fountain, hereinafter fountain-top entrainment
), has been neglected until now. This neglect, which modifies the energetic balance in a fountain, compromises the predictive ability of existing models. Our aim is to quantify
by shedding light on the physical processes that are responsible for fountain-top entrainment. First, estimates for
are obtained by applying, in turn, an entrainment closure in the vein of Morton et al. (Proc. R. Soc. Lond., vol. 234, 1956, pp. 1–23) and then of Shrinivas & Hunt (J. Fluid Mech., vol. 757, 2014, pp. 573–598) to the time-averaged fountain top. Unravelling the assumptions that underlie these approaches, we argue that neither capture the dynamical behaviour of the flow observed at the fountain top; the top being characterised by quasi-periodic fluctuations, during which large-scale eddies reverse and engulf parcels of ambient fluid into the fountain. Therefore, shifting our mindset to a periodical framework, we develop a new phenomenological model in which we emphasise the role of the fluctuations in entraining external fluid. Our model suggests that
is similar in magnitude to the volume flux supplied to the fountain top by the upflow (
, in agreement with experimental evidence. We conclude by providing guidance on how to implement fountain-top entrainment in existing models of turbulent fountains.