We derive expressions relating the entrainment fluxes of momentum and kinetic energy, relative to the mass flux entrained into a turbulent wake exposed to a turbulent background. These expressions contain correlations between the entrainment velocity and the turbulent
fluctuations within the background. We perform high-resolution, simultaneous PIV and PLIF experiments and observe these correlations to be negligible in the far wake such that momentum and kinetic energy are entrained into the wake with the same relative efficiency to mass as from an idealised, non-turbulent background. This is a useful result in the context of modelling since the entrainment hypothesis (Turner 1986) can still be used to model the
entrainment of momentum and kinetic energy. Nevertheless, the entrainment rate of mass is shown to vary spatially, and with the specific nature of the background turbulence, so this in turn drives a spatial/background-turbulence-specific entrainment rate of momentum/kinetic
energy. Contrastingly, in the near wake, whilst momentum is entrained from a turbulent background with the same relative efficiency to mass as for an idealised non-turbulent
background this is not the case for kinetic energy. Due to the sum of multiple positive, small-valued correlations between the fluctuations in the background and the entrainment velocity, kinetic energy is entrained more efficiently than in the idealised case. This includes
entrainment from a non-turbulent background where small correlations are observed between the irrotational background fluctuations and the entrainment velocity. Evidence is also presented that the entrainment velocity scales with the Kolmogorov velocity scale when the background is turbulent.