The stability of an axisymmetric turbulent wake produced behind a stationary sphere in a fluid moving with uniform velocity is investigated. The dispersion relation indicates that the interface is unstable at all wave numbers, if the wake is treated as a viscous medium. From the dispersion relation the surface‐strain energy density spectrum of a known initial disturbance is obtained. The dynamic similarity of the distributions of the phase velocity and the surface‐strain energy density at high Reynolds number is demonstrated. From the energy equation one obtains a critical wavenumber beyond which the energy transport to the wake through the interface is cut off. A critical time is obtained based on the assumption that the momentum deficit in the wake is due to the viscous drag. The critical time and the critical wavenumber are used to explain the existence of an entrainment cycle.