Interaction of two axisymmetric turbulent wakes

The interaction between turbulent axisymmetric wakes plays an important role in many industrial applications, notably in the modelling of wind farms. While the non-equilibrium high Reynolds number scalings present in the wake of axisymmetric plates has been shown to modify the averaged streamwise scalings of individual wakes, little attention has been paid to their consequences in terms of wake interactions. We propose an experimental setup that tests the presence of non-equilibrium turbulence using the streamwise variation of velocity fluctuations between two bluff bodies facing a laminar flow. We have studied two different sets of plates (one with regular and another with irregular peripheries) with hot-wire anemometry in a wind tunnel. We first show that the wake interaction length, that quantifies the streamwise position where the wakes start interacting, can be deduced from the streamwise profiles of turbulence intensity, a quantity that is easy to resolve even in challenging field measurements. By acquiring streamwise profiles for different plate separations and identifying the wake interaction length for each separation it is therefore possible to study the interaction between two axisymmetric turbulent wakes in terms of its energy cascade and, in this case, to show that the interaction between them is consistent with non-equilibrium scalings. This work also generalises previous studies concerned with the interaction of plane wakes to include axisymmetric wakes. We find that a simple mathematical expression for the wake interaction length based on non-equilibrium turbulence scalings can be used to collapse the streamwise developments of the second, third and fourth moments of the streamwise fluctuating velocity.