An assessment of the scalings for the streamwise evolution of turbulent quantities in wakes produced by porous objects

Experimental results are presented for the evolution of three turbulent quantities in the wake of a porous object, analogous to a wind-turbine wake. These are the mean velocity deficit, the turbulence intensity, and the characteristic wake width. It is noted that characteristic wake widths can be defined both in terms of the mean velocity deficit profile and the profile of turbulence intensity. Both definitions of wake width are observed to grow linearly, although not at the same rate, with that defined by turbulence intensity growing more rapidly than velocity deficit. The streamwise scaling of both wake width, and velocity deficit is found to conform to a non-equilibrium dissipation scaling in which the dissipation rate within the wake is out of equilibrium with the inter-scale energy flux within the mean cascade of turbulent kinetic energy. The cumulative effect of turbulence intensity produced by N upstream porous objects is also considered. It is shown that when the object spacing is sufficiently large that the wake-added turbulence decays substantially only consideration of the most immediately upstream wake is important. Contrastingly, when the spacing between adjacent objects is small then summing the contributions from all upstream wakes in the array is necessary.