Between streamwise distances 4d and at least 10d in the planar turbulent wake of a square prism of side length d, the turbulent fluctuating velocities are highly non-Gaussian, the turbulent energy spectrum has a close to −5/3 power law range, and the turbulence dissipation rate obeys the nonequilibrium dissipation scaling if the energy of the coherent structures is not included in the scaling. In this same range of streamwise distances, the coherent structure dissipation rate decays proportionally to the stochastic turbulence dissipation rate and there is a strong tendency of alignment or antialignment between fluctuating velocities and fluctuating vorticities which appears to coincide with the presence of coherent structures.