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A turbulent two-vortex system at equilibrium, that is typical of aircraft wakes in the far field, is first obtained using large eddy simulation and is characterized: circulation distributon of the vortices; energy of the mean and fluctuating fields; energy dissipation rate associated with the turbument equilibrium. A wall-resolved simulation of that system further interacting with a smooth ground is then performed at  Re_Γ = 2 x 10⁵ , which allows to capture the high Reynolds number behaviour. The high release height of the system also ensures a physically correct approach to the ground. For comparison, we also simulate the case of a system with non-turbulent vortices interacting with the same ground at the same Reynolds number. The flow topologies are discussed, and significant differences are highlighted regarding the separation of the boundary layer generated at the ground, and the way this secondary vorticity interacts with the primary vortices and makes them decay. The vortex trajectories are also measured, together with their circulation distribution and global circulation evolution, and the differences are discussed.