We present the Direct Numerical Simulations of high Reynolds numbers aircraft wakes employing vortex particle methods. The simulations involve a highly efficient implementation of vortex methods on massively parallel computers, enabling unprecedented simulations using billions of particles. The method relies on the Lagrangian discretization of the Navier–Stokes equations in vorticity–velocity form and relies on remeshing of the particles in order to ensure the convergence of the method. The remeshed particle locations are utilized for the computation of the field quantities, the discretization of the differential operators for diffusion and vortex stretching, and the solution of the Poisson equation for the advection velocity field. The method exhibits excellent scalability up to 16k BG/L nodes. The results include unprecedented Direct Numerical Simulations of the onset and the evolution of multiple wavelength instabilities induced by ambient noise in aircraft vortex wakes at Re = 6000.