Flow Turbulence Combust (2011) 87:673–705 DOI 10.1007/s10494-011-9351-2 DNS of Fractal-Generated Turbulence Sylvain Laizet · John Christos Vassilicos Received: 4 January 2011 / Accepted: 4 May 2011 / Published online: 29 May 2011 © Springer Science+Business Media B.V. 2011 Abstract An innovative approach which combines high order compact schemes, Immersed Boundary Method and an efficient domain decomposition method is used to perform high fidelity Direct Numerical Simulations (DNS) of four spatially evolving turbulent flows, one generated by a regular grid and three generated by fractal square grids. The main results which we have been able to obtain from these simulations are the following: the vorticity field appears more clustered when generated by fractal square grids compared to a regular grid; fractal square grids generate higher vorticities and turbulence intensities than a regular grid; the flow holds clear geometrical imprints of the fractal grids far downstream, a property which could be used in the future for flow design, management and passive control; the DNS obtained with fractal grids confirmed the existence of two turbulent regions, one where the turbulence progressively amplifies closer to the grid (the production region) followed by one where the turbulence decays; the energy spectra of fluctuating turbulent velocities at various locations in the production region of the flow provide some information on how the turbulence is generated at the smallest scales first near the grid where the smallest wakes are dominant, followed by progressively smaller turbulent frequencies further downstream where progressively larger wakes interact. Keywords Turbulence · Direct numerical simulation · Immersed boundary method · Vortex dynamics S. Laizet (B ) · J. C. Vassilicos Department of Aeronautics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK e-mail: s.laizet@imperial.ac.uk J. C. Vassilicos e-mail: j.c.vassiliocs@imperial.ac.uk