Direct Numerical Simulations of a turbulent channel flow have been performed. The lower wall of the channel is made of staggered cubes with a second fluid locked in the cavities. Two viscosity ratios have been considered, m = µ 1 /µ 2 = 0.02 and 0.4 (the subscript 1 indicates the fluid in the cavity and 2 the overlying fluid) representing superhydrophobic surfaces (SHS) and liquid infused surfaces (LIS) respectively. A first set of simulations with a slippery interface has been performed and results agree well with those in literature for perfect slip conditions and Stokes approximations. To assess how the dynamics of the interface affects the drag, a second set of DNS has been carried out at W e = 100 and 1, 000 corresponding to W e + ≃ 10 −3 and 10 −2. The deformation of the interface is fully coupled to the Navier-Stokes equation and tracked in time using a Level Set Method. Two gas fractions, GF = 0.5 and 0.875, have been considered to assess how the spacing between the cubes affects the deformation of the interface and therefore the drag. For the dimensions of the substrate here considered, under the ideal assumption of flat interface, staggered cubes with GF = 0.875 provide about 20% drag reduction. However, a rapid degradation of the performances is observed when the dynamics of the interface is considered, and the same This work was supported under ONR MURI Grants N00014-12-0875 and N00014-12-1-0962, Program Manager Dr. Ki-Han Kim. Numerical simulations were performed on the Texas Advanced Computer Center.

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