9 th HSTAM International Congress on Mechanics Limassol, Cyprus, 12 – 14 July, 2010 MODELING THE STRUCTURE FUNCTIONS IN LINEARLY FORCED ISOTROPIC TURBULENCE E. Gravanis , E. Akylas , M.M. Fyrillas , D. Rousson and S.C. Kassinos 1 1 2 3 4 1 Department of Civil Engineering and Geomatics Cyprus University of Technology P.O.BOX 50329, 3603, Limassol, Cyprus e-mail: evangelos.akylas@cut.ac.cy 2 Department of Mechanical Engineering Frederick University 1303, Nicosia, Cyprus e-mail: m.fyrillas@frederick.ac.cy 3 Sandia National Laboratories, Livermore, CA 94550, United States e-mail: rouson@sandia.gov 4 Department of Mechanical and Manufacturing Engineering University of Cyprus P.O.BOX 20537, 1678 Nicosia, Cyprus e-mail: kassinos@ucy.ac.cy Keywords: Structure functions, Linear forcing, Isotropic turbulence, Karman-Howarth equation Abstract. The physics of the linear forcing of isotropic turbulence, allows for some useful estimates of the characteristic length scales of the turbulence produced during the statistically stationary phase. With such estimates we could practically define uniquely the stationary statistics by means of the box-size of the simulation, the linear forcing parameter and the viscosity of each case. We use such estimations in the Karman-Howarth equation and we solve it in terms of the second and third order structure functions using a generalized Oberlack- Peters closure scheme. The resulting forms and the respective spectra are in very good agreement with experimental and DNS data. 1 INTRODUCTION Numerical simulations of isotropic turbulence play a key role in studying basic features of turbulent flows. The two most frequently studied types of isotropic turbulence are freely decaying, and forced statistically stationary turbulence. For studies in which one wishes stationarity for statistical sampling, forced turbulence is preferable over decaying turbulence. In 2003, a very interesting paper by Lundgren proposed an alternative to the band-limited methods of forcing turbulence, using a linear forcing factor. Apart from its simplicity, the profound advantage of linear forcing is the possibility of applying this method in both physical and Fourier space. Problems that do not admit fully periodic boundary conditions, for instance simulating interactions of turbulence with combustion in which conditions upstream and downstream of the flame are inherently different, are often simulated using numerical codes formulated in physical space, such as finite differences. The application of band-limited forcing schemes requires knowledge of the wavenumbers and Fourier-transformed velocities, quantities that are not readily available in codes formulated in physical space. Rosales and Meneveau , in 2005, have shown that the application of linear forcing in both physical and spectral space renders practically equivalent results, reflecting the profound equivalence of the method in both spaces. Thus, the linear-forcing method opens wide opportunities for application in both physical and spectral space. Furthermore, the resemblance of the forcing parameter to an applied shear promises the achievement of stationary spectra, where the structure of the large scale is more realistic. In this direction, Ludgren showed that linear forcing produces statistics at scales between the integral scale and the inertial range (e.g. structure function curving) that resemble the curving observed from experimental data. In 2009, Akylas et al. continued the work of Rosales and Meneveau investigating the statistical stationarity that is produced by applying the linear forcing method in spectral space and quantifying the characteristic scales of the statistically stationary turbulence produced. Furthermore, they presented some arguments on the prediction of the stationary spectra and their importance in initializing linearly forced direct numerical simulations (DNS). [1] [2] [1] [3] [2] In this work we investigate the linearly forcing method through the Karman-Howarth equation in terms of the second and third order structure functions. More specifically, we solve numerically the stationary version using a generalized closure which is based on Oberlack and Peters model, and investigate the behavior of the [1,4] [5]