Data reduction in viscoelastic turbulent channel flows based on extended Karhunen–Loeve analysis

A previously attempted data reduction in turbulent viscoelastic channel flow [J. Non-Newton. Fluid Mech., 160 (2009) 55–63] used projections of the numerical velocity fields onto the most energetic, large scale, Karhunen–Loeve (K–L) modes of the fluctuating kinetic energy. However, the conformation field could not be adequately reproduced from the reduced velocity data when those were used in integrating the constitutive model (Giesekus) in a post-processing step. Here we investigate three different data reduction approaches in order to introduce small-scale information. Simultaneously, we also develop a novel formulation, which extends the K–L decomposition to more general objective functions. First, we use as a new objective function a weighted average of the pseudodissipation and the fluctuating kinetic energy. Second, we use the enstrophy. Third, we use the standard K–L approach, but this time in the reconstruction stage of the conformation tensor, we compensate for the loss of information of the flow deformation by suitably rescaling the Weissenberg number. It is shown that, whereas the first two methods fail to give any improvement over the classical K–L approach, the conformation field can be reconstructed fairly accurately using the third.