On the use of biorthogonal interpolating wavelets for large-eddy simulation of turbulence

Recent work in the field of turbulence modelling has demonstrated the benefits of the wavelet-based multiresolution analysis technique as a tool for the formulation of the large-eddy simulation (LES) equations. In this formalism, the LES equations are obtained by projecting the Navier-Stokes equations onto a hierarchy of wavelet spaces. This paper investigates the use of biorthogonal interpolating wavelets as a basis for this projection, placing special emphasis on the wavelet-based differential operators that define this mapping. A detailed analysis of their convergence properties is presented and compared to those of their orthogonal counterpart, the Daubechies wavelets. Based on this study, we highlight the weaknesses of the unlifted interpolating wavelet representation for LES sub-grid modelling. Finally, we establish a link between the unlifted framework and the sampling-based LES approach recently proposed in the literature.