Energy analysis of turbulent channel flow using biorthogonal wavelets

Turbulent flows exhibit many different length and time scales. Hence, it is important to study energy transfer between the scales, in order to gain deeper insight into turbulence. Wavelets offer potential for the analysis of the energy transfer in a turbulent flow. This is mainly due to their locality and scalability property. The present work involves a wavelet decomposition of the terms in the turbulent kinetic energy transport equation of a fully developed channel flow and a study of the behavior of the important terms. A detailed analysis of the energy transfer term is performed. An attempt is made to identify some well-known structures in the flow at different scales of decomposition. The dynamics of these coherent structures is examined based on their contribution to energy transfer in the flow at discrete scales. This is performed by correlating the velocity and energy transfer in the flow. To analyze energy transfer due to spatial structures, we utilize the concept of “triad interaction” in wavelet space. The study involves computing all possible combinations of wavelet modes and finding the most energetic ones. We investigate these interactions to capture the dynamics of the local structures and their contribution to the energy transfer.