Energy and Entropy in Turbulence Decompositions

The role of energy and entropy in the decomposition of turbulent velocity flow-fields is shown in this paper. Decomposition methods based on the energy concept are taken into account—proper orthogonal decomposition (POD) and its extension bi-orthogonal decomposition (BOD). The methods are well known; however, various versions are used and the interpretation of results is not straightforward. To make this clearer, the specific definition of modes is suggested and specified; moreover, energy- and entropy-motivated views on the decomposed modes are presented. This concept could offer new possibilities in the physical interpretation of modes and in reduced-order modeling (ROM) strategy efficiency evaluation.