On the decomposition of turbulent flow fields for the analysis of coherent structures

Summary The decomposition of the turbulent velocity, pressure, and vorticity fields for the analysis of coherent structures is examined from a fundamental theoretical standpoint. It is shown that the commonly used double and triple decompositions yield coherent and incoherent parts of the turbulence that are not Galilean invariant and, consequently, severe doubts are raised concerning their general usefulness for the eduction of coherent structures. Alternative triple decompositions are proposed which are invariant under an arbitrary change of observer. Applications of this triple decomposition to the construction of helicity fluctuations which are more suitable for the study of coherent structures are also discussed.