Energy Transfer Mechanisms of Coherent Structures in Wakes via Mode Decomposition*

Instabilities and compact vorticity are induced in turbulent wakes, which give rise to multi-scale coherent structures.  The transfer of energy between turbulence scales plays a major role in coherent structure formation, evolution, and breakdown.  The evolution of kinetic energy associated with the coherent fluctuations of these features can be quantified through a triple decomposition of the velocity fluctuations.  A methodology is developed to quantify the transfer and transport of kinetic energy of individual coherent structure scales through mode decomposition, whereby the total coherent velocity is separated into a set of velocities classified on the scale of the mode.  A highly interconnected system of equations of scale-specific coherent kinetic energy is used to describe inter-scale transport, transfer of energy, and coherent structure contributions to dissipation and from production. The coherent kinetic energy and its budget produced by the flow around a square cylinder at low and high Reynolds numbers obtained from direct numerical simulations are detailed.  Dyadic and triadic interactions of modes that comprise terms in the coherent kinetic energy balance are explored, and interactions of turbulence scales are quantified.