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A methodology is developed to quantify the transfer and transport of kineticenergy of specific scales associated with coherent structures. Coherent motionsare characterized by the triple decomposition of a multi-scale flow and used todefine mean, coherent, and random kinetic energy. Specific scales of individualcoherent structures are identified through mode decomposition, whereby thetotal coherent velocity is separated into a set of velocities classified by thescale of the mode based on frequency to embed spectral characteristics. The setof scale-specific coherent velocities are used to identify scale-specificcoherent kinetic energy, which quantifies the kinetic energy of a specificscale, and an equation for the balance of scale-specific coherent kineticenergy. Each equation includes terms with velocity triads, which represent theinter-scale transfer. The methodology is assessed in the wake behind a squarecylinder, where scales of the flow are related to the vortex shedding. Thescale-specific inter-scale transfer identifies that kinetic energy initially inthe near wake is transferred from vortex shedding to scales associated withhigher harmonics of the vortex shedding. In the far wake, inter-scale transferis homogeneous and transfer occurs over many frequencies. While the inter-scaletransfer is identified over a range of scales, the scale-specific transport,convection, and dissipation of coherent kinetic energy are associated with onlythe largest, dominant scales. The wake flow is subjected to unsteady inflow atvarious frequencies to identify the changes to inter-scale transfer andcoherent kinetic energy induced by other frequencies.

A methodology to characterize the energy transfer and inter-scale transport of coherent structures using mode decomposition