  A methodology is developed to quantify the transfer and transport of kinetic
energy of specific scales associated with coherent structures. Coherent motions
are characterized by the triple decomposition of a multi-scale flow and used to
define mean, coherent, and random kinetic energy. Specific scales of individual
coherent structures are identified through mode decomposition, whereby the
total coherent velocity is separated into a set of velocities classified by the
scale of the mode based on frequency to embed spectral characteristics. The set
of scale-specific coherent velocities are used to identify scale-specific
coherent kinetic energy, which quantifies the kinetic energy of a specific
scale, and an equation for the balance of scale-specific coherent kinetic
energy. Each equation includes terms with velocity triads, which represent the
inter-scale transfer. The methodology is assessed in the wake behind a square
cylinder, where scales of the flow are related to the vortex shedding. The
scale-specific inter-scale transfer identifies that kinetic energy initially in
the near wake is transferred from vortex shedding to scales associated with
higher harmonics of the vortex shedding. In the far wake, inter-scale transfer
is homogeneous and transfer occurs over many frequencies. While the inter-scale
transfer is identified over a range of scales, the scale-specific transport,
convection, and dissipation of coherent kinetic energy are associated with only
the largest, dominant scales. The wake flow is subjected to unsteady inflow at
various frequencies to identify the changes to inter-scale transfer and
coherent kinetic energy induced by other frequencies.
