Spectral Analysis of the Energy Budget of Canopy Flows

To understand the turbulent kinetic energy production, transport, and dissipation in canopy flows, we perform a spectral analysis on the energy budget of canopy flows with a range of filament flexibilities.  Our simulation resolves the filaments in the canopy and solves the interaction between the flow and flexible filaments with an immersed boundary method, such that the dynamic deformation of the filaments can be captured and no prescribed drag coefficient is necessary.  We distinguish two scales that have significances in the energy budget: the monami scale related to the progressive waving of the canopy (also known as "monami" or "honami") and the wake scale related to the wake behind each filament.  We examine the waving term associated with the correlation between the fluctuations of canopy drag and velocity.  In a flexible canopy, this term transports turbulent kinetic energy from lower canopy to upper canopy at the monami scale, and serves as a main source of dispersive kinetic energy at the wake scale.  Moreover, this term transports energy to the wake scale from the larger scales, a phenomenon termed the energy shortcut mechanism in the literature (e.g. Kaimal and Finnigan, 1994; Finnigan, 2000).  This phenomenon does not occur in the inter-scale transport term associated with the nonlinear interaction of different flow scales.  Therefore, we conclude that the energy shortcut is mainly due to the waving term, not the inter-scale transport term.