A Methodology to Quantify Interscale Energy Transfer at Solid Boundaries

Abstract

Far away from solid boundaries, energy can be transferred between different flow scales due to the non-linear self-advection of velocity. This energy transfer can be quantified using well-established Fourier diagnostics or filtering methods. However, these diagnostic tools fail to provide a physical representation of the linear energy transfer that may occur during the formation of oceanic boundary layers or Rossby wave reflections. In this document, I outline a novel filtering methodology that is able to quantify this linear energy transfer by combining coarse-graining with volume-penalization. Its utility is illustrated by quantifying the down-scale energy transfer occuring during a Rossby wave reflection off a western boundary. The conceptual framework developed here is thought to be broadly applicable to the study of multi-scale energetics of bounded geophysical fluid flows.