Modal force partitioning – a method for determining the aerodynamic loads for decomposed flow modes with application to aeroacoustic noise

Aerodynamic loads play a central role in many fluid dynamics applications, and we present a method for identifying the structures (or modes) in a flow that make dominant contributions to the time-varying aerodynamic loads in a flow. The method results from the combination of the force partitioning method (Menon & Mittal, 2021, J. Fluid Mech. , vol. 907, A37) and modal decomposition techniques such as Reynolds decomposition, triple decomposition and proper orthogonal decomposition, and is applied here to three distinct flows – two-dimensional flows past a circular cylinder and an aerofoil, and the three-dimensional flow over a revolving rectangular wing. We show that the force partitioning method applied to modal decomposition of velocity fields results in complex, and difficult to interpret inter-modal interactions. We therefore propose and apply modal decomposition directly to the $Q$ -field associated with these flows. The variable $Q$ is a nonlinear observable that is typically used to identify vortices in a flow, and we find that the direct decomposition of $Q$ leads to results that are more amenable to interpretation. We also demonstrate that this modal force partitioning can be extended to provide insights into the far-field aeroacoustic loading noise of these flows.