Abstract

We present an energy balance for the time-dependent scattering problem on a cascade of flat plates in uniform mean flow. The Kutta condition at the trailing edge leads to the appearance of a hydrodynamic mode which induces a wake downstream of the cascade. This set of vortex sheets support a jump in tangential velocity leading to a non-trivial contribution that must be accounted for when studying the fluctuating energy in the flow. In particular, the change of fluctuating energy is governed not only by acoustic power but also by the interface flux (arising from interaction terms of acoustic and hydrodynamic modes on the vortex sheets), which has been previously defined and studied by Crighton and Oswell and by Arzoumanian in the case of incompressible flow. We present numerical examples that demonstrate the importance of this term in the total power balance and show that its presence can explain perhaps surprising phenomena such as the increase of total sound power through the scattering process.