On the relation between the global modes and the spectra of drag and lift in periodic wake flows

In this Note we are interested in the relation between the symmetry properties of the global mode envelopes in wake flows and the spectra of the drag and lift forces. We consider the “impulse” formula for the hydrodynamic force and show that the drag force consists of contributions from the even harmonics, and the lift force of contributions from the odd harmonics, only. Our argument explains this well-known empirical fact and is also supported by the computational evidence we provide. Finally, we identify the unsteady wake flows, both controlled and uncontrolled, as belonging to a broader family of “streaming flows”.