The inviscid Euler limit as a critical boundary for moment-based aerodynamic system identification

Finite-dimensional state-space representations of unsteady aerodynamics implicitly assume a system with fading memory. However, the impulse response of the two-dimensional inviscid (Euler) equations is characterized by an asymptotic $t^{-3/2}$ power-law decay due to the persistence of shed vorticity. The present work demonstrates that this decay rate constitutes a critical boundary for moment convergence: the second temporal moment diverges logarithmically, causing the characteristic memory time to grow as $\sqrt{\ln T}$ with the observation window $T$. As a result, no window-independent characteristic time scale exists, and finite-dimensional models fitted to inviscid data effectively parameterize the observation horizon rather than intrinsic flow physics. To quantify this behavior, a temporal-moment diagnostic, $\nu_t(T)$, is introduced based on the ratio of the second and zeroth windowed moments of the impulse response kernel. Exponential models exhibit stable memory time plateaus, as their sufficiently fast decay ensures convergence of the moment diagnostic. Compressible Euler simulation results confirm the predicted $\sqrt{\ln T}$ scaling at intermediate times, while numerical dissipation inherent to the discretization acts as an artificial regularizer that enforces convergence at late times. These results establish the two-dimensional inviscid limit as a critical boundary for moment-based system identification, where the absence of a dissipative mechanism prevents the definition of a window-independent characteristic memory time.