Asymptotic model-based estimation of a wake oscillator for a tethered sphere in uniform flow

We derive and investigate the nonlinear dynamics of a tethered sphere in uniform flow. A Lagrangian based model augmented by wake oscillators for the streamwise vertical and transverse directions enables model-based estimation of both structural and aeroelastic parameters via asymptotic analysis of internal resonance conditions between the transverse wake frequency and its structural counterpart. Validation of the proposed methodology is demonstrated by comparison of results with those of a benchmark experiment for a light sphere in water conducted by Govardhan and Williamson (1997) and by analysis of a spherical aerostat experiment conducted by Coulomb-Pontbriand and Nahon (2009). A numerical bifurcation analysis of the validated system reveals existence of possible quasiperiodic and non-stationary solutions that are consistent with documented instabilities of aerostats in severe environmental conditions and shed light on control mechanisms required for suppression of finite amplitude limit-cycle oscillations.