Theoretical aspects of transverse galloping

We investigate theoretical aspects of a reduced-order model for transverse galloping, which is derived directly from the full governing equations, i.e., the fluid mass and momentum balances, the fluid far-field boundary condition, the kinematic and dynamic conditions at the interface, and the bluff body equation of motion. We show that the presence of low-intensity turbulence and back-action from the slow transverse oscillations of the bluff body yield a correction to the hydrodynamic force of the quasi-steady theory in the form of additive random excitation. The reduced-order model consists of a pair of nonlinear Langevin equations for the amplitude and phase of the transverse motion of the bluff body. We show that while the phase dynamics is associated with a strongly diffusive random walk motion, the amplitude dynamics is associated with a relatively weak diffusion and can be mapped onto the motion of an overdamped particle trapped in a potential well. This mapping provides a highly useful tool for understanding both the deterministic (no random excitation) and the stochastic (weak random excitation) amplitude dynamics, and hence, for yielding theoretical insights on the overall system dynamics.