In recent years, nonlinear wake oscillator models have been shown to arise as a leading order approximation to the vortex shedding instability from a circular cylinder in a uniform flow (Alberéde and Monkewitz, 1992). Skop and Balasubramanian (1995) and Balasubramanian and Skop (1996) have extended the Van der Pol oscillator to model vortex shedding in non-uniform flow scenarios by introducing an axial diffusive coupling term in the equation. The results of their investigations have yielded a universal linear relationship between a turbulent kinematic viscosity that scales the diffusive coupling term and the shear parameter that quantifies the shear in the flow.
In this paper, following Skop and Balasubramanian (1997), we use the diffusively coupled Van der Pol oscillator as the governing equation for one component of the fluctuating lift force on the cylinder. The second component of the lift force is represented by a stall term which is linearly proportional to the transverse velocity of the cylinder. The coupled fluid-structural equations are employed to numerically simulate the response of a uniform pivoted cylinder in uniform and shear flow. The numerically predicted response amplitudes and bounds of lock-in are compared to available experimental results.