UNSTEADY DRAG ON A CYLINDER DUE TO TRANSVERSE OSCILLATION AT FINITE AMPLITUDE

Transverse oscillations of a cylinder in a viscous fluid generate a force on the fluid that becomes non-linear at large oscillation amplitudes. When the cylinder motion is sinusoidal, non-linearity produces odd order harmonic distortion in the force. Numerical simulations based on the incompressible Navier–Stokes equations are used to explore (1) departures from linear theory and (2) the approach to quasi-steady behaviour, for oscillations over a wide frequency range at peak Reynolds numbers between 10−2and 10. Non-linearity appears once the displacement amplitude becomes comparable with the viscous penetration depth at the oscillation frequency. The results provide insight into the attenuation of sound in air-filled fibrous materials, where non-linear behaviour has been observed at sound pressure levels around 150 dB and upwards (see the paper by H.L. Kuntz and D.T. Blackstock 1987 Journal of the Acoustical Society of America81, 1723–1731 [3]).