Unsteady drag on a cylinder due to transverse oscillation at finite amplitude

Transverse oscillations of a cylinder in a viscous fluid generate a force o n the fluid that becomes non-linear at large oscillation amplitudes. When t he 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 the ory and (2) the approach to quasi-steady behaviour, for oscillations over a wide frequency range at peak Reynolds numbers between 10(-2) and 10. Non-l inearity appears once the displacement amplitude becomes comparable with th e viscous penetration depth at the oscillation frequency. The results provi de insight into the attenuation of sound in air-filled fibrous materials, w here 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 J ournal of the Acoustical Society of America 81, 1723-1731 [3]). (C) 2001 Ac ademic Press.