Fiber Dynamics in Turbulent Flows: Specific Taylor Drag

Abstract

In [N. Marheineke and R. Wegener, SIAM J. Appl. Math., 66 (2006), pp. 1703–1726], an aerodynamic force concept for a general air drag model based on a stochastic k-$\epsilon$ description for a turbulent flow field is derived. The turbulence effects on the dynamics of a long, slender, elastic fiber are specifically modeled by a correlated random Gaussian force and in its asymptotic limit on a macroscopic fiber scale by Gaussian white noise with flow-dependent amplitude. The present paper states quantitative similarity estimates and numerical comparisons for the choice of a Taylor drag model in a given application.