The paper at hand presents a slender body theory for the dynamics of a curved inertial viscous Newtonian ber. Neglecting surface tension and temperature dependence, the ber ow is modeled as a three-dimensional free boundary value problem via instationary incompressible Navier-Stokes equations. From regular asymptotic expansions in powers of the slenderness parameter leading-order balance laws for mass (cross-section) and momentum are derived that combine the unrestricted motion of the ber center-line with the inner viscous transport. The physically reasonable form of the one-dimensional ber model results thereby from the introduction of the intrinsic velocity that characterizes the convective terms.
Part I: General Modeling Framework The paper at hand deals with the modeling of turbulence effects on the dynamics of a long slender elastic fiber. Independent of the choice of the drag model, a general aerodynamic force concept is derived on the basis of the velocity field for the randomly fluctuating component of the flow. Its construction as centered differentiable Gaussian field complies thereby with the requirements of the stochastic k-turbulence model and Kolmogorov’s universal equilibrium theory on local isotropy. Part II: Specific Taylor Drag In , an aerodynamic force concept for a general air drag model is derived on top of a stochastic k-epsilon description for a turbulent flow field. The turbulence effects on the dynamics of a long slender elastic fiber are particularly 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 paper at hand now presents quantitative similarity estimates and numerical comparisons for the concrete choice of a Taylor drag model in a given application.