Motion of a Thread in Compressible Turbulence

Particles that float on a turbulent tank of water form a system that is compressible in the two dimensions on which they move. Here we study, with an overhead camera, the snake-like motion of a 10 $\mu$m thread that floats on the surface. The thread, of length much greater than the integral scale $L_I$ of the underlying turbulence, cannot respond to the small-scale turbulent motions at the surface; its Young's modulus is too large. As a result, the mean curvature of the thread is of the order $1/L_I$. Measured properties include velocity structure functions of the thread $S_{n}(r)$ (including the third moment), the local curvature along the thread (a random variable), and ``Richardson diffusion'' of pairs of points along the thread separated by distances $r$. Supported by NSF Grant DMR 0604477 and the Okinawa Institute of Science Technology.