On the Differential Geometry of Particle Trajectories in Turbulence
Nordita Astrophysics seminars
Wednesday 12 March 2014
to 14:15 at
Dhrubaditya Mitra (Nordita)
We study intrinsic geometrical properties of trajectories of particles advected by a turbulent flow. The particles are inertial heavy particles, i.e., their sizes are much smaller than the scale of the smallest turbulent eddies (Kolmogorov scale) and the flow acts on them via Stokes drag law. From direct numerical simulations, we show that the PDF of the curvature of particle trajectories has a power-law tail, whose exponent is independent on the Stokes number of the particles and is approximately -2. We propose that the complexity of particle trajectories can be quantified by calculating the number of inflection point (points where the curvature changes sign) per unit time. We further show that the complexity decreases with the Stokes number as a power-law with an exponent approximately equal to 0.33.