A first-passage-time problem for tracers in homogeneous and isotropic fluid turbulence

by Dhrubaditya Mitra

Wednesday 6 May 2020, 13:30 → 14:30 Europe/Stockholm

https://stockholmuniversity.zoom.us/j/530682073

https://arxiv.org/abs/2001.01260

We define a new first-passage-time problem for Lagrangian tracers that are advected by a statistically stationary, homogeneous, and isotropic turbulent flow: By direct numerical simulations of the three-dimensional (3D) incompressible, Navier-Stokes equation, we obtain the time tR at which a tracer, initially at the origin of a sphere of radius R, crosses the surface of the sphere \textit{for the first time}. We obtain the probability distribution function P(R,tR) and show that it displays two qualitatively different behaviors: (a) for R≪LI, P(tR) has a power-law tail ∼t−αR, with the exponent α=4 and LI the integral scale ; (b) for LI≲R, the tail of P(R,tR) decays exponentially. We develop models that allow us to obtain these asymptotic behaviors analytically.