Two-dimensional Turbulence: Fluids, Polymeric Fluids, and Superfluids

by Rahul Pandit (Dept. of Physics, Indian Institute of Science, Bangalore)

Thursday 30 Aug 2012, 13:30 → 14:30 Europe/Stockholm

122:026 (Nordita Astrophysics Seminar Room)

We present an overview of our recent studies of two-dimensional turbulence. We provide, first, natural frameworks for studying (a) the persistence problem and (b) the dynamic multiscaling of vorticity structure functions in two-dimensional fluid turbulence; this part of our work uses Eulerian, Lagrangian, and Quasi-Lagrangian descriptions. We then show how to obtain such vorticity structure functions and persistence-time probability density functions from our extensive direct numerical simulations (DNSs) of the two-dimensional Navier-Stokes equation with air-drag-induced friction. Next we give the essential results of our state-of-the-art DNS of two-dimensional fluid turbulence with polymer additives; here we concentrate on dissipation reduction, the modification of the energy spectrum, and the suppression of small-scale structures by such additives. We end with our extensive DNS of Gross-Pitaevskii turbulence in the unforced, dissipationless, two-dimensional (2D) case. In particular, we explore the time evolution of different initial conditions (or initial states) to examine which statistical properties, e.g., energy and occupation spectra and order-parameter correlation functions, of the resulting solutions of the 2D GP equation, show universal features. The studies of fluid turbulence and fluid turbulence with polymer additives have been carried out with D. Mitra, P. Perlekar, S.S. Ray, and A. Gupta. The studies of Gross-Pitaevskii turbulence have been carried out with V. Shukla and M.-E Brachet.