7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Elastic and Binary-fluid Turbulence: An overview
Rahul Pandit1
1Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science,
Bangalore 560012, Indiae-mail (speaker): rahul@iisc.ac.in
This talk will begin with a summary of what we know
about elastic turbulence in fluids with polymer additives.
It will then (a) elucidate the analogue of such turbulencein binary-fluid mixtures and (b) explore the relations of
this turbulence with two-dimensional (2D)
magnetohydrodynamic (MHD) turbulence. This talk will
be based principally on work from our group on
turbulence in fluids with polymer additives and in multiphase flows [see, e.g., Refs. (1-4)] and it will build on thestudies of Refs. (5-8) to explore relations with 2D MHD.
We will use the paradigm of the turbulence-induced
melting of a nonequilibrium vortex crystal [Ref. (9)]to examine elastic turbulence and its analogues in thesystems mentioned above.
For example, for the case of elastic turbulence in a fluidwith polymer additives, we will summarise the results ofour direct numerical simulations (DNSs) of the forced,incompressible two-dimensional Navier-Stokes equation
coupled with the FENE-P equations for the polymerconformation tensor [Ref. (2)]: The forcing in this DNS
is such that, without polymers and at low Reynolds
numbers Re, the film attains a nonequilibrium steadystate with a cellular flow that comprises a square latticeof vortices and antivortices. An increase in theWeissenberg number Wi, leads to nonequilibrium phasetransitions, to spatially distorted, but temporally steady,crystals, then to crystals that oscillate in time
(periodically, at low Wi, and quasiperiodically, as Wi isenhanced), until spatiotemporal chaos and elastic
turbulence set in.
We will then examine the binary-fluid generalizations[Ref. (4)] of the melting of such cellular flows in fluids[Ref. (9)] and 2D MHD [Refs. (5-8)]. In particular, wewill characterize (a) the emergent spatiotemporal chaos
in low-Re binary-fluid mixtures, (b) their energy spectra,
which exhibit broad power-law regimes, as inconventional fluid turbulence, and (c) mixing properties
by using Lagrangian-tracer statistics (specifically, we will
demonstrate that the mean-square-displacement (MSD)of tracer trajectories displays long-time diffusive
behaviour).
References:
1. N. Pal, P. Perlekar, A. Gupta, and R. Pandit, Binaryfluid turbulence: Signatures of multifractal droplet
dynamics and dissipation reduction, Phys. Rev. E,
93:063115, (2016).

2. A. Gupta and R. Pandit, Melting of a nonequilibrium
vortex crystal in a fluid film with polymers: Elasticversus fluid turbulence, Phys. Rev. E, 95:033119, (2017).
3. N. Pal, R. Ramadugu, P. Perlekar, and R. Pandit,
Ephemeral Antibubbles: Spatiotemporal Evolution from
Direct Numerical Simulations, Physical Review Research
4, 043128 (2022).
4. N.B. Padhan, D. Vincenzi, and R. Pandit, Emergent
spatiotemporal chaos in low-Reynolds-number binaryfluid mixtures (in preparation).
5. X. Fan, P.H. Diamond, L. Chacon, and H. Li, Phys.
Rev. Fluids 1, 054403 (2016).
6. X. Fan, P.H. Diamond, and L. Chacon, Phys. Rev. E,96, 041101(R) (2017).
7. X. Fan, P.H. Diamond, and L. Chacon, Phys. Rev. E,99, 041201(R) (2019).
8. F.R. Ramirez and P.H. Diamond, Staircase Resiliency
in a Fluctuating Cellular Array, preprint (privatecommunication).
9. P. Perlekar and R. Pandit, Turbulence-induced melting
of a nonequilibrium vortex crystal in a forced thin fluid
film, New Journal of Physics, 12, 023033 (2010).