Author: Xiang Fan
Requested Type: Pre-Selected Invited
Submitted: 2017-03-14 20:09:55
Co-authors: P.H.Diamond, L.Chacon
University of California, San Diego
9263 Regents Rd Unit 309
La Jolla, CA 92037
Concerns central to understanding turbulence and transport include: 1) Dynamics of dual cascades in EM turbulence; 2) Understanding ‘negative viscosity phenomena’ in drift-ZF systems; 3) The physics of blobby turbulence (re: SOL). Here, we present a study of a simple model – that of Cahn-Hilliard Navier-Stokes (CHNS) Turbulence – which sheds important new light on these issues.
The CHNS equations describe the motion of binary fluid undergoing a second order phase transition and separation called spinodal decomposition. The CHNS system and 2D MHD are analogous , as they both contain a vorticity equation and a “diffusion” equation for an active scalar. The CHNS system differs from 2D MHD by the appearance of negative diffusivity, and a nonlinear dissipative flux. An analogue of the Alfven wave exists in the 2D CHNS system.
DNS shows that mean square concentration spectrum Hψ_k scales as k^−7/3 in the elastic range. This suggests an inverse cascade of Hψ. Also we observe a concentration blob scale evolution in time of l~t2/3. However, the kinetic energy spectrum EK_k scales as k^−3, as in the direct enstrophy cascade range for a 2D fluid (not MHD!). The resolution is that the feedback of capillarity acts only at blob boundaries. Thus, as blob merger progresses, the packing fraction of interfaces decreases, thus explaining the weakened surface tension feedback and the outcome for EK_k.
We also examine the evolution of scalar concentration in a single eddy in the Cahn-Hilliard system. This extends the classic problem of flux expulsion in 2D MHD. The simulation results show that a target pattern is formed during the early stage, and the bands align with the stream lines. The results indicate that the target pattern is a meta stable state, since the band merger occurs on a time scale much longer than the dissipation time. Band merger is similar to step merger in drift-ZF staircases.
 Phys. Rev. Fluids 1, 054403.