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approvedsherwood_2018.pdf2018-05-01 23:24:19Xiang Fan


Author: Xiang Fan
Requested Type: Poster
Submitted: 2018-03-01 19:23:23

Co-authors: P.H.Diamond, L.Chacon

Contact Info:
9500 Gilman Dr
San Diego, CA   92093

Abstract Text:
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 [1], as they both contain a vorticity equation and a “diffusion” equation. 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 $H^ψ_k$ scales as $k^{−7/3}$ in the elastic range. This suggests an inverse cascade of $H^ψ$. However, the kinetic energy spectrum $E^K_k$ 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 interfaces. Thus, as blob merger progresses, the packing fraction of interfaces decreases, thus explaining the weakened surface tension feedback and the outcome for $E^K_k$.

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. Target pattern is a meta stable state, since the band merger process continues on a time scale exponentially long relative to the eddy turnover time. Band merger resembles step merger in drift-ZF staircases.

[1] Phys. Rev. Fluids 1, 054403.