Formation and evolution of target patterns in Cahn-Hilliard flows

Fan, Xiang; Diamond, P. H.; Chacòn, Luis

doi:10.1103/physreve.96.041101

Cited by 8 publications

(4 citation statements)

References 27 publications

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“…(iii) The dispersion relation of linear elastic wave in the CHNS system is similar to Alfvén wave in the MHD system 2,3 . However, the kinetic energy spectrum in the CHNS system is different from that in the MHD system.…”

Section: Basic Plasma Theorymentioning

confidence: 88%

Summary of the fundamental plasma physics session in the first AAPPS-DPP conference

Hao

Diamond

2019

Rev. Mod. Plasma Phys.

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Understanding of fundamental plasma physics contributes to progress in plasma science in many fields, such as magnetic confinement fusion, solar/space physics and application of plasma techniques. Intersecting common fundamental problems stimulate cross-fertilization of different topical areas. This paper summarizes highlights of progress reported in the Fundamental Plasma Physics Session of the 1st conference of Association of Asia Pacific Physical Societies-Division of plasma physics (AAPPS-DPP). Progress in the following fields is reviewed: (i) basic plasma theory; (ii) self-organization; (iii) reconnection and particle acceleration; (iv) magneto-hydrodynamics (MHD) instabilities and energetic particle physics; (v) magnetic confinement physics fundamentals; and (vi) exploiting fundamentals for performance.

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Section: Basic Plasma Theorymentioning

confidence: 88%

Summary of the fundamental plasma physics session in the first AAPPS-DPP conference

Hao

Diamond

2019

Rev. Mod. Plasma Phys.

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“…Indeed, the physics of the zonal flow scale are still unclear [10,22,23]. Staircases result from an inhomogeneous mixing process (as in potential vorticity homogenization), and are frequently linked to antidiffusion (as for the Cahn-Hilliard equation) [24][25][26] and self-sharpening of shears (as in jet formation) [27,28]. These processes play out in a variety of ways, in a wide variety of models.…”

Section: Introductionmentioning

confidence: 99%

Staircase formation by resonant and non-resonant transport of potential vorticity

Yan

Diamond²

2022

Nucl. Fusion

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The E×B staircase is a quasi-periodic pattern of pressure profile corrugations. In this work, we present a new mechanism for E×B staircase formation, that involves resonant transport verses non-resonant transport. We start from a potential vorticity evolution system and use quasi-linear theory, a model dispersion relation, and a bi-Lorentzian spectrum approximation, to construct the relation between the fluxes and the profiles. With these fluxes, we close the profile evolution equations and the extended turbulence intensity evolution equation, which together constitute a turbulence-profile evolution system. In this system, the Doppler effect from the E×B mean flow can cause resonance between trapped ion precession motion and the trapped ion mode, which drives a resonant transport contribution to the fluxes. The profiles will be flattened where the resonant transport is switched on. In contrast, for the regions of non-resonant transport, profiles are steeper. A quasi-periodic pattern of profile corrugation (the E×B staircase) spontaneously emerges in this system, which is the two states mentioned above, arranged as alternating layers in space. The feedback processes during the staircase pattern formation are identified. An estimate of the critical value of the boundary heat flux is obtained, above which staircase formation will be triggered. An estimate scaling of the step size in the staircase pattern is obtained. The resonant turbulent transport is also a mechanism for collisionless saturation of zonal flow. This work is related to internal transport barrier(ITB) formation and suggests some new scenarios, such as an enhanced confined L mode.

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“…We develop a natural, multiphase model for antibubbles and demonstrate how we can use direct numerical simulations (DNSs) to follow the spatiotemporal development of ephemeral, but beautiful, antibubbles. We show that the Cahn-Hilliard-Navier-Stokes (CHNS) equations, which have been used to study a variety of problems in binary-fluid flows [26][27][28][29][30][31][32][33][34][35], provide a minimal theoretical framework for studying the spatiotemporal evolution of antibubbles; in addition to a velocity field, the CHNS system employs a phase field φ that distinguishes between the two fluid phases. We use the CHNS equations [26,27,[29][30][31][32] to study antibubbles in twodimensions (2D) and in three dimensions (3D) by using extensive DNSs.…”

Section: Introductionmentioning

confidence: 99%

Ephemeral Antibubbles: Spatiotemporal Evolution from Direct Numerical Simulations

Pal¹,

Ramadugu²,

Perlekar³

et al. 2021

Preprint

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Antibubbles, which consist of a shell of a low-density fluid inside a high-density fluid, have several promising applications. We show, via extensive direct numerical simulations (DNSs), in both two and three dimensions (2D and 3D), that the spatiotemporal evolution of antibubbles can be described naturally by the coupled Cahn-Hilliard-Navier-Stokes (CHNS) equations for a binary fluid. Our DNSs capture elegantly the gravity-induced thinning and breakup of an antibubble via the time evolution of the Cahn-Hilliard scalar order parameter field φ, which varies continuously across interfaces, so we do not have to enforce complicated boundary conditions at the moving antibubble interfaces. To ensure that our results are robust, we supplement our CHNS simulations with sharpinterface Volume-of-Fluid (VoF) DNSs. We track the thickness of the antibubble and calculate the dependence of the lifetime of an antibubble on several parameters; we show that our DNS results agree with various experimental results; in particular, the velocity with which the arms of the antibubble retract after breakup scales as σ 1/2 , where σ is the surface tension.

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Formation and evolution of target patterns in Cahn-Hilliard flows

Cited by 8 publications

References 27 publications

Summary of the fundamental plasma physics session in the first AAPPS-DPP conference

Summary of the fundamental plasma physics session in the first AAPPS-DPP conference

Staircase formation by resonant and non-resonant transport of potential vorticity

Ephemeral Antibubbles: Spatiotemporal Evolution from Direct Numerical Simulations

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