Weakly nonlinear incompressible Rayleigh-Taylor instability growth at cylindrically convergent interfaces

Journal Article · Mon Apr 15 04:00:00 EDT 2013 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4803067· OSTI ID:22130459

Wang, L. F.; He, X. T. ^[1]; Wu, J. F.; Zhang, W. Y. ^[1]; Ye, W. H. ^[1]

---

1. Institute of Applied Physics and Computational Mathematics, Beijing 100094 (China)

A weakly nonlinear (WN) model has been developed for the incompressible Rayleigh-Taylor instability (RTI) in cylindrical geometry. The transition from linear to nonlinear growth is analytically investigated via a third-order solutions for the cylindrical RTI initiated by a single-mode velocity perturbation. The third-order solutions can depict the early stage of the interface asymmetry due to the bubble-spike formation, as well as the saturation of the linear (exponential) growth of the fundamental mode. The WN results in planar RTI [Wang et al., Phys. Plasmas 19, 112706 (2012)] are recovered in the limit of high-mode number perturbations. The difference between the WN growth of the RTI in cylindrical geometry and in planar geometry is discussed. It is found that the interface of the inward (outward) development spike/bubble is extruded (stretched) by the additional inertial force in cylindrical geometry compared with that in planar geometry. For interfaces with small density ratios, the inward growth bubble can grow fast than the outward growth spike in cylindrical RTI. Moreover, a reduced formula is proposed to describe the WN growth of the RTI in cylindrical geometry with an acceptable precision, especially for small-amplitude perturbations. Using the reduced formula, the nonlinear saturation amplitude of the fundamental mode and the phases of the Fourier harmonics are studied. Thus, it should be included in applications where converging geometry effects play an important role, such as the supernova explosions and inertial confinement fusion implosions.

• OSTI ID: 22130459
• Journal Information: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 4 Vol. 20; ISSN PHPAEN; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
BUBBLES
COMPARATIVE EVALUATIONS
CYLINDRICAL CONFIGURATION
DENSITY
EXPLOSIONS
GEOMETRY
INERTIAL CONFINEMENT
INTERFACES
NONLINEAR PROBLEMS
PLASMA
RAYLEIGH-TAYLOR INSTABILITY
VELOCITY