The motion of a single bubble or spike in Rayleigh-Taylor unstable interfaces

Abstract The Rayleigh-Taylor instability in single-bubble systems has been studied by applying the front tracking method to the full two-dimensional Euler equations. The development of the instability is characterized by the penetration of the light (heavy) fluid into the heavy (light) fluid. A dynamic equation is proposed to model such penetrations. Extensive numerical simulations show good aggeement between the analytic results of the dynamical model and the numerical solutions of the full Euler equations. The dependence of the characteristic physical parameters at each development stage of the instability on the density and compressibility of fluids are established for the parameter range studied. The distribution of fluid density has a significant influence on the dynamic behavior of the systems. An exponentially stratified density distribution produces a dramatic effect on the penetration of light fluid into heavy fluid at late times. The proposed dynamic model plays an important rule in the study of chaotic flow in multibubble systems.

[1]  James Glimm,et al.  Subgrid resolution of fluid discontinuities, II , 1980 .

[2]  G. Taylor.  The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[3]  David H. Sharp,et al.  Front Tracking Applied to Rayleigh–Taylor Instability , 1986 .

[4]  Garrett Birkhoff,et al.  RISING PLANE BUBBLES , 1957 .

[5]  André Vanderbauwhede,et al.  Local bifurcation and symmetry , 1982 .

[6]  Sharp,et al.  Chaotic mixing as a renormalization-group fixed point. , 1990, Physical review letters.

[7]  Steven A. Orszag,et al.  Nonlinear effects of multifrequency hydrodynamic instabilities on ablatively accelerated thin shells , 1982 .

[8]  R. Seydel.  Numerical computation of branch points in nonlinear equations , 1979 .

[9]  G. Tryggvason.  Numerical simulations of the Rayleigh-Taylor instability , 1988 .

[10]  David L. Book,et al.  Effect of compressibility on the Rayleigh–Taylor instability , 1983 .

[11]  K. I. Read,et al.  Experimental investigation of turbulent mixing by Rayleigh-Taylor instability , 1984 .

[12]  P. R. Garabedian,et al.  On steady-state bubbles generated by Taylor instability , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[13]  M. Dellnitz,et al.  Computational methods for bifurcation problems with symmetries—with special attention to steady state and Hopf bifurcation points , 1989 .

[14]  H. W. Emmons,et al.  Taylor instability of finite surface waves , 1960, Journal of Fluid Mechanics.

[15]  Jean-Pierre Serre,et al.  Linear representations of finite groups , 1977, Graduate texts in mathematics.

[16]  I. Prigogine,et al.  Symmetry Breaking Instabilities in Dissipative Systems. II , 1968 .

[17]  Qiang Zhang,et al.  Validation of the chaotic mixing renormalization group fixed point , 1990 .

[18]  D. Youngs,et al.  Numerical simulation of turbulent mixing by Rayleigh-Taylor instability , 1984 .

[19]  D. Sharp.  An overview of Rayleigh-Taylor instability☆ , 1984 .

[20]  Oliver A. McBryan,et al.  A computational model for interfaces , 1985 .

[21]  David H. Sharp,et al.  The dynamics of bubble growth for Rayleigh-Taylor unstable interfaces , 1987 .

[22]  Steven A. Orszag,et al.  Vortex simulations of the Rayleigh–Taylor instability , 1980 .

[23]  Juan A. Zufiria,et al.  Bubble competition in Rayleigh–Taylor instability , 1988 .

[24]  James Glimm,et al.  Front tracking for hyperbolic systems , 1981 .

[25]  Walter Knödel,et al.  Graphentheoretische Methoden und ihre Anwendungen , 1969 .

[26]  Ralph Menikoff,et al.  Rayleigh--Taylor instability and the use of conformal maps for ideal fluid flow , 1983 .

[27]  Qiang Zhang,et al.  A numerical study of bubble interactions in Rayleigh–Taylor instability for compressible fluids , 1990 .