Initial value problem for Rayleigh–Taylor instability of viscous fluids

1978 ◽  
Vol 21 (10) ◽  
pp. 1674 ◽  
Author(s):  
R. Menikoff ◽  
R. C. Mjolsness ◽  
D. H. Sharp ◽  
C. Zemach ◽  
B. J. Doyle
Keyword(s):  
Initial Value Problem ◽  
Taylor Instability ◽  
Viscous Fluids ◽  
Initial Value ◽  
Rayleigh Taylor Instability

Rayleigh–Taylor instability in a finite cylinder: linear stability analysis and long-time fingering solutions

2013 ◽  
Vol 734 ◽  
pp. 338-362 ◽  
Author(s):  
H. Sweeney ◽  
R. R. Kerswell ◽  
T. Mullin
Keyword(s):  
Density Ratio ◽  
Linear Instability ◽  
Taylor Instability ◽  
Viscous Fluids ◽  
Finite Cylinder ◽  
Dimensional Parameter ◽  
Instability Problem ◽  
Time Flow ◽  
Long Time ◽  
Rayleigh Taylor Instability

AbstractWe consider the Rayleigh–Taylor instability problem of two initially stationary immiscible viscous fluids positioned with the denser above the less dense in a finite circular cylinder, such that their starting fluid–fluid interface is the horizontal midplane of the cylinder. The ensuing linear instability problem has a five-dimensional parameter space – defined by the density ratio, the viscosity ratio, the cylinder aspect ratio, the surface tension between the fluids and the ratio of viscous to gravitational time scales – of which we explore only part, motivated by recent experiments where viscous fluids exchange in vertical tubes (Beckett et al., J. Fluid Mech., 2011, vol. 682, pp. 652–670). We find that for these experiments, the instability is invariably ‘side-by-side’ (of azimuthal wavenumber 1 type) but we also uncover parameter regions where the preferred instability is axisymmetric. The fact that both ‘core-annular’ (axisymmetric) and ‘side-by-side’ (asymmetric) long-time flows are seen experimentally highlights the fact that the initial Rayleigh–Taylor instability of the interface does not determine the long-time flow configuration in these situations. Finally, long-time flow solutions are presented on the basis that they will be slowly varying fingering solutions.

Sign in / Sign up

Export Citation Format

Share Document