A sufficient criterion for Rayleigh-Taylor instability of incompressible viscous three-layer flow
Abstract
Normal mode analysis was used to investigate Rayleigh-Taylor instability (RTI) for three-layer viscous stratified incompressible steady flow. When the top third and bottom first layers extend up to infinity, the middle layer has a small thickness delta. It is assumed that the wave Reynolds number is sufficiently small. A dispersion relation is obtained which is valid up to the order of the maximal value of all possible K exp j (j is less than or equal to 0, and K is the wave number). A sufficient condition for instability is found to depend on ratios alpha and beta of the coefficients of viscosity, delta, the surface tension ratio, and wave number. This new analytical criterion for RTI of three-layer fluids recovers the results of the corresponding problem for two-layer fluids.
- Publication:
-
International Journal of Engineering Science
- Pub Date:
- 1991
- Bibcode:
- 1991IJES...29.1439P
- Keywords:
-
- Flow Stability;
- Incompressible Flow;
- Stratified Flow;
- Taylor Instability;
- Viscous Flow;
- Boundary Layer Stability;
- Interfacial Tension;
- Numerical Analysis;
- Reynolds Number;
- Steady Flow;
- Viscosity;
- Wavelengths;
- Fluid Mechanics and Heat Transfer