The sustained R-T instability pattern is formed when the top fluid is heavier in the conventional problem. If the top fluid is lighter compared to the bottom one, is it correct to say that still R-T instability is formed but damped in very less time compared to the other case?
You might want to look at the following publication which you can download from Researchgate : Yiantsios and Higgins, "Rayleigh-Taylor instability in thin viscous films", Phys Fluids A 1, 1989. The instability mechanism, the role of the viscosity ratio for the two layers, and the fate of the instability e.g., formation of plumes is discussed in detail. But back to your question:
For two immiscible fluids, with constant surface tension, the fate of any disturbance is is going to be dictated by capillary forces ( capillary pressure gradients), viscous forces and gravitational body forces. If the lower fluid has a larger density, then any disturbance to the interface of an initial static system will eventually be damped out by capillary pressure. This is known as the leveling problem and the damping factor is controlled by both gravity and surface tension. If the base flow is in motion ( e.g., two layer flow down an incline plane), the interface may be come unstable, but now the instability mechanism is different as is related to the mismatch in viscosities, which generates a vorticity mismatch at the interface that results in traveling interfacial waves.
If the lower fluid has a smaller density and the system is initially static, now the interface may become unstable: it depends on the wavelength of the disturbance. For short wavelength disturbances capillary forces can damp out the waves and the system is stable. Of course in practice a disturbance typically has a spectrum of wavelengths and so the longer wavelengths ( which are unstable) are likely to dominate the dynamics. Check out the paper for more details.
In such configuration you can have instability instead of stability for accelerated moving system, with acceleration directed parallel to gravitational one and grater it a>g. Such a situation is analogical to weight loss in the lift going down with acceleration. Other factors such as velocity shear can also change growth rate. Look my paper in JGR, 1993, N 12.
Flowing fluid or fluid at rest may become unstable and undergo drastic changes to its flow characteristic or geometric configuration under the influence of small disturbances in some or all of the parameters associated with the fluid. The system consisting lighter fluid top of the heavier fluid is stable for all disturbances while the most unstable configuration of the two fluid interfaces is one in which heavy fluid on the top of lighter fluid.
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