Numerical study on the detailed nonlinear dynamics of a single-mode Rayleigh–Taylor instability

For a horizontal gas layer overlaid by a liquid layer under gravity, round-ended air columns penetrate into the liquid at a constant velocity. This classical problem is revisited to gain new physical insight into the counter problem of liquid atomization by a Rayleigh–Taylor (RT) instability from an outward moving liquid layer undergoing deceleration. In this case, the constant descent velocity of the trough surface leads to a steady liquid atomization rate. Analyses of the present two-dimensional calculation results revealed two key mechanisms underlying the steadiness: (1) the bulk liquid layer was dynamically freed from the long liquid ligament (jet) by the formation of a maximum pressure point at the ligament root, and (2) the inertial force was only effective at the ligament root region to drive outward the liquid concentrating from the trough portion. Analytical expressions were derived for characteristic surface deformation quantities. The velocity and width of the liquid entering the freed liquid jet at the maximum pressure location mirrored those associated with a vertical jet emanating downwards from an orifice injector under gravity. Thus, the results from laboratory low-speed jet emanation experiments were useful to predict the disintegration behavior of a liquid jet formed by an RT instability.