Analytical Correlations for Rayleigh-Taylor Instability Growth

Modifications of Rayleigh-Taylor instability growth by a gradual density increase instead of a step increase, finite fluid thickness, convection (or ablation), three-dimensional disturbances, nearby stable stratification or fixed boundaries, and nonlinear saturation are quantitatively assessed in typical model cases. To account for gradual density transitions, novel approximate but conservative correlations are given that can replace a hitherto widely used incorrect relation. The stabilizing effects of stable stratification, a fixed boundary (below), and a free surface (above) close to the instability zone are discussed in detail for the first time. For the effect of convection a new and simple derivation of Bodner’s formula is presented, which reveals that the formula describes a fictitious effect due to observation of the disturbance at a moving location. A half-analytical procedure is proposed that allows an account at the same time for several effects resulting from the actual density profile and the possible variations of this profile and its acceleration with time, for example, during ablative acceleration of thin foils.