Rayleigh–Taylor instability in two dimensions and phase-field method

Abstract

The Rayleigh–Taylor (RT) instability [1, 2] is a fluid-mixing mechanism occuring at the interface of two fluids of different densities, subjected to an external acceleration. The relevance of this mixing mechanism embraces many different phenomena occuring in completely different contexts (e.g., supernovae explosions [3] and solar flare formation [4]). In many of these situations the two fluids are immiscible owing to a non negligible surface tension. By means of Direct Numerical Simulations we investigate the immiscibile two-dimensional setting in the limit of small Atwood numbers. The surface tension introduces serious problems in numerical description: the interface is sharp and subject to morphological changes such as breakup, coalescence and reconnections (see Fig. 1). These obstacles can be overcome by using a phase-field description [5, 6]. We present an accurate numerical study that validates the phase-field method by testing known results of immiscibile RT instability both at level of linear and weakly nonlinear analysis.