Topological Analysis Provides Deeper Insight into Hydrodynamic Instabilities

The VACET group at Lawrence Livermore National Laboratory, led by Valerio Pascucci, has developed the first feature-based analysis of extremely high-resolution simulations of turbulent mixing. The focus is on Rayleigh-Taylor instabilities, which are created when a heavy fluid is placed above a light fluid and tiny vertical perturbations in the interface create a characteristic structure of rising bubbles and falling spikes. Rayleigh-Taylor instabilities have received much attention over the past half-century because of their importance in understanding many natural and man-made phenomena, ranging from the rate of formation of heavy elements in supernovae to the design of capsules for inertial confinement fusion. However, systematic, detailed analysis has been difficult due to the extremely complicated features found in the mixing region.

Members of VACET, the Visualization and Analytics Center for Enabling Technology funded under SciDAC, at Livermore developed a novel approach to the analysis of the complex topology of the Rayleigh-Taylor mixing layer based on robust Morse theoretical techniques. This approach systematically segments the envelope of the mixing interface into bubble structures and represents them with a new multi-resolution model allowing a multi-scale quantitative analysis of the rate of mixing based on bubble count. This analysis enabled new insights and deeper understanding of this fundamental phenomenon by highlighting and providing precise measures for four fundamental stages in the turbulent mixing process that scientists could previously only observe qualitatively.

This work has been documented in a paper named “best application paper” at the IEEE visualization conference and later presented at the International Workshop on the Physics of Compressible Turbulent Mixing. Follow-up work also allowed, for the first time, direct comparison of two simulations based on different physics models, grid point resolutions, and initial conditions. Although comparison by superposition of the simulations could not yield a meaningful result, the new topological approach highlighted fundamental similarities through a multi-scale feature-based comparison. This, in turn, validated the lower resolution large eddy simulation with respect to the higher resolution direct numerical simulation.