Persistent Homology of Flows on Extrasolar Planets
Abstract
High-resolution simulations and observations generate copious amounts of high dimensional, large volume, heterogeneous datasets, which are increasingly difficult (if not prohibitive) for analysis by traditional (statistical, spectral, or graphical) methods alone. Persistent homology is a novel computational method for practically ascertaining the topological 'shape' of such data. Here the shape is characterized by tallying the number of connected elements and n-dimensional 'holes' (e.g., closed loops, three and higher dimensional voids, etc.), as well as 'coves' (depressions or protrusions on the holes), in the data. An example is the recent high-resolution, long-duration simulations of hot-Jupiter atmospheres that produce highly complex flow and temperature fields, containing up to many thousands of storms across a wide range of spatial and temporal scales. To clearly demonstrate the efficacy of the homology analysis method, we use it to analyze an idealized vortex model of these storms, focusing on the nonlinear evolution of such storms at the extremely high Reynolds number associated with planetary flows. Features, such as the number of storms and filaments around their periphery, their 'tubular' or 'blobby' morphologies, and periodic bursts of instability are captured and quantified. Understanding such features is crucial for validating theory and numerical models, as well as for interpreting and guiding observations. Broadly, homological analysis is a widely applicable tool that can help to directly address the large data problem faced in many areas.
- Publication:
-
AAS/Division for Extreme Solar Systems Abstracts
- Pub Date:
- August 2019
- Bibcode:
- 2019ESS.....433205S