Variational Pattern Selection

TL;DR

This paper introduces a variational principle based on entropy maximization to address pattern selection in nonlinear interface dynamics, successfully applying it to Hele-Shaw cell problems and challenging the necessity of surface tension in such selections.

Contribution

It presents a novel variational approach to pattern selection that does not require surface tension, differing from traditional non-variational methods.

Findings

Results agree with experimental data

Universal fjord opening angle determined

Surface tension not necessary for pattern selection

Abstract

We address pattern selection problems in nonlinear interface dynamics by maximizing the entropy of the most probable (classical) scenario associated with the processes. This variational principle we applied to well-known selection problems in a Hele-Shaw cell: stationary Saffman-Taylor finger in a channel and self-similar finger in a wedge. The obtained results excellently agree with experiments. We also address the universal fjord opening angle. This principle complements a non-variational selection developed earlier. Surface tension is not needed for selection in both approaches, contrary to the common belief.