Nonlinear dynamics of two-dimensional undercompressive shocks

Mark Bowen, Jeanman Sur, Andrea L. Bertozzi, Robert P. Behringer

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

We consider the problem of a thin film driven by a thermal gradient with an opposing gravitational force. Under appropriate conditions, an advancing film front develops a leading undercompressive shock followed by a trailing compressive shock. Here, we investigate the nonlinear dynamics of these shock structures that describe a surprisingly stable advancing front. We compare two-dimensional simulations with linear stability theory, shock theory, and experimental results. The theory/experiment considers the propagation of information through the undercompressive shock towards the trailing compressive shock. We show that a local perturbation interacting with the undercompressive shock leads to nonlocal effects at the compressive shock.

Original languageEnglish
Pages (from-to)36-48
Number of pages13
JournalPhysica D: Nonlinear Phenomena
Volume209
Issue number1-4 SPEC. ISS.
DOIs
Publication statusPublished - 2005 Sep 15
Externally publishedYes

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Keywords

  • Marangoni effect
  • Shocks
  • Thin films
  • Undercompressive shocks

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

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