Nonlinear dynamics of two-dimensional undercompressive shocks

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)


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
Issue number1-4 SPEC. ISS.
Publication statusPublished - 2005 Sept 15
Externally publishedYes


  • Marangoni effect
  • Shocks
  • Thin films
  • Undercompressive shocks

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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