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

Fingerprint

Thermal gradients
Nonlinear Dynamics
Shock
shock
Thin films
Experiments
Nonlocal Effects
Stability Theory
Linear Stability
Thin Films
Propagation
Gradient
Perturbation
perturbation
gradients
propagation
Experimental Results
thin films
Experiment
Simulation

Keywords

  • Marangoni effect
  • Shocks
  • Thin films
  • Undercompressive shocks

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

Nonlinear dynamics of two-dimensional undercompressive shocks. / Bowen, Mark; Sur, Jeanman; Bertozzi, Andrea L.; Behringer, Robert P.

In: Physica D: Nonlinear Phenomena, Vol. 209, No. 1-4 SPEC. ISS., 15.09.2005, p. 36-48.

Research output: Contribution to journalArticle

Bowen, Mark ; Sur, Jeanman ; Bertozzi, Andrea L. ; Behringer, Robert P. / Nonlinear dynamics of two-dimensional undercompressive shocks. In: Physica D: Nonlinear Phenomena. 2005 ; Vol. 209, No. 1-4 SPEC. ISS. pp. 36-48.
@article{4114d2343d844159a294bba24fa4b0ee,
title = "Nonlinear dynamics of two-dimensional undercompressive shocks",
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.",
keywords = "Marangoni effect, Shocks, Thin films, Undercompressive shocks",
author = "Mark Bowen and Jeanman Sur and Bertozzi, {Andrea L.} and Behringer, {Robert P.}",
year = "2005",
month = "9",
day = "15",
doi = "10.1016/j.physd.2005.06.011",
language = "English",
volume = "209",
pages = "36--48",
journal = "Physica D: Nonlinear Phenomena",
issn = "0167-2789",
publisher = "Elsevier",
number = "1-4 SPEC. ISS.",

}

TY - JOUR

T1 - Nonlinear dynamics of two-dimensional undercompressive shocks

AU - Bowen, Mark

AU - Sur, Jeanman

AU - Bertozzi, Andrea L.

AU - Behringer, Robert P.

PY - 2005/9/15

Y1 - 2005/9/15

N2 - 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.

AB - 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.

KW - Marangoni effect

KW - Shocks

KW - Thin films

KW - Undercompressive shocks

UR - http://www.scopus.com/inward/record.url?scp=24144498689&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=24144498689&partnerID=8YFLogxK

U2 - 10.1016/j.physd.2005.06.011

DO - 10.1016/j.physd.2005.06.011

M3 - Article

AN - SCOPUS:24144498689

VL - 209

SP - 36

EP - 48

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 1-4 SPEC. ISS.

ER -