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Linear stability analysis in a liquid layer with a surface velocity gradient.

Jarosław Białecki1, Janusz A Hołyst

  • 1Faculty of Physics and Center of Excellence for Complex Systems Research, Warsaw University of Technology, Koszykowa 75, PL-00-662 Warsaw, Poland. bialecki@if.pw.edu.pl

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
PubMed
Summary

This study generalizes combined planar Couette-Poiseuille flow by introducing a surface velocity gradient model. It derives a critical surface velocity gradient, revealing an infinite critical Reynolds number at this point.

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Area of Science:

  • Fluid dynamics
  • Hydrodynamic stability

Background:

  • Combined planar Couette-Poiseuille flow is a fundamental model in fluid dynamics.
  • Understanding the stability of such flows is crucial for various engineering applications.

Purpose of the Study:

  • To generalize the combined planar Couette-Poiseuille flow with vanishing horizontal flux.
  • To introduce and analyze a novel model for the surface velocity gradient.
  • To determine the critical conditions for flow stability.

Main Methods:

  • Derivation of a relation analogous to the Orr-Sommerfeld equation for the proposed model.
  • Calculation of the critical value for the surface velocity gradient.
  • Estimation of critical Reynolds number behavior near the critical point using approximation methods.

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Main Results:

  • A generalized model for combined planar Couette-Poiseuille flow was established.
  • The critical surface velocity gradient was determined.
  • An infinite critical Reynolds number was found to correspond to the critical point.
  • The behavior of the critical Reynolds number for slightly overcritical gradients was estimated.

Conclusions:

  • The introduced surface velocity gradient model provides a new perspective on flow stability.
  • The findings highlight the significant impact of surface conditions on hydrodynamic stability.
  • Further investigation into approximate methods can yield valuable insights into flow behavior near critical points.