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Mixing-induced global modes in open active flow.

Arthur V Straube1, Arkady Pikovsky

  • 1Department of Physics, University of Potsdam, Am Neuen Palais 10, PF 601553, D-14415, Potsdam, Germany.

Physical Review Letters
|November 13, 2007
PubMed
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Local mixing can make a convectively unstable field absolutely unstable in open flows. This study analytically finds the transition point and critical exponent, confirmed by 2D simulations.

Area of Science:

  • Fluid dynamics
  • Instability phenomena
  • Nonlinear dynamics

Background:

  • Convective instability in open flows is common.
  • Understanding transitions to absolute instability is crucial for predicting system behavior.
  • Local mixing effects can significantly alter flow dynamics.

Purpose of the Study:

  • To investigate how local mixing transforms convective instability into absolute instability.
  • To analytically determine the transition point to an unstable global mode.
  • To characterize weakly nonlinear regimes beyond the instability threshold.

Main Methods:

  • Modeling the mixing region as having locally enhanced effective diffusion.
  • Analytical derivation of the linear transition point.

Related Experiment Videos

  • Derivation of the critical exponent for weakly nonlinear regimes.
  • Comparison with numerical simulations of a 2D flow problem.

    • Main Results:

    • Local mixing was shown to transition a convectively unstable field to absolute instability.
    • An analytical method was developed to find the transition point.
    • The critical exponent characterizing nonlinear regimes was derived.
    • Numerical simulations validated the analytical findings.

    Conclusions:

    • Local mixing is a key factor in the transition from convective to absolute instability.
    • The analytical framework provides accurate predictions for instability thresholds.
    • The study offers insights into the complex dynamics of unstable flows.