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Time-dependent rotating stratified shear flow: exact solution and stability analysis.

A Salhi1, C Cambon

  • 1Département de Physique, Faculté des Sciences de Tunis, 1060, Tunis, Tunisia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 16, 2007
PubMed
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This study analyzes fluid dynamics instabilities in stratified shear flows. Even with stabilizing vertical stratification, time-varying horizontal density gradients and shear rates can cause parametric resonance and flow instability.

Area of Science:

  • Fluid dynamics
  • Geophysical fluid dynamics
  • Stratified flows

Background:

  • The Euler equations with Boussinesq approximation model fluid motion.
  • Spatially uniform density stratification and time-dependent shear flows are common in geophysical systems.
  • Understanding flow stability is crucial for predicting oceanic and atmospheric phenomena.

Purpose of the Study:

  • To derive and analyze a solution for the Euler equations with Boussinesq approximation.
  • To investigate the stability of unbounded flows with vertical and horizontal density stratification and time-dependent shear.
  • To explore the role of Coriolis effects and parametric resonance in flow instability.

Main Methods:

  • Derivation of a base flow solution for the Euler equations with Boussinesq approximation.

Related Experiment Videos

  • Stability analysis of the derived base flow subjected to disturbances.
  • Examination of parametric resonance using dispersion relations.
  • Inclusion of Coriolis effects and dimensionless parameters like Richardson number and f(v).

    • Main Results:

    • A base flow with vertical and horizontal density stratification and time-dependent shear is established.
    • The flow is shown to be unstable to certain disturbances, amplified by a Floquet mechanism, even with stabilizing vertical stratification.
    • Parametric resonance between inertia-gravity waves and oscillating shear is demonstrated in the limit of a modified Richardson number approaching zero.
    • The parametric instability is linked to baroclinic and elliptical flow instabilities.

    Conclusions:

    • Time-varying horizontal density gradients and shear rates can destabilize stratified flows.
    • Floquet mechanism and parametric resonance are key drivers of instability in these systems.
    • The findings have implications for understanding complex instabilities in geophysical fluid flows.