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Area of Science:

  • Fluid Dynamics
  • Turbulence Theory
  • Geophysics and Astrophysics

Background:

  • Thin fluid layers exhibit two-dimensional flows with bottom friction, common in industrial and natural phenomena.
  • The driving mechanism significantly influences the stability and behavior of these large-scale flows.

Purpose of the Study:

  • To investigate the contrasting turbulence sustentation capabilities of wall-driven (Couette) and pressure-driven (Poiseuille) flows.
  • To characterize the emergent flow structures and scaling laws in thin fluid layers under different driving conditions.

Main Methods:

  • Direct numerical simulations (DNS) were employed to analyze flow behavior up to a Reynolds number (Re) of 10^6.
  • Perturbation analysis was used to determine flow stability under varying viscosity and friction parameters.

Main Results:

  • Plane Couette flow was found to be unable to sustain turbulence, with all perturbations decaying.
  • Poiseuille flow, under specific conditions, transitions from laminar to a turbulent state characterized by traveling waves, jets, and wall vortices.
  • A new scaling law for the Reynolds number dependence of the friction factor was derived and validated by DNS.

Conclusions:

  • The method of driving a fluid layer fundamentally dictates its turbulent potential and resulting flow structures.
  • Traveling waves represent a stable, albeit complex, state in pressure-driven thin-layer flows, even at high Reynolds numbers.
  • The derived scaling law provides a novel predictive tool for friction factor behavior in such systems.