Turbulence Appearance and Nonappearance in Thin Fluid Layers

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.