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Dynamics of Slow and Fast Viscous Flows: Insights into Momentum Conservation and Turbulent Transition

This comprehensive study explores the behavior of viscous flows in various contexts, including slow flow in slots and pipes, oscillating flows, and fast flows around objects. Key topics include the conservation of momentum, the roles of inertia, pressure, and gravity, and the implications for phenomena like glacier movement, groundwater flow, sediment transport, and turbulent transitions. Additional insights are provided on unsteady viscous flows, wave dynamics, and the significance of boundary layers in different environments, enhancing understanding of fluid mechanics in natural and engineered systems.

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Dynamics of Slow and Fast Viscous Flows: Insights into Momentum Conservation and Turbulent Transition

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Presentation Transcript

  1. Introduction

  2. Conservation of momentum inertia pressure/gravity viscous

  3. Flows and force balances • 1. Slow flow in a slot • 2. Oscillating slow flow • 3. Small-amplitude waves • 4. Fast flow away from an object • 5. Fast flow near an object • a. inertia ~ pressure/gravity • b. viscous ~ inertia ~ pressure • c. viscous ~ inertia • d. viscous ~ pressure

  4. Viscous flow in a slot or pipe U Flow driven by a moving wall Flow driven by a pressure gradient

  5. Viscous slot flow: extensions Glacier movement Groundwater Flow in the mantle

  6. Viscous slot flow: extensions Particle settling Swimming of organisms Sediment transport

  7. Turbulent flow in a slot or pipe Transition to turbulence “Law of the wall”

  8. Turbulent pipe flow: extensions Open channel flow Glacier movement Municipal hydraulics Flow in vegetated channels

  9. Unsteady viscous flow U U Oscillating plate Impulsively started plate

  10. Unsteady viscous flow: extensions River mixing

  11. Waves Surface waves of small amplitude

  12. Waves: extensions Wave spectra Internal waves Solitary waves

  13. Boundary layers

  14. Boundary layers: extensions Gravity currents and salt wedges Biofilms Jets & plumes Diffusive BL in a lake

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