Sedimentology Flow and Sediment Transport (1) Reading Assignment: Boggs, Chapter 2

Key Concepts I.Earth surface transport systems II.Properties of water, air & ice III.Characterizing fluid flow IV.Grain entrainment V.Modes of grain movement VI.Sediment-gravity flows

Earth Surface Transport Systems Planet re-surfacing driven by tectonic, eustatic & climatic cycles Resultant redistribution of sediment is by surface transport systems Erosional landscapes Depositional landscapes Three sediment-transport systems Water Air Glacial ice There are also sediment-gravity flows where the fluid is NOT the primary transporter

Earth Surface Transport Systems Driving force Water: gravity-driven for most natural flows Air: usually pressure-driven (high to low pressure), but gravity-driven winds (e.g., katabatic) can be important Glacial ice: gravity-driven Sediment-gravity flow: gravity acting upon the body of sediment, the fluid acts more like pore fluid

Properties of Water, Air & Ice Water & Air are fluids. Fluids have no shear strength so that they deform with every increment of shear stress. Water is a liquid Air is a gas Glacial ice is a solid but it flows like a plastic & typically has a basal liquid surface Density (  M/V) Water: ~ 1 g/cm 3 or 1000 kg/m 3 Air: 1.29 kg/m 3 or ~ 1/800 as dense as water Ice: : 917 kg/m 3

Properties of Water, Air & Ice Dynamic or Absolute Viscosity  )  resistance of a fluid to deformation (flow) with applied shear stress; a measure of the internal friction of a fluid Units of stress/strain rate → Pa/(1/t) = Ns/m 2 = Pa s Air μ ~ Pa s Water (20°C) μ = Pa s Ice μ ~ Pa s Kinematic Viscosity 

Characterizing Fluid Flow = scale velocity= scale length Froude Number Reynolds Number

Laminar vs. Turbulent Flow In theory, Re <1 Laminar flow: stable to small disturbances – perturbations decay with time. Re >>> 1 Turbulent flow: unstable to small disturbances – perturbations grow with time. In nature you always have disturbances, question is when do they decay versus grow? Re < 500 laminar flow Re > 500 turbulent flow (dominant style for natural flows of water and air)

Velocity Profiles in Laminar Flow τ = μ(du/dy) τ is linear with y u is parabolic with y A relationship that can be calculated!

Velocity Profiles in Turbulent Flow – Not as Simple Because of the Nature of Turbulence Momentum transfer by turbulent eddies Law-of-the-Wall Equation u z = (u * /κ)(ln z/z o ) u * is shear or friction velocity (units of velocity) κ is von Karman’s constant (0.4) of mixing length z o is roughness height where u = 0

Comparison of Velocity Profiles

How Does Sediment Get Entrained? Force of gravity is holding grains to surface and there is friction between the grains Flowing fluid results in a drag force and lift force on the grains Grains are transported when combined fluid forces > forces holding grain to the surface

Complexities & Need to Simplify! Many grain factors influence how easily grains will be transported – grain density, size, shape, sorting, cohesion between grains, bed roughness,…… Stochastic nature of turbulence means spatial and temporal deviations from mean stress exerted on bed There is more organized turbulent structure caused by bed topography Impractical / impossible to do a grain-by-grain calculation of transport for natural beds

Some More Simplifications Basic questions How can sediment entrainment be related to easily measured flow parameters? How much of the sediment is moving as bedload vs. suspended load? Experiments provide the basis for a simplified route….

The Route: Step #1- Sediment Entrainment  b = boundary shear stress (force exerted upon sediment bed)  cr is the critical shear stress to move sediment, so that entrainment occurs when  b >  cr We need to know  cr for a bed of sediment  b needs to be related to the mean flow velocity u

Wiberg and Smith (1985)  cr has been determined experimentally for a wide range of sediment in Shield’s Diagram  cr is often presented in the dimensionless form  * =  cr /[(  s -  )gD]

Important definition: = Boundary shear stress = Shear velocity C d = hydraulic drag coefficient Boundary shear stress can be related to the mean flow velocity, by Relating  b to u Also,

The Route: Step #2 – Bedload vs. Suspended Load Ws = grain fall velocity, suspension occurs when upward component of fluid motion = downward pull of gravity Ws has been experimentally related to u*

W s calculated assuming: 1)density of quartz 2)Water temp = 20  C 3)Spheroid grain shapes 4)Subrounded grains Particle settles at constant speed when the gravitational force is exactly balanced by the sum of resistant forces This constant speed = settling velocity or fall velocity of the particle.

Key connections between solid and fluid phase Summary of Relationships Experimental Results: Pure Bedload:  b >  cr & w s /u * > 3 Suspension: w s /u * ≤ 1