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

Key Concepts Earth surface transport systems Properties of water, air & ice Characterizing fluid flow Grain entrainment Modes of grain movement 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 Note: In sediment-gravity flows, 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 (r = M/V) Water: ~ 1 g/cm3 or 1000 kg/m3 Air: 1.29 kg/m3 or ~ 1/800 as dense as water Ice: : 917 kg/m3

Properties of Water, Air & Ice Dynamic or Absolute Viscosity (m) - 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/m2 = Pa s Air μ ~ 10-5 Pa s Water (20°C) μ = 10-3 Pa s Ice μ ~ 1010 Pa s Kinematic Viscosity u = m/r

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

Characterizing Fluid Flow = scale velocity = scale length Fr <1 => subcritical flow Fr>1 => supercritical flow Froude Number Toss a pebble into flowing water… Do the expanding surface ripples travel upstream as well as downstream? If yes, then subcritical. … Tells us about whether a flow can transmit information upstream. Do the expand but all translate downstream? If yes, then supercritical Fr is a measure of inertia versus gravitational forces.

Characterizing Fluid Flow = scale velocity = scale length Re is measure of turbulence 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)

https://www.youtube.com/watch?v=XeURH6Tpaeg

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!

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

Comparison of Velocity Profiles

End of part 1

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 tb = boundary shear stress (force exerted upon sediment bed) tcr is the critical shear stress to move sediment, so that entrainment occurs when tb > tcr We need to know tcr for a bed of sediment tb needs to be related to the mean flow velocity u

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] u* is shear velocity, is a form by which a shear stress may be re-written in units of velocity. It is useful as a method in fluid mechanics to compare true velocities, such as the velocity of a flow in a stream, to a velocity that relates shear between layers of flow Wiberg and Smith (1985)

Relating tb to u Important definition: = Boundary shear stress = Shear velocity Boundary shear stress can be related to the mean flow velocity, <u> by Also, Cd = hydraulic drag coefficient

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*

Ws calculated assuming: density of quartz Water temp = 20C Spheroid grain shapes 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.

Summary of Relationships Key connections between solid and fluid phase Experimental Results: Pure Bedload: tb > tcr & ws/u* > 3 Suspension: ws/u* ≤ 1 Fully suspended: ws/u* ≤ 1

Modes of Grain Movement Bedload consists of creep and saltation

Bedload transport https://www.youtube.com/watch?v=O9GVRKnMch8&list=PL4BwvUWoIyLNgTjmUEacM9tPIgcKq7JWA&index=30

Bedload and suspended load: https://www. youtube. com/watch

Saltation in Air: Hop length and height can be 100-1000’s of grain diameters Saltation in Water: Hop Height < 10 particle diameters Hop Length <100 particle diameters In air or water saltation grain speed < fluid speed (but is greater in air). Why?

Suspended Sediment Load Concentration Profiles Concentration of suspended sediment near bed Grain trajectory Length >>> particle diameter Suspended Grain Velocity ≈ Fluid flow velocity.

Concentration Profiles of Suspended Load Volume of fluid >> volume of suspended sand – rarely more than a few percent When greater than 10% turbulence is completely damped (more on this in sediment gravity flows)

All Three Modes of Transport

All Three Modes of Transport

Sediment Discharge per Unit Width: s = average thickness of sediment transport layer <us> = average velocity of moving sediment <s> = average volume concentration of moving sediment z y Sediment discharge per unit width or Volume Flux of Sediment = [(V×<s> )×us]/A (units of Length2/Time)

Sediment-Gravity Flows Whole class of flow where sediment concentration is much higher than in fluid- gravity flows that are addressed above. Sediment/fluid form a single phase that gravity acts upon A range from dilute turbidity currents to debris flows Much more when we talk about slope and basin transport

Sediment gravity flow https://www.youtube.com/watch?v=4r9ndJ80_1Y&list=PL4BwvUWoIyLNgTjmUEacM9tPIgcKq7JWA&index=19

Questions You Should be Able to Answer What are the global-scale drivers that cause re-surfacing of the Earth’s surface? What are the roles of flowing water, air or ice in shaping the Earth’s surface? How are sediment-gravity flows different from fluid-gravity flows? What usually makes water flow, the wind blow and glaciers move? What is a fluid? What is different about the fluids water and air? What is density? What are the densities of water, wind and ice? Why does it matter in terms of sediment transport? What is dynamic viscosity? What does it measure? What is kinematic viscosity? What is the Froude Number? What is the Reynolds Number?

Questions You Should be Able to Answer 10. What is the difference between laminar and turbulent flow? How/why can these be characterized by the Reynolds Number? 11. What do flow pathlines look like in laminar and turbulent flow? 12. How do the velocity profiles in laminar and turbulent flow compare? 13. Why can the velocity profile in laminar flow be analytically calculated in laminar flow, but not in turbulent flow? 14. What is the Law-of-the-Wall? What does it do for you? 15. What are the forces acting upon grains subject to flowing fluid? 16. If we know the forces acting upon grains with fluid flow, why don’t we just directly calculate sediment transport? 17. What is the Hjulstrom Diagram? What does it show? Why are beds of clay harder to erode than beds of sand? 18. What is boundary shear stress? What is the critical shear stress to move sediment? How are these related to initiate sediment movement?

Questions You Should be Able to Answer 19. How has the critical shear stress to move sediment been determined? What is a Shield’s Diagram? What does it tell you about grain transport? 20. How is the boundary shear stress related to the mean flow velocity? 21. What is the grain fall or settling velocity? How is it determined? When does grain suspension occur? 22. Simplifications have been made to make it practical to calculate sediment transport for flowing fluids. What are the key connections that have been made? 23. Under what conditions of boundary shear stress and setting velocity does transport occur as pure bedload? 24. Under what condition of settling velocity does suspension occur? 25. What are the modes of grain movement? What are the components of bedload? 26. In typical suspended transport, where are most of the grains?

Questions You Should be Able to Answer 27. What concentration of suspended sediment might you expect in a flowing river? 28. How is total sediment discharge calculated? 29. What are examples of sediment-gravity flows? How are grain concentrations different in sediment-gravity flows than in fluid-gravity flows?