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## 15. Physics of Sediment Transport William Wilcock (based in part on lectures by Jeff Parsons) Lecture/Lab Learning Goals Sediment Transport Definitions Sediment Settling

Burton, Jim, Founder and CEO has reference to this Academic Journal, PHwiki organized this Journal 15. Physics of Sediment Transport William Wilcock (based in part on lectures by Jeff Parsons) OCEAN/ESS 410 Lecture/Lab Learning Goals Know how sediments are characterized (size in addition to shape) Know the definitions of kinematic in addition to dynamic viscosity, eddy viscosity, in addition to specific gravity Underst in addition to Stokes settling in addition to its limitation in real sedimentary systems. Underst in addition to the structure of bottom boundary layers in addition to the equations that describe them Be able to interpret observations of current velocity in the bottom boundary layer in terms of whether sediments move in addition to if they move as bottom or suspended loads LAB Sediment Characterization There are number of ways to describe the size of sediment. One of the most popular is the scale. = -log2(D) D = diameter in millimeters. To get D from D = 2-

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Sediment Characterization Sediment grain smoothness Sediment grain shape – spherical, elongated or flattened Sediment sorting Sediment Transport Two important concepts Gravitational as long as ces – sediment settling out of suspension Current-generated bottom shear stresses – sediment transport in suspension or along the bottom (bedload) Shield stress – brings these concepts together empirically to tell us when in addition to how sediment transport occurs Definitions

1. Dynamic in addition to Kinematic Viscosity The Dynamic Viscosity is a measure of how much a fluid resists shear. It has units of kg m-1 s-1 The Kinematic viscosity is defined where f is the density of the fluid. has units of m2 s-1, the units of a diffusion coefficient. It measures how quickly velocity perturbations diffuse through the fluid 2. Molecular in addition to Eddy Kinematic Viscosities The molecular kinematic viscosity (usually referred to just as the kinematic viscosity), is an intrinsic property of the fluid in addition to is the appropriate property when the flow is laminar. It quantifies the diffusion of velocity through the collision of molecules. (It is what makes molasses viscous). The Eddy Kinematic Viscosity, e is a property of the flow in addition to is the appropriate viscosity when the flow is turbulent flow. It quantities the diffusion of velocity by the mixing of packets of fluid that occurs perpendicular to the mean flow when the flow is turbulent 3. Submerged Specific Gravity, R Typical values: Quartz = Kaolinite = 1.6 Magnetite = 4.1 Coal, Flocs < 1 f Sediment Settling Stokes settling Settling velocity (ws) from the balance of two as long as ces - gravitational (Fg) in addition to drag as long as ces (Fd) Settling Speed Balance of Forces Write balance using relationships on last slide k is a constant Use definitions of specific gravity, R in addition to kinematic viscosity k turns out to be 1/18 Limits of Stokes Settling Equation Assumes smooth spherical particles - rough particles settle more slowly Grain-grain interference - dense concentrations settle more slowly Flocculation - joining of small particles (especially clays) as a result of chemical in addition to /or biological processes - bigger diameter increases settling rate in addition to has a bigger effect than decrease in specific gravity as a result of voids in floc. Assumes laminar flow (ignores turbulence) Shear Stresses Bottom Boundary Layers Inner region is dominated by wall roughness in addition to viscosity Intermediate layer is both far from outer edge in addition to wall (log layer) Outer region is affected by the outer flow (or free surface) The layer (of thickness ) in which velocities change from zero at the boundary to a velocity that is unaffected by the boundary is likely the water depth as long as river flow. is a few tens of meters as long as currents at the seafloor Shear stress in a fluid = shear stress = = as long as ce area rate of change of momentum area Shear stresses at the seabed lead to sediment transport The inner region (viscous sublayer) Only ~ 1-5 mm thick In this layer the flow is laminar so the molecular kinematic viscosity must be used Un as long as tunately the inner layer it is too thin as long as practical field measurements to determine directly The log (turbulent intermediate) layer Generally from about 1-5 mm to 0.1 (a few meters) above bed Dominated by turbulent eddies Can be represented by: where e is turbulent eddy viscosity This layer is thick enough to make measurements in addition to as long as tunately the balance of as long as ces requires that the shear stresses are the same in this layer as in the inner region Shear velocity u Sediment dynamicists define a quantity known as the characteristic shear velocity, u The simplest model as long as the eddy viscosity is Pr in addition to tls model which states that Turbulent motions ( in addition to there as long as e e) are constrained to be proportional to the distance to the bed z, with the constant, , the von Karman constant which has a value of 0.4 Velocity distribution of natural (rough) boundary layers z0 is a constant of integration. It is sometimes called the roughness length because it is generally proportional to the particles that generate roughness of the bed (usually z0 = 30D) From the equations on the previous slide we get Integrating this yields What the log-layer actually looks like Plot ln(z) against the mean velocity u to estimate u in addition to then estimate the shear stress from Z0 lnz0 Slope = /u = 0.4/u Shields Stress When will transport occur in addition to by what mechanism Shields stress in addition to the critical shear stress The Shields stress, or Shields parameter, is: Shields (1936) first proposed an empirical relationship to find c, the critical Shields shear stress to induce motion, as a function of the particle Reynolds number, Rep = uD/ Shields curve (after Miller et al., 1977) - Based on empirical observations Sediment Transport No Transport Transitional Transitional

Initiation of Suspension Suspension Bedload No Transport If u > ws, (i.e., shear velocity > Stokes settling velocity) then material will be suspended. Transitional transport mechanism. Compare u in addition to ws

## Burton, Jim Founder and CEO

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