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Sediment Transport Mechanics. Sediment is the currency of geomorphology – it is the building block of the landscape over a range of scales. Why do bedforms, like ripples, arise and what sets their spacing? Martian windstorms and abrasion of optical sensors.
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Sediment Transport Mechanics Sediment is the currency of geomorphology – it is the building block of the landscape over a range of scales. Why do bedforms, like ripples, arise and what sets their spacing? Martian windstorms and abrasion of optical sensors. Sediment transport problems have both deterministic (trajectory of a saltating grain) elements, which must be computed from first principles, and stochastic (impact splash pattern of bombarded grains) elements, for which we rely on statistical descriptions.
Bed Load vs. Suspended Load Show YouTube Video of Bed Load: http://www.youtube.com/watch?v=OAt-G5mIEZc&feature=BF&list=FLz2qNgPEmhpI&index=4
Grain Entrainment Entrainment of sediment is a thresholded problem. Forms the basis of the concept of transport competency. Not grain weight vs. lift force, but rather grain weight vs. drag force. Drag force, resulting from fluid moving past the grain, is responsible for torquing the grain out of its resting pocket and exposing more grain surface area to a swifter portion of the flow with a longer lever arm => a positive feedback kicks in directly after incipient grain motion and the process is irreversible.
Incipient Motion: Torque Balance on a Grain Occurs when: Torque tending to move the grain is the product of the drag force and the appropriate lever arm: Torque keeping a grain in place is the product of the buoyant weight of the particle and the lever arm about a point of contact:
Incipient Motion: Torque Balance on a Grain Setting these two torques equal, and rearranging yields:
Incipient Motion: Torque Balance on a Grain Need to fill in some details of this equation: Need the drag coefficient – recall at high Re: Need expressions for the lever arms: Need expression for the mean velocity. Obtain from Law of the Wall and the Mean Value Theorem: Lastly, we’ll assume that this bed of spherical grains makes:
Incipient Motion: Torque Balance on a Grain Plugging the details (Rg, Rd, U, ect.) into the torque balance, Leaves us with the following: Constants / geometric factors that depend on the grain's specific position in pocket can be subsumed into q: • Bed shear stress necessary to entrain sediment increases linearly with particle size. • Flow velocity required increase as a power law function of particle diameter (what’s the power?) • For k=0.4 and a=60o, q= 0.08. • Comparing with empirical data –plots on right.
Shields Parameter, q Question to you: Why might the empirically observed Shield’s parameter be less than the theoretically derived value of 0.08? Possible Reasons: The pocket geometry is highly simplified, so alpha values may be lower than 60 deg. But why would this not be cancelled out by alpha values greater than 60 deg? The Law of the Wall represents a time-averaged version of the turbulent velocity profile. Higher velocity bursts may kick in that positive feedback of grain entrainment at lower than expected values of the Shield’s parameter.
For small grain sizes, why does the Shield’s relationship break down? Particle-particle forces: Ratio of A/V gets large, so electrostatic forces dominate over gravitational forces. Linear relationship between critical entrainment stress and particle diameter breaks down; gravity is no longer dominant force to be exceeded by fluid drag. Platey shapes don't help. Flow within the boundary layer: Near flow base, velocity decreases (lowers Re) transition from turbulent to laminar flow. Hence, a viscous sublayer exists, within which small grains can hide from the turbulent bursts Net result is a trough in the entrainment diagram.
Observing Incipient Motion = Not so easy. http://www.youtube.com/watch?v=o3llzwvv1zc&NR=1
Suspended Sediment – Proglacial Kennicott River in full flood, near McCarthy Alaska.
Grain Approach - Saltation Trajectories By increasing the grain size, we decrease the variability in saltation path
Suspended Sediment – Continuum approach derivation – Definition sketch
