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Problems with using Sediment Grain Size Alone. Shape can affect grain-fluid interactions, but… shape is very difficult to quantify, making it problematic to account for in a mathematical relationship. Particle density – this we can deal with – today’s lecture. - PowerPoint PPT Presentation
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Problems with using Sediment Grain Size Alone
Shape can affect grain-fluid interactions, but… shape is very difficult to quantify, making it problematic to account for in a mathematical relationship.
Particle density – this we can deal with – today’s lecture
Sediment Grain Size - Settling Velocity
Steps in the Derivation of Stokes’ Law (on blackboard)
1. Downward directed grav. Force
2. Balanced by upward directed drag force
3. CTSV - no acceleration, so by Newton’s 2nd - the sum of the forces must =0.
4. Equate the Forces, solve for velocity.
5. Identify relationship for drag coefficient as a fcn. of Re?
6. We’re there...
CD = f(Re)
Why use settling velocity?
Valuable predictor of entrainment/suspension in the surf zone
Bagnold’s concept of autosuspension - if settling velocity (ws) was less than product of swash velocity (u) and beach slope (S), then settling would never occur. (see p. 55 in Komar):
And since orbital (swash) velocity, is proportional to wave height (H) and inversely proportional to wave period (T):
Dean number, considers suspension height and wave period.
€
ws < uS
€
ws <πHS
T
€
ws <δh
T
Example
Consider a beach with an average slope of 3˚ (S = ?), an orbital velocity of 25 cm/sec, and a wave period of 10 sec.
Bagnold’s autosuspension equation would yield: ws< 1.25cm/sec (~= to 0.15 mm diameter quartz sphere)
At a suspension level of 10 cm, Dean’s relationship would yield: ws < 1 cm/sec (~= to 0.1 mm diameter quartz sphere)
Anything finer would be remain in suspension and be (eventually) washed out to sea.
Entrainment of sedimentDerivation of incipient grain motion (blackboard example):
start w/ torque balance on a grain
Sediment Sorting
Cross Shore Sorting - Lake Michigan
Cross-shore Sorting - Duck, NC (FRF)
From Komar, 1998From Komar, 1998
va- very angulara – angularsa- sub-angularsr – sub-roundedr – roundedvr – very rounded
Histograms of roundness for Augite
Longshore Sorting of Beach Sediments
Longshore Sorting - Willard Bascom
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