1. 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

2. Sediment Grain Size - Settling Velocity
Steps in the Derivation of Stokes’ Law (on blackboard)
Downward directed grav. Force
Balanced by upward directed drag force
CTSV - no acceleration, so by Newton’s 2nd - the sum of the forces must =0.
Equate the Forces, solve for velocity.
Identify relationship for drag coefficient as a fcn. of Re?
We’re there...
Quartz is most common – heavy minerals are the dark specks. Where no terriginous source exists – shell fragments. Olivine from volcanic rocks. Mixed material from reworked glacial till.

3. CD = f(Re)

4. 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.

5. 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.

6. Entrainment of sediment
Derivation of incipient grain motion (blackboard example):
start w/ torque balance on a grain

7. Sediment Sorting
Quartz is most common – heavy minerals are the dark specks. Where no terriginous source exists – shell fragments. Olivine from volcanic rocks. Mixed material from reworked glacial till.

8. Cross Shore Sorting - Lake Michigan

9. Cross-shore Sorting - Duck, NC (FRF)

10. Histograms of roundness for Augite
va- very angular
a – angular
sa- sub-angular
sr – sub-rounded
r – rounded
vr – very rounded
Roundness can indicate chemical instability or a sediment deposit very far from its source. Sand souce of tillamook head is rounder
From Komar, 1998

11. Longshore Sorting of Beach Sediments

12. Longshore Sorting - Willard Bascom