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