Equilibrium Beach Profiles

Derive the Equilibrium Beach Profile

Kinematic ApproachDynamic ApproachEmpirical Approach

Forces acting on profile:

ConstructiveDestructive

EBP good for design; already used for retreat

Kinematic: calculate forces and trajectories; dynamic: force balance

Constructive: Dean’s breaking argument, onshore mean streaming, net onshore shear stressDestructive: gravity, return flow

Dynamic Theory for EBP

Turbulence as a destructive force, represented by energy dissipation per unit volume of water

y’ is onshore direction

Dissipation varies with the beach slope

D* is a function of grain size (d)Assumptions: H=kappa h, C_g = sqrt(gh)

Equilibrium Profile

where A is f(d), profile parameter, dimensional

depth of closure

width of profile

Integrate with respect to y

substituting

Integrate with respect to y

Data Sets

Empirical Evidence Dean, 1977

503 profiles

East Coast of Florida

Hughes and Chiu, 1978

Empirical Fits

Hughes and Chiu, 1978

Profile Parameter

Sand Size, mm

Profile Factor as a Function of Grain Size

To convert to ft1/3, multiply by 1.5

NOTE: A formula

Tests on Other Data

A=0.82 m1/3

A=0.25 m1/3

Examination of h = A y2/3

Beach slope

slope

Not a real problem

2.8 for

Variable A

Variable A

A varies by reach: A1 for y1 to y2; A2 for y2 to y3, ...

Final expression

Changing A with distance

For fixed depth profiles, h ho

slope

foreshore slope

Bodge (1992), Komar and McDougal (1994)

Bruun Rule

Barrier Island Retreat

Dean and Maurmeyer (1983)

Since not all sediment goes offshore for building the profile, recession is greater.

Also h_o - h_L is small, so bigger R

Other Recession Rates

Edelman Method (1972)

For fixed dune elevation

Equilibrium Profile and Storm Recession

Equilibrium Recession with Surge

Planar Slope Recession

Type 1

Suh and Dalrymple, 1988

Planar Profiles

Planar Beach Recession