Equilibrium Beach Profiles
Derive the Equilibrium Beach Profile
EBP good for design; already used for retreat
Kinematic Approach
Dynamic Approach
Empirical Approach
Forces acting on profile:
Constructive
Destructive
Kinematic: calculate forces and trajectories; dynamic: force balance
Constructive: Dean’s breaking argument, onshore mean streaming, net
onshore shear stress
Destructive: 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
Integrate with respect to y
where A is f(d), profile parameter, dimensional
depth of closure
width of profile
substituting
Integrate with respect to y
Data Sets
Empirical Evidence
503 profiles
Dean, 1977
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
Bodge (1992), Komar and McDougal (1994)
slope
foreshore slope
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