Equilibrium Beach Profiles - Johns Hopkins University · 2010. 10. 4. · Dynamic Theory for EBP...
Transcript of Equilibrium Beach Profiles - Johns Hopkins University · 2010. 10. 4. · Dynamic Theory for EBP...
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Equilibrium Beach Profiles
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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
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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)
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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
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Data Sets
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Empirical Evidence Dean, 1977
503 profiles
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East Coast of Florida
Hughes and Chiu, 1978
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Empirical Fits
Hughes and Chiu, 1978
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Profile Parameter
Sand Size, mm
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Profile Factor as a Function of Grain Size
To convert to ft1/3, multiply by 1.5
NOTE: A formula
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Tests on Other Data
A=0.82 m1/3
A=0.25 m1/3
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Examination of h = A y2/3
Beach slope
slope
Not a real problem
2.8 for
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Variable A
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Variable A
A varies by reach: A1 for y1 to y2; A2 for y2 to y3, ...
Final expression
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Changing A with distance
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For fixed depth profiles, h ho
slope
foreshore slope
Bodge (1992), Komar and McDougal (1994)
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Bruun Rule
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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
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Other Recession Rates
Edelman Method (1972)
For fixed dune elevation
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Equilibrium Profile and Storm Recession
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Equilibrium Recession with Surge
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Planar Slope Recession
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Type 1
Suh and Dalrymple, 1988
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Planar Profiles
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Planar Beach Recession