MODELING

1
MODELING

• Physical
• Tanks basins and flumes
• Similitude should always be a concern
• Analytical
• Mathematical equations that can be solved in
  closed form
• AnswerF(variables)
• Numerical
• No general solution
• Requires computer to solve discretized equations
• Delft3D, Nearcomm, genesis, your favorite here
• Most of Coastal Engineering is headed this way

2
PHYSICAL
Must be concerned with similitude Geometric sys
the ratio of length scales is constant Dynamic
says the ratio of forces is maintained (think
Froude, Reynolds, Shields etc) Dynamic is
preferred.
3
ANALYTICAL
One-line model Describe the time-history of the
shoreline contour when coupled with sediment
continuity
waves
Sediment continuity
Unit Normal to Shoreline
4
ONE-LINE MODEL
Couple with continuity
Go through and Expand the sin term simplifying
where possible assuming dy/dx is small
End up with
Where
Known as longshore diffusivity (coastal constant
to Europeans)
5
ONE-LINE MODEL
Qo is the transport on a coast with shoreline
parallel to x-axis Second term is additional (or
less) transport associated with non-parallel
shoreline
Substitute into transport gradient term to get
Upon substitution into the continuity equation
This is the well known 1D Diffusion equation
(think heat in a rod)
6
SOLUTIONS
Periodic Beach Initial shoreline of the form
Solutions are
Same shape but decay exponentially in time
7
SOLUTIONS
Point Fill Think of volume M being dumped at
single location described by Kronecker Delta
Solution is
8
SOLUTIONS
Rectangular fill Since diffusion equation
linear, we can superpose many point fills
Solution
Script l is the project length and Y is the
project width
9
SOLUTIONS
Proportion of volume remaining
Defines project success
10
SOLUTIONS
Project Half-Life Look at plot of project life
as a function of normalized time in addition to
the asymptote given by