Transcript Document 7542675

What a drag!
A numerical model of time-dependent
flow over topography
Sally Warner
Advised by Parker MacCready
December 6, 2006
What is drag?
Drag is a force from a body acting parallel to
the direction of relative fluid motion.
Friction drag
Form (pressure) drag
large wake
smooth surface
medium wake
rough surface
small wake
Why do oceanographers care
about form drag?
>> Form drag works to
– dissipate tidal energy
– generate eddies and internal waves
– produce turbulence and mixing
>> Unlike frictional drag, form drag is not well
resolved in coastal and larger scale models
Form drag in the Puget Sound
In their Puget Sound tidal
model, Lavelle et al. (1988)
originally used a frictional drag
coefficient of
CD =
3x10-3.
But they found that some areas
needed a much larger
coefficient of CD = 20x10-3 to
match tidal observations.
Form drag at Three Tree Point
• Three Tree Point is a
1 km headland in the
Main Basin of the
Puget Sound
• MacCready and others
found the form drag to
be 20 times larger than
frictional drag
MacCready
Motivating questions
>> Why is there such a large form drag in
places like Three Tree Point?
>> How can I parameterize the form drag into
a new drag coefficient (CD_FORM)?
Solution approach
>> Idealized numerical model
The model: basic setup
The model: Gaussian bump
First experiment: 15 different bump sizes
The model: stratification
N = 0.0125 s-1
The model: grid size
The model: tidal forcing
– Forced with a propagating tidal wave
– Fluid entering boundaries has original stratification
Vertically averaged velocity
u  Au sin( t  u )
Surface height
  A sin( t   )
A 3.6° phase lag between left and right makes sense for a 20 km channel
with a surface gravity wave speed of c = 44 m/s.
How do I measure form drag?
Form drag   
AB

pB
dAB
x
pB = bottom pressure

= bottom slope
x
AB = bottom area
H
L
MacCready
2 tidal cycles = 24 lunar hours
Form drag  Adrag sin( t  drag )
Form drag  Adrag sin( t  drag )
Fr >1
Power = drag * velocity
Bump height is 10% of total depth
drag = 102°
Bump height is 20% of total depth
drag = 130°
– Average Power
Results in the same range as the 0.7 MW of power
dissipated at Three Tree Point.
Questions to answer
• What are the factors that create the very large form
drag measured in places like Three Tree Point?
• How does form drag contribute to the generation of
internal tides and eddies?
• How does the magnitude of the form drag compare
with the magnitude of the frictional drag?
• What role does form drag play in the energy budget
of coastal regions?
Future goal: parameterization
CD_FORM = function( bump height,
bump width,
stratification,
tidal velocity,
tidal period,
channel width,
channel length,
channel height )
Thank you
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Parker MacCready
David Darr
Tom Connolly
Natalia Stefanova
Neil Banas
Betty Bottler (ARCS Fellowship donor)