What a drag A numerical model of timedependent f low over topography

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What a drag!A numerical model of time-dependent
f low over topography

• Sally Warner
• Advised by Parker MacCready
• December 6, 2006

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What is drag?

• Drag is a force from a body acting parallel to
  the direction of relative f luid motion.

Friction drag
Form (pressure) drag
large wake
smooth surface
medium wake
rough surface
small wake
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Why do oceanographers care about form drag?

• gtgt Form drag works to
• dissipate tidal energy
• generate eddies and internal waves
• produce turbulence and mixing
• gtgt Unlike frictional drag, form drag is not well
  
• resolved in coastal and larger scale models

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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.

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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
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Motivating questions
gtgt Why is there such a large form drag in
places like Three Tree Point? gtgt How can I
parameterize the form drag into a new drag
coefficient (CD_FORM)?
Solution approach
gtgt Idealized numerical model
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The model basic setup
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The model Gaussian bump
First experiment 15 different bump sizes
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The model stratif ication
N 0.0125 s-1
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The model grid size
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The model tidal forcing
Forced with a propagating tidal wave Fluid
entering boundaries has original stratification
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Vertically averaged velocity
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Surface height
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.
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How do I measure form drag?

• pB bottom pressure
• bottom slope
• AB bottom area

H
L
MacCready
2 tidal cycles 24 lunar hours
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Fr gt1
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Power drag velocity
Bump height is 20 of total depth
Bump height is 10 of total depth
?drag 102
?drag 130
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Average Power
Results in the same range as the 0.7 MW of power
dissipated at Three Tree Point.
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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?

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Future goal parameterization

• CD_FORM function( bump height,
• bump width,
• stratification,
• tidal velocity,
• tidal period,
• channel width,
• channel length,
• channel height )

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Thank you

• Parker MacCready
• David Darr
• Tom Connolly
• Natalia Stefanova
• Neil Banas
• Betty Bottler (ARCS Fellowship donor)