Modeling Sand Ripple Evolution Under Wave Boundary Layers

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Modeling Sand Ripple Evolution Under Wave
Boundary Layers
Allison M. PenkoUniversity of Florida
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Acknowledgements

• Office of Naval Research and the Sand Ripple DRI
  project
• American Society of Engineering Education and the
  National Defense Science and Engineering Graduate
  Research Fellowship
• Dr. Don Slinn, Dr. Tian-Jian Hsu, and Dr. Dan
  Hanes
• Fellow grad students
• Family and friends

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Motivation

• Sand ripples significantly affect the dynamics of
  the nearshore
• acoustic properties
• of seabed
• sediment transport
• beach erosion
• scour
• bottom friction
• near-bed turbulence
• BBL flow

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Objective

• Adapt 3D Sheet Flow Mixture model (Slinn 2006)
• Demonstrate the model can produce and maintain
  ripples
• Compare model results with lab data
• Determine applicability of the model
• Show the effect of suspended/bed load transport
  on ripple growth/decay

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Mixture Approach
Separate Species Sand Particles Water
Mixture Theory Sand Water Combination
Sand-Water Mixture
Water
Viscosity f(C) Density f(C)
time
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Comparing Approaches
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Mixture Density

• mixture
• density
• ?s sand density
• 2.65 g/cm3
• ?f water density
• 1.0 g/cm3
• C volumetric
• concentration
• of sand

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Mixture Viscosity

• mixture
• viscosity
• ?f water
• viscosity
• 0.0131 g/cm/s
• Cp maximum
• packing
• concentration

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Governing Equations - Sediment
Sediment Continuity
advection
diffusion
settling
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Governing Equations - Mixture
Mixture Momentum
where
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Governing Equations - Mixture
Mixture Continuity
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Particle Pressure

• Normal force between sand grains
• Represented with a bed stiffness coefficient

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Bed Stiffness Coefficient

• Acts as a particle pressure at high concentration
  
• Opposes resultant forces
• Rigidity Function
• Forces ? Cn
• umix ? 0

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Solution Strategy

• Discretization Method
• Control volume approach on a staggered grid
• One-sided differences
• Time advancement Methods
• Third-order Adams-Bashforth
• Pressure solver
• Projection method

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Solution Strategy
Staggered Grid
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Initial and Boundary Conditions

• Boundary Conditions
• x- and y-Directions periodic
• z-direction

Initial Conditions C f(x,y,z) ui 0
Bottom
Top
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Steady-State Ripples (Nielsen, 1981)

• Ripple Height

• Ripple Length

where
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Flow Simulation Parameters
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Model Simulations
Oscillatory Flow
Example of Initial Bed State
d50 0.4 mm
Quasi-two-dimensional
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Ripple Amplitude Simulations
Initial Bed States (1) sinusoidal ripple with
varying heightsDomain Size 12 cm x 8
cm Flow Parameters Uo 40 cm/s T 2 s
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Growing ripple ?o 1 cm
Slightly decaying ripple ?o 2 cm
Rapidly decaying ripple ?o 3 cm
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Ripple Height Evolution
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Ripple Shape
Growing ripple
Rapidly decaying ripple
Slightly decaying ripple
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Bed and Suspended load fluxes
Growing ripple
Rapidly decaying ripple
Slightly decaying ripple
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Sediment fluxes
Growing ripple
Rapidly decaying ripple
Slightly decaying ripple
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Horizontally- and time-averaged sediment
fluxes
Growing ripple
Rapidly decaying ripple
Slightly decaying ripple
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Ripple Height Simulation Results
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Ripple Amplitude Flow Velocity Simulations
Initial Bed States (1) sinusoidal ripple with
similar heights and varying maximum
free-stream velocitiesDomain Size from 8-16
cm x 8-16 cm Flow Parameters Uo 20-120
cm/s T 2-4 s
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Low energy ?o 2.2 cm Uo20 cm/s
T2 s
Mid energy ?o 1.6 cm Uo60 cm/s
T2 s
High energy ?o 1.6 cm Uo120 cm/s
T4 s
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Ripple Height Evolution
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Ripple Amplitude Flow Velocity Simulation Results
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Two-Ripple Wavelength Simulations
Initial Bed States A double-crested ripple and
(2) sinusoidal ripples Domain Size 12 cm x
8 cm Flow Parameters Uo 40 cm/s T 2 s
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Double-crested ripple ?o 1.4
cm
Two ripples ?o 1.6 cm
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Ripple Height Evolution
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Two-Ripple Wavelength Simulation Results
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One- and Three-Ripple Wavelength Simulations
Initial Bed States (1) and (3) sinusoidal
ripples Domain Size 24 cm x 8 cm Flow
Parameters Uo 40 cm/s T 2 s
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One- ripple ?o 0.8 cm ?o 12 cm
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Three- ripple ?o 0.8 cm ?o 12 cm
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Ripple Height Evolution
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One- and Three-Ripple Wavelength Simulation
Results
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Flatbed Simulation
Initial Bed State Flat bed with small
perturbation Domain Size 8 cm x 4 cm Flow
Parameters Uo 20 cm/s T 1 s
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Ripple Height Evolution
Flatbed
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Flatbed Simulation Results
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Bed and Suspended load fluxes
Instantaneous Load Fluxes
Cumulative Load Fluxes
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Three-Dimensional Simulation
Initial Bed State (1) 2 cm sinusoidal ripple
Domain Size 12 cm x 6 cm x 8 cm Flow
Parameters Uo 40 cm/s T 2 s
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Ripple Height Evolution
Three-dimensional ripple
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Three-Dimensional Simulation Results
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Ripple Height SimulationSummary
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Ripple Length Simulation Summary
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Conclusions Model Applicability

• Basic modeling approach is capable of producing
  realistic ripple behavior and features
• 2-D 3-D simulations produce different bed
  responses
• Computational time needs to be decreased

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Conclusions Ripple Shape

• Transitions from sinusoidal ripple to more
  peaked, steeper ripple shape
• Ripple height comes within 75 of predicted
  height for two-dimensional cases reaching a
  steady-state
• Ripple length comes within 99 of predicted
  length for cases reaching a steady-state
• Model shows a trend towards equilibrium when the
  ripple is not initialized near the equilibrium
  height or length

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Conclusions Ripple Shape

• Steady-state ripple shape, amplitude, and
  wavelength are independent of initial ripple
  state
• Ripples forming on a flat bed have wavelengths
  about half as long as in equilibrium
• Running the simulations until ripples are in a
  steady-state is necessary for further model
  investigations

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Conclusions Ripple Morphology

• Predicts a steady-state
• Bed load transport dominant mechanism in ripple
  growth and decay
• Suspended sediment is considerable in in higher
  energy simulations but does not necessarily cause
  ripple growth or decay
• Advective fluxes are the significant mechanism
  driving sediment
• Model has the potential to advance the present
  knowledge of coastal sediment transport and
  morphology

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Thank you for your time!Questions?
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Future Work

• Compare concentration and velocity fields with
  lab data
• Ripple fields
• Add mean current
• Parallelize code
• Scour around objects

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Bed and Suspended Load Definition

• Bed Material Packed bed, no motion
• Cbed gt 0.57 cm3sed/cm3
• Bedload Intergranular Forces
• 4.6 grain diameters thick (above immobile bed)
• Suspended load Fluid Drag
• gt 4.6 grain diameters above stable bed
• Threshold debatable but reasonably chosen
• Previous research
• Visual inspection of model output

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Flux Calculations