1. Modelling Overwash of Ice Floes by Water Waves
Presented by:
David Skene – PhD Student, University of Adelaide
Supervised by:
Dr Luke Bennetts – University of Adelaide
Dr Mike Meylan – University of Newcastle
Thanks to:
The University of Adelaide
CSIRO
Australian Antarctic Division

2. The Marginal Ice Zone (MIZ)
Interface between open ocean and frozen ocean
“the part of the ice cover which is close enough to the open ocean boundary to be affected by its presence”
Width of kms
Contains thin O(cm) but long O(10-100m) ice sheets called floes
Important due to effect on ice coverage and wave propagation

3. Mathematical Modelling of Waves in the MIZ
Wave models built on solitary floes
Developed since 1970s
Based on Linear Potential Theory
Linear Potential Theory:
Water as incompressible inviscid irrotational fluid
Floes as thin and long (often elastic) plates
Linearization of surfaces
Floe

4. Validation of Wave-Ice Modelling
In recent years, experiments in wave tanks to validate models
Used thin plastic plates as floes
Frequent observation has been what we call Overwash
Overwash is not currently included in mathematical models

5. So what is Overwash? Plate oscillations causes edges to dip into water
This dipping causes fluid to wash over the top
We call this process overwash
Overwash Fluid
Plate’s Edge Dips into Water

6. Experiment to Observe and Quantify Overwash
Wave tank testing conducted at Plymouth University, UK
1m square PVC and Polypropylene was used
Thicknesses of 5mm – 40mm
Regular incident waves of varying Wavelength and Steepness
Overwash recorded via depth probe and camera

7. Example Overwash Video
Overwash Bores
Incident
Wave Direction

8. A Key Note from these Experiments
Parallel experiments measuring plate motion
Linear Potential Theory models motion accurately
Motion of Plate Comparison

9. 2D Model of Overwash Key Modelling Assumptions:
Linear Potential Theory models plate and surrounding water
Shallow Water Equations models overwash
Overwash has a negligible effect on the surrounding domain
Linear Potential Theory drives the Shallow Water Equations using one-way coupling
Shallow Water Equations
One Way Coupling
Incident Wave Direction
Linear Potential Theory

10. Linear Potential Theory
Assumptions:
Water as inviscid incompressible irrotational fluid:
Plate modelled as Euler-Bernoulli beam
Plate has no lateral drift
Linearization of surfaces
No overwash effects
Model gives:
Waves in terms of incident, reflected, and transmitted
Motion of the plate
Time harmonic system i.e. everything oscillates at e-iωt
Reflected Wave
Transmitted Wave
Incident Wave Direction
Linear Potential Theory

11. Modelling the Overwash Domain
Observations of Overwash Showed:
Thin relative to length
Bores
Small plate accelerations
Consistent with:
Shallow Water Equations
Mathematical Properties:
Bores are shocks
Nonlinear
Very different to Linear Potential Theory
A time harmonic solution does not exist
Simple numerical methods develop unnatural oscillations
Numerical Solving:
Solved via RK2 time-stepping and complicated x-discretisation

12. One-Way Coupling of Domains
Linear Potential Theory gives boundary conditions for Shallow Water Equations
Boundary conditions given:
Edge fluid depth
Edge fluid velocity
Plate surface height

13. Video of Comparison 1

14. Video of Comparison 2

15. Comparison of Overwash Depth Variation
Video 1
Video 2
Centre Depth Variation (mm)
Time (s)
Time (s)
Experiment in Red, Theoretical Model in Blue

16. Comparison of Overwash Average and Deviation
Results for 10mm Thick PVC
x-axis varies with incident wave properties
Experiment in Red, Theoretical Model in Blue

17. Video of Comparison For High Steepness and Wavelength

18. Causes of Disagreement
Strong bore collisions
Strong coupling effect
Edge wave breaking
Bores created by side edges
Video 3
Centre Depth Variation (mm)
Time (s)
Experiment in Red, Theoretical Model in Blue

19. Summary
Overwash can be modelled using Linear Potential Theory, the Shallow Water Equations, and one-way coupling
This model is accurate for low wavelengths and steepnesses
It is not accurate for long wavelengths and steepnesses
Could be extended by modelling wave breaking, coupling effects and 3D effects
Remaining question: What is the effect of overwash on the surrounding system?

20. Acknowledgements Dr Luke Bennetts – University of Adelaide
Dr Mike Meylan – University of Newcastle
Assoc. Prof. Alessandro Toffoli – Swinburne University of Technology
The University of Adelaide
CSIRO
Australian Antarctic Division