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

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 10-100 kms Contains thin O(cm) but long O(10-100m) ice sheets called floes Important due to effect on ice coverage and wave propagation

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

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

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

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

Example Overwash Video Overwash Bores Incident Wave Direction

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

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

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

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

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

Video of Comparison 1

Video of Comparison 2

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

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

Video of Comparison For High Steepness and Wavelength

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

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?

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