Wave-Ice Interactions in the MIZ

Sveinung Løset, dr.ing., prof.

Marine Civil Engineering GroupDepartment of Civil Engineering and Transport

Norwegian University of Science and Technology (NTNU)

Analysis

• Simultaneous measurement of the motion of two ice floes in a wave field (9 min. segment with overlap). Floe 1: 5 km from the edge, Floe 2: 10.5 km

• The heave motion amplitude used to interpret the wave amplitude

• The PSD is a measure of a floe’s energy.• Spectral analysis used to investigate the response of the floes

in a wave filed relative to the wave amplitude at several different frequencies

• Comparison of the calculated wave amplitude at these two locations gave the wave attenuation coefficient

• RAO’s: non-dimensional response amplitude operators • Essentially no difference between the floe energy attenuation

and the wave attenuation.

Other studies

• The range of the wave attenuation coefficient can be quite large

• Bering Sea/Greenland Sea: (0.2-8.7)x10-4 m-1

• Different ice field compositions result in different wave attenuation

• High ice concentrations; floe-floe interactions could contribute significantly to alter the wave characteristics

Wadhams, P., V.A. Squire, D.J. Goodman, A.M. Cowan and S.C. Moore (1988):The attenuation rates of ocean waves in the marginal ice zone. J. Geophysical Res.,93(C6), pp. 6799-6818.

Waves?

Study site

Waverider Buoy

Accelerometer

MIZ

Ice edge (78°50’N 23°20’E), 24.04.1990

Transition zone (~20 km inside the edge)

Location and duration

Definitions

R5=13.0, R1=12.1, R2=8.0, R3=16.4, R4=9.6 m

Floe #2

Floe #3

Wave attenuation

• Centre of mass of the floes has to be obtained• Verify that the heave motion follows the water

displacement due to the wave• The RAO gives the energy component of the wave

in each of the six degrees of freedom motion as a function of frequency

• From the RAO – the kinetic energy of the floes may be directly computed from their translational and rotational velocities

Total energy of each floe

2 22 2 2 2 2 2( ) ( )

2 8 4ice ice ice

total cx cy cz x y zm m r m rE v v v ω ω ω= + + + + +

v - translational velocityω - rotational velcityr - ice floe radiusmice – floe mass

Kinetic energy of the ice floes per unit area

2 22 2 2 2 2 21 ( ) ( )

2 8 4ice ice

total ice ice cx cy cz x y zm r m rE h v v vρ ω ω ω

⎡ ⎤= + + + + +⎢ ⎥

⎣ ⎦

ρice – 920 kg/m3

h – 1.3 m

Assumptions:100 % ice concentrationEtotal/πr2 kinetic energy per unit area

Total wave energy density per unit area

1 ( )2 watergP fρ

where P(f) is the PSD as a funtion of frequency f

The total wave energy density per unit area includingboth the potential and the kinetic energy at a givenfrequency is given by:

Attenuation of floe energy

2 1 2 1ln( / /( )E E x xβ = − −

E1 and E2 are the total energy for Floes 1 & 2x1 and x2 are the distances from the edge

Heave response, Floes 1&2

(a) Raw data, (b) corresponding filtered data, (c) PSD of the filtered data

Filtered heave amplitude PSD (m2s)

Floe 1

Floe 2

Ratio Floe1/Floe2

Wave attenuation coeff. vs. frequency

RAO’s

Sway

Surge

Pitch

Roll

Yaw

Comparison between floe and wave energy density

(a) Floe energy density (Ns/m), (b) Wave energy density ( Ns/m), (c) ratio

Floe energy attenuation coeff. vs. frequency

Conclusive remarks

• Ice field: brash ice and individual floes• Studied two ice floes, six independent directions• Heave motion analysed to interpret the wave

amplitude• Floe-floe interaction and wave spreading due to

directional scattering cause wave attenuation in the MIZ

• The wave attenuation coefficient ranged from 2.0·10-4 to 6.0·10-4 m-1 over a corresponding frequency range 0.04-0.16 Hz.

Shoulder Ice Barrier Design