Report 10 Calm Surface Problem 10 Calm Surface

Report 10 Calm Surface 劉富蘭克林

Problem # 10 • Calm Surface • When wind blows across a water surface, waves can be observed. If the water is covered by an oil layer, the waves on the water surface will diminish. Investigate the phenomenon. 2021/5/24 Reporter: 劉富蘭克林 1

Overview • Introduction – Observation – Problem Analysis • Experiment – Experimental Setup – Experiment • Results and Discussion • Conclusions & Summary • References 2021/5/24 Reporter: 劉富蘭克林 2

Introduction • Observation • Water surface waves can be categorized into two types: • Capillary wave regime (wavelength<1. 73 cm) • Gravity wave regime (wavelength>1. 73 cm) 2021/5/24 Reporter: 劉富蘭克林 3

Introduction • Wind on water surface: 1. Wind picks up on small disturbances on water surface, giving the waves energy. 2. The water oscillates in a circular motion 3. The surface becomes a trochoid 2021/5/24 Reporter: 劉富蘭克林 4

• Wind on oil over water surface: • Gibbs elasticity: Change of surface tension to change of area of surfactant layer. • different wave speeds in different materials-> phase difference in water and oil layer-> shear gradient • Oil applies a reaction force on wave -> Energy loss Behroozi, Peter. Et. Al. The calming effect of oil on water. AJP, Vol. 75, Issue 5, pp. 407 -414 Reporter: 劉富蘭克林 5 (2007)2021/5/24

• Calming effect failure: • Large waves (gravity wave regime) – Oil layer may be broken and lose calming effect • Thick layer of oil on water surface: – Wave height is much smaller than oil layer thickness – Waves form directly on oil surface oil water 2021/5/24 Reporter: 劉富蘭克林 6

Experiment • Parameters: – Oil layer thickness – Wind speed (small waves vs. large waves) – Attenuation of point-source waves through a distance 2021/5/24 Reporter: 劉富蘭克林 7

Experiment Setup • Screen and camera 2021/5/24 • Wide ripple tank (55 x 55 cm 2) • Light projector • Crossflow fan with parallel vanes Reporter: 劉富蘭克林 8

• Second ripple Experiment Setup tank with wave • Micro-pipette generator and • Anemometer • Mineral oil stroboscope 2021/5/24 Reporter: 劉富蘭克林 9

Experiment Method • The fan is turned on, and ripples start to form. • The projector projects the image onto the screen. • A camera on fixed manual adjustments is used to capture the images 2021/5/24 Reporter: 劉富蘭克林 10

Experiment Method 1 cm 2021/5/24 • Light bands indicate crests • Dark bands indicate troughs • If the waves were larger, the brightness of the photos would be more contrasted • By analyzing the brightness deviation of the photo, we can compare the “roughness” of the surfaces Reporter: 劉富蘭克林 11

Experiment 1: Oil layer thickness • Different amounts of oil are used added to the water surface (total thickness=1 cm): • Pure water • 1 ml oil-> thickness: 4. 7 x 10 -6 m • 5 ml oil-> thickness: 1. 6 x 10 -5 m • 20 ml oil-> thickness: 6. 6 x 10 -5 m • 1. 5 L of water+ 1. 5 L of oil-> thickness: 0. 5 cm 2021/5/24 Reporter: 劉富蘭克林 12

Experiment 1: Oil layer thickness Wind speed: 7. 7 m/s 1 ml oil pure water 2021/5/24 5 ml oil Reporter: 劉富蘭克林 oil ½ 20 ml water+oil 13

Experiment 1: Oil layer thickness • Video: Disturbances on water surface when shear stress is applied 2021/5/24 Reporter: 劉富蘭克林 14

2021/5/24 Reporter: 劉富蘭克林 15

Experiment 1: Results 0. 09 Standard deviation of pixel brightness (Roughness of water surface) 0. 08 0. 07 0. 06 0. 05 0. 04 0. 03 Standard deviation of pixel brightness 0. 02 0. 01 0 Pure water 1 ml oil on water 5 ml oil on water 20 ml oil on water 1/2 oil+water • Oil resists the shear gradient applied by water waves (Gibbs elasticity) -> Calming effect • A thin layer of oil has the best calming effect • If excess oil is used, ripples form directly on the oil 2021/5/24 Reporter: 劉富蘭克林 16

Experiment 2: Wind speed • Wind speed: 7. 7 m/s • Wind speed: 6. 4 m/s • Oil has better calming effect when wind speed is lower, because at high wind speeds the oil layer tends to break 2021/5/24 Reporter: 劉富蘭克林 17

Experiment 3: Attenuation of waves 2021/5/24 Reporter: 劉富蘭克林 18

Experiment 3: Attenuation of waves • Oil on water also has attenuation effect on point-source waves • The frequency remains unchanged Oil on water Pure water 2021/5/24 Reporter: 劉富蘭克林 19

Conclusions & Summary • Waves travel at different speeds in different media • The Gibbs elasticity property of an oil film makes it resist the shear gradient applied by water waves -> Calming effect 2021/5/24 Reporter: 劉富蘭克林 20

Conclusions & Summary • Oil layer thickness: • A thin layer of oil has the best calming effect • If excess oil is used, ripples form directly on the oil Standard deviation of pixel brightness (Roughness of water surface) 0. 1 0. 08 0. 06 0. 04 0. 02 • Wind speed: Standard. . . 0 Pure water 1 ml oil on water 5 ml oil on water 20 ml oil on water 1/2 oil+water • Oil has better calming effect when wind speed is lower, because at high wind speeds the oil layer tends to break • Attenuation of waves from a point source: • While enhancing the decay of the waves, the frequency remains unchanged Reporter: 劉富蘭克林 2021/5/24 21