HW1: No Answer Key1d) how does the Arctic-Atlantic exchange of water/sea ice may affect climate?

1f) For an Aqua planet (Earth is all covered by water without any land), which climatic phenomena that you have discussed in 1b)-1e) will still exist and which one(s) will not, and why do you think so? (6pts)o Smith et al. 2006: Global Climate and Ocean Circulation on an Aquaplanet Ocean–Atmosphere

General Circulation Model. J. Clim.o http://oceans.mit.edu/JohnMarshall/research/climate-dynamics/page-1/o https://journals.ametsoc.org/jas/article/55/8/1373/24601/An-Aquaplanet-Monsoon

2c) Provide an example for the use of SOFAR channel to observe ocean currents. SOFAR/RAFOS floats;ReciprocaltomographybetweenATOCtransmitters

3a) What instrument do you want to use to measure the current variability (assume you can only afford one type of instruments), and why do you choose this type of instrument (discuss its advantages over other instruments)? (5pts) Regional study: Argo – measure T & S profile (parking depth ~1000m current)

ATOC 5051 INTRODUCTION TO PHYSICAL OCEANOGRAPHY

Lecture 10

1. Surface gravity waves (continue);2. Adjustment under gravity in a non-rotating fluid;3. Wave refraction and breaking in shallow waters;4. Swells and tsunamis.

Learning objectives: understand gravity waves& their roles in oceanic adjustment (for f=0);

explain wave refraction & breaking

1. Surface gravity waves (continue): • Maximum amplitude at the ocean surface;• A homogeneous ocean: isolates surface gravity waves &

excludes internal gravity waves;• Restoring force: gravity

[1] Long surface gravity wave (shallow water wave)

• Non-dispersive; propagate in all directions;• Barotropic: feels the bottom – p independent of z;• Fast speed ~can be 200m/s;• Satisfies hydrostatic balance.

( )

€

c = cg = ± gD

€

ω = ± gDκ

!

Frequency ~0: unrealisticbecause of ignoring Erath’s

rotation f

Previous class:

For L>>D, dispersion relation: 𝜔 = 𝑔𝐷 𝜅

[2] Short surface gravity waves (also called deep waterwaves)

Short surface gravity waves:• Propagate in all directions;• Dispersive waves (phase speed and group velocity change with frequency and wavenumber)

𝐿~1𝜅≪ 𝐷, 𝜅D>>1

Z<0, solutions exponentially decay. Non-hydrostatic

Short surface gravity waves:• Surface trapped; • Non-hydrostatic.

Solutions:

Particle motion associated with Surface waves & Stokes drift

http://en.wikipedia.org/wiki/File:Deep_water_wave.gif

2. Adjustment of the ocean under gravity in a non-rotating system: f=0

[1] Initial state: quiescent ocean (or lake)

Math:

Quiescent ocean

[2] Perturbation: (assumptions , f=0)

Math: €

Ro <<1,

€

Ek <<1

[4] Equilibrium state:

Long & short surface waves

After waves propagate away, quiescent ocean (or pond) again€

κ

€

ω

[3] Free waves in this system: Long & short surface gravity waves - energy dispersion

Radiating gravity wave

3. Refraction and breaking in shallow water

Above: Long surface gravity waves.

Set up by forcing€ €

Cp = Cg = ± gD

€

ω = ±κc

Refraction: long surface gravity waves approach the coast: observe – what changes do you see?

Wave Refraction: More parallel to shore;

Long surface gravity waves:

Set up by forcing€

€

Cp = Cg = ± gD

€

ω = ±κc

increases (L reduces)𝜅

Observe:What hashappened to the waves?

Conserved.

Wave breaking!

4. Swells and TsunamisWind driven swells: long surface gravity wavesPersistent wind forcing from storms:

Travel for long distances:Non-dispersive, group together

Tsunamis: Long, surface gravity waves 1960 Chilean Tsunami

Aerial view of coastal area on Isla Chiloe, Chile, showing tsunami damage and wave extent.

200 deaths were reported here from the tsunami generated just off Chile's coast bythe magnitude 8.6 earthquake.

Energy speed:

Ocean depth

1. S.America

N. AmericaAsia

Australia

The PacificThe IndianOcean

2. Indonesia

Chile

Aftermath of the Chilean tsunami in the Waiakea area of Hilo, Hawaii, 10,000 km from thegeneration area.

Along the Peru-Chile coast the estimated lost of life from the tsunami ranged from 330 to 2000 people;A city along the western coast of the United States which received notable run-up was Crescent City, California, where the run-up reached 1.7 m and the first wave arrived 15.5 hrsafter the tsunami was triggered.

• Numerical Models For 1960 Chilean Tsunami (play the movie)

This animation (2.3 MB), produced by Professor Nobuo Shuto of the Disaster Control Research Center, Tohoku University, Japan, shows the propagation the earthquake-generated 1960 Chilean tsunami across the Pacific. Note the vastness of the area across which the tsunami travels - Japan, which is over 17,000 km away from the tsunami's source off the coast of Chile, lost 200 lives to this tsunami. Also note how the wave crests bend as the tsunami travels - this is called refraction. Wave refraction is caused by segments of the wavemoving at different speeds as the water depth along the crest varies. (The QuickTime movie presented here

was digitized from a video tape produced from the original computer-generated animation.)

Model for 1960 Chilean Tsunami: also pay attention to wave refraction

(https://www.youtube.com/watch?v=0yha559FvaY)

December 26, 2004 Indian Ocean Tsunami

http://www.youtube.com/watch?v=OGkeMvxotzI

http://www.youtube.com/watch?v=YReIrrrOeqY

NOAA 2004 Tsunami simulation

Tsunami warning

• NOAA: West Coast & Alaska Tsunami warning center (Alaska);

• Pacific Tsunami Warning Center (Hawaii)

• Predict earthquake & generation of Tsunami

Rogue waves are relatively large and spontaneous ocean surface waves that occur far out at sea; active area of research. (Strong winds + currents – cause merged waves; nonlinearity, etc.)