# Lecture 10 ATOC 5051 INTRODUCTION TO PHYSICAL OCEANOGRAPHY

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1 ATOC 5051 INTRODUCTION TO PHYSICAL OCEANOGRAPHY Lecture 10 Learning objectives: understand gravity waves & their roles in oceanic adjustment (for f=0); should be able to explain wave refraction & breaking phenomena 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.

2 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

3 ! [1] Long surface gravity wave L>>D, dispersion relation: c = c g = ± gd ω = ± gdκ apple ( ) Non-dispersive; propagate in all directions; Barotropic: feels the bottom p independent of z; Fast speed ~can be 200m/s; Satisfies hydrostatic balance.

4 [2] Short surface gravity waves (also called deep water waves). Short surface gravity waves: Propagate in all directions; Dispersive waves (phase speed and group velocity change with frequency and wavenumber)

5 Solutions: Z<0, solutions exponentially decay. Non-hydrostatic Short surface gravity waves: Surface trapped; Non-hydrostatic.

6 Particle motion associated with Surface waves & Stokes drift File:Deep_water_wave.gif

7 2. Adjustment of the ocean under gravity in a non-rotating system: f=0 [1] Initial state: quiescent ocean (or lake); Math:

8 [2] Perturbation: (assumptions R o <<1, E k <<1, f=0) Math:

9 [3] Free waves in this system: Long & short surface gravity waves - energy dispersion ω Long & short surface waves κ [4] Equilibrium state: Quiescent ocean (or pond) again. Refer equations.

10 3. Refraction and breaking in shallow water Above: Long surface gravity waves. C p = C g = ± gd ω = ±κc Set up by forcing

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

12 Wave Refraction: More parallel to the shore; k reduces Long surface gravity waves: C p = C g = ± gd ω = ±κc Set up by forcing

13 Observe: What has happened to the waves?

14 Conserved. Wave breaking!

15 4. Swells and Tsunamis Wind driven swells: long surface gravity waves Persistent wind forcing from storms: Travel for long distances: Non-dispersive, group together

16 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 by the magnitude 8.6 earthquake. Energy speed: Ocean depth

17 Asia N. America 2. Indonesia Australia The Pacific 1. S. America The Indian Ocean

18 Aftermath of the Chilean tsunami in the Waiakea area of Hilo, Hawaii, 10,000 km from the generation 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 hrs after the tsunami was triggered.

19 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 wave moving 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.)

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

21 December 26, 2004 Indian Ocean Tsunami NOAA 2004 Tsunami simulation

22 Tsunami warning NOAA: West Coast & Alaska Tsunami warning center (Alaska); Pacific Tsunami Warning Center (Hawaii) Predict earthquake & generation of Tsunami

23 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.)

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