1. New Topic - Waves Always wind, so always waves Transfer of energy from a windy area to a narrow coastal band General topics to cover: (1) Generation (2) Dispersion and Travel (3) Shoaling Transformation (4) Breaking

2. Sea, Swell, Surf

3. Wave Anatomy - Periodic Waves T = wave period f = wave frequency = 1/T L = wave length C = L/T = phase velocity or celerity H = wave height  = water surface displacement h = water depth Can think of waves w.r.t. a spatial framework, or w.r.t. a temporal framework. d = horizontal water particle orbital diameter s = vertical water particle orbital diameter u = horizontal water particle velocity w = vertical water particle velocity

4. Motion of water in waves Red dot on the surface - sees the wave form pass, but moves in a circular orbit When red dot is at bottom of it’s orbital, it’s in the trough of the wave, when at the top of its orbital, it’s at the crest of the wave Orbital size (diameter) decreases with depth Waves propagate through the medium

5. Dispersion – sorting by wave period

6. Formation of Wave Groups two wave trains of slightly different wave lengths, superposed, can create wave groups

7. Wave Superposition run animation of wave superposition

8. Spectral Energy of Water Level Fluctuations Classification of wave motions is based on restoring force.

9. Wave Measurement Three main types of in-situ measurement devices: 1.Surface Piercing 2.Pressure Sensing 3.Surface Following Other Measurement Considerations: Directional Measurements Satellites

10. Wave Heights from a Time Series of Water Levels Zero up-crossing vs. zero down-crossing

11. Wave Analysis Statistical Analysis - time domain analysis which uses a wave height measurement technique (e.g. zero upcrossing) to determine a series of characteristic heights (H sig, H rms, H 1/10, H max ) vs. Spectral Analysis – which is carried out in the frequency domain, and is a fairly standard technique today.

12. “Characteristic Waves” Derived from a Time Series of Wave Heights

13. MATLAB examples of artificial waves fft analysis and Santa Cruz deep & shallow waves fft analysis Fourier Analysis – based on the concept that any complex time series can be represented by a combination of various sine and cosine functions. By performing a Fourier Transform of the “time domain” data, we obtain a function in the “frequency domain” which describes which frequencies are present in the original function.

14. Frequency-Direction Spectra Representative Values? H s = H 1/3 = 4  = 4*sqrt(var) H rms = 2*sqrt(2)*sqrt(var) f p, the frequency at the spectral peak  p, the direction at the spectral peak Use Fourier Analysis to deconvolve individual wave components Can Identify Spectra of Frequencies and Spectra of Directions Example above shows 2 distinct wave sources http://cdip.ucsd.edu/

15. Wave Data Sources - NOAA/NDBC http://www.ndbc.noaa.gov/ Other sources: WIS

16. Analyses of Wave Records - Extreme Events Akin to flood-frequency prediction in hydrology: 1.Don’t have a hundred year long record? Extrapolate! 2.Rank the annual highs (Hsig) 3.P n = n/(N+1) 4.R = 1/(1-P(H))5. Special paper - Weibull distribution plots a straight line