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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
Sea, Swell, Surf
Wave Anatomy - Periodic Waves
T = wave periodf = wave frequency = 1/TL = wave lengthC = L/T = phase velocity or celerityH = wave height = water surface displacementh = water depth
Can think of waves w.r.t. a spatial framework, or w.r.t. a temporal framework.
d = horizontal water particle orbital diameters = vertical water particle orbital diameteru = horizontal water particle velocityw = vertical water particle velocity
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
Dispersion – sorting by wave period
Formation of Wave Groups
two wave trains of slightly different wave lengths, superposed, can create wave groups
Wave Superposition
run animation of wave superposition
Spectral Energy of Water Level Fluctuations
Classification of wave motions is based on restoring force.
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
Wave Heights from a Time Series of Water Levels
Zero up-crossing
vs.
zero down-crossing
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 (Hsig, Hrms, H1/10, Hmax)
vs.
Spectral Analysis – which is carried out in the frequency domain, and is a fairly standard technique today.
“Characteristic Waves” Derived from a Time Series of Wave Heights
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.
Frequency-Direction Spectra
Representative Values?
Hs = H1/3 = 4 = 4*sqrt(var)
Hrms = 2*sqrt(2)*sqrt(var)
fp, 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/
Wave Data Sources - NOAA/NDBC
http://www.ndbc.noaa.gov/
Other sources: WIS
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. Pn = n/(N+1)
4. R = 1/(1-P(H)) 5. Special paper - Weibull distribution plots a straight line