New Topic - Waves

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