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8. Wave Definitions and Measurement Always wind, so always waves Transfer of energy from a large, windy area to a narrow coastal zone General topics to cover: (1) Generation (2) Dispersion and Travel (3) Shoaling Transformation (4) Breaking

Sea, Swell, Surf

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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 η = 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

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

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Dispersion – sorting by wave period

Day of Year 2003

Wave sort themselves out by wave period. So, from a region of wave generation (open ocean storm), the longer period waves travel faster across the ocean, and hence arrive at a point on the coast earlier than short period waves.

Wave Superposition

Fig. 4.9 in Davidson-Arnott textbook.

Addition of two or more wave forms leads to constructive and destructive interference as dictated by the heights and periods of the constituent wave forms.

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Wave Superposition

file:///Users/pna/Work/Teaching/Animations/WaveInterfere3D.html

Formation of Wave Groups

two wave trains of slightly different wave lengths, superposed, can create wave groups

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Spectral Energy of Water Level Fluctuations

Classification of wave motions is based on restoring force.

Spectral Energy of Water Level Fluctuations

Fig. 4-2 in Davidson-Arnott textbook.

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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

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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

HS=H1/3, originating from calibration of “inter-ocular data collection”. Where would we find H1/10?

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Frequency-Direction Spectra

Representative Values? Hs = H1/3 = 4σ = 4*sqrt(var) Hrms = 2*sqrt(2)*sqrt(var) fp, the frequency at the spectral peak θp, 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/

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.

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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

Wave Data Sources - NOAA/NDBC

http://www.ndbc.noaa.gov/

Other sources: WIS