Waves for Paddlers Understanding Lake and Ocean Waves with Pictures
Greg Anderson Northeastern Illinois University
2017
The Gales 2017 G. Anderson Waves for Paddlers – slide 1 / 64
By Florian K - Own work, CC BY-SA 3.0 Local Motion In A Water Wave
In deep water, waves oscillate in circles. The radius decreases with depth.
The Gales 2017 G. Anderson Waves for Paddlers – slide 4 / 64 Local Motion In A Water Wave
In deep water, waves oscillate in circles. The radius decreases with depth.
The Gales 2017 G. Anderson Waves for Paddlers – slide 4 / 64 Local Motion In A Water Wave
In deep water, waves oscillate in circles. The radius decreases with depth.
The Gales 2017 G. Anderson Waves for Paddlers – slide 4 / 64 Local Motion In A Water Wave
In deep water, waves oscillate in circles. The radius decreases with depth.
The Gales 2017 G. Anderson Waves for Paddlers – slide 4 / 64 Local Motion In A Water Wave
In deep water, waves oscillate in circles. The radius decreases with depth.
The Gales 2017 G. Anderson Waves for Paddlers – slide 4 / 64 Local Motion In A Water Wave
In deep water, waves oscillate in circles. The radius decreases with depth.
The Gales 2017 G. Anderson Waves for Paddlers – slide 4 / 64 Local Motion In A Water Wave
In deep water, waves oscillate in circles. The radius decreases with depth.
The Gales 2017 G. Anderson Waves for Paddlers – slide 4 / 64 Local Motion In A Water Wave
In deep water, waves oscillate in circles. The radius decreases with depth.
The Gales 2017 G. Anderson Waves for Paddlers – slide 4 / 64 Local Motion In A Water Wave
In deep water, waves oscillate in circles. The radius decreases with depth.
The Gales 2017 G. Anderson Waves for Paddlers – slide 4 / 64 The Great Wave The Wave Local Motion In A Water Wave Wavelength & Period, & Height Wavelength (λ) Wave Period (T ) Idealized Wave Spectrum Wavelength & Period, Wave Height Lake Superior Buoy 45004 (2016) & Height Wave Speed & Dispersion Reflection, Refraction & Diffraction Combining Waves Shoaling and Breaking
Group Velocity
Stokes Drift
The Gales 2017 G. Anderson Waves for Paddlers – slide 5 / 64 Wavelength (λ)
Wavelength: the distance over which a periodic wave repeats.
λ Distance 1λ 2λ 3λ λ
The Gales 2017 G. Anderson Waves for Paddlers – slide 6 / 64 Wave Period (T )
Period: the time interval in which a periodic wave repeats.
T Time 1T 2T 3T T
Wave frequency = f =1/T .
The Gales 2017 G. Anderson Waves for Paddlers – slide 7 / 64 Idealized Wave Spectrum
Wave Period Wavelength Cause Capillary < 0.1 s < 0.02 m local wind Chop 1–10 s 1–10 m local wind Swell 10–30 s 102 m distant storms ∼ Seiche 10 m–10 hr 102 km pressure, storm surge ∼ Tsunami 10 60 min submarine disturbance − Tide 12.4, 24.8 hr 103 km Sun, moon ∼
The Gales 2017 G. Anderson Waves for Paddlers – slide 8 / 64 Wave Height
Wave height: The vertical distance from peak to trough.
MWL Height
H . λ/7 (deep water) H . d/1.8 (shallow water)
Amplitude: One half of the Wave Height. The vertical distance from Mean Water Level (MWL) to the peak or trough.
The Gales 2017 G. Anderson Waves for Paddlers – slide 9 / 64 bbbbbbbbbbbbbbbbbb
Lake Superior Buoy 45004 (2016)
water depth = 237 m b 5 b
b b NOAA NDBC b
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b b (m)
b
s 4
b b H
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The Gales 2017 G. Anderson Waves for Paddlers – slide 10 / 64 The Great Wave The Wave Local Motion In A Water Wave Wavelength & Period, & Height Wave Speed & Dispersion Wave Speed Dispersion Wave Speed & Estimating Wave Speeds Wave Speeds in Deep Water Dispersion (d > λ/2) Deep vs Shallow Regimes Reflection, Refraction & Diffraction Combining Waves Shoaling and Breaking
Group Velocity
Stokes Drift
The Gales 2017 G. Anderson Waves for Paddlers – slide 11 / 64 Wave Speed
The phase velocity of the wave satisfies: λ = cT
t =0 x
The Gales 2017 G. Anderson Waves for Paddlers – slide 12 / 64 Wave Speed
The phase velocity of the wave satisfies: λ = cT
t = 1T 8 x
The Gales 2017 G. Anderson Waves for Paddlers – slide 12 / 64 Wave Speed
The phase velocity of the wave satisfies: λ = cT
t = 2T 8 x
The Gales 2017 G. Anderson Waves for Paddlers – slide 12 / 64 Wave Speed
The phase velocity of the wave satisfies: λ = cT
t = 3T 8 x
The Gales 2017 G. Anderson Waves for Paddlers – slide 12 / 64 Wave Speed
The phase velocity of the wave satisfies: λ = cT
t = 4T 8 x
The Gales 2017 G. Anderson Waves for Paddlers – slide 12 / 64 Wave Speed
The phase velocity of the wave satisfies: λ = cT
t = 5T 8 x
The Gales 2017 G. Anderson Waves for Paddlers – slide 12 / 64 Wave Speed
The phase velocity of the wave satisfies: λ = cT
t = 6T 8 x
The Gales 2017 G. Anderson Waves for Paddlers – slide 12 / 64 Wave Speed
The phase velocity of the wave satisfies: λ = cT
t = 7T 8 x
The Gales 2017 G. Anderson Waves for Paddlers – slide 12 / 64 Wave Speed
The phase velocity of the wave satisfies: λ = cT
t = T x
The Gales 2017 G. Anderson Waves for Paddlers – slide 12 / 64 Dispersion
Deep water is dispersive. Wave speed depends on wavelength. In deep water, longer waves move faster than shorter • waves.
slower faster In shallow water, waves travel slower as the depth • decreases.
faster slower
The Gales 2017 G. Anderson Waves for Paddlers – slide 13 / 64 Estimating Wave Speeds
Deep water: 1 • c (6 knots) λ/6(meters) ≈ × (6 knots) √p#boat lengths ≈ × Shallow water: • c (6 knots) d (meters)
1 ≈ × 1m/s 2 knots p The Gales 2017≈ G. Anderson Waves for Paddlers – slide 14 / 64 Wave Speeds in Deep Water (d>λ/2)
Wave speed is proportional to the period T : • c = g T (1.6m/s) T 2π ≈ × 1 seconds (3.0 knots) T ≈ × 1 second To speed you up on a downwind run: • c> 6 knots, T> 2 seconds
“Good” swell for surfing: • T = 10 seconds, c = 30 knots
The Gales 2017 G. Anderson Waves for Paddlers – slide 15 / 64 Deep vs Shallow Regimes
c c c
Vertical scale 2× Wave height 5×
Deep Transition Shallow λ λ λ d>λ/2 20 gλ c = 2 c = √gd q π In the transition zone, c, λ ↓ 1/3.27 ∼ 1/3, v/c ↑ 2 H ↑ 1.28 ∼ 2, and Hλ ↑ 4.18 ∼ 4 The Gales 2017 G. Anderson Waves for Paddlers – slide 16 / 64 The Great Wave The Wave Local Motion In A Water Wave Wavelength & Period, & Height Wave Speed & Dispersion Reflection, Refraction & Reflection, Refraction & Diffraction Reflection A Typical Beach Refraction Diffraction A Beach (seen from above) Huygens’ Principle Diffraction OAS Shoreline Combining Waves Shoaling and Breaking Group Velocity Stokes Drift The Gales 2017 G. Anderson Waves for Paddlers – slide 17 / 64 Wave Reflection Cliff Wave Reflection θ θ Cliff Wave Reflection θ θ Cliff deep Refraction shallow deep Refraction shallow Huygens’ Principle Huygens’ Principle: Every point on a wave front can be considered as a source of tiny wavelets that spread out in the forward direction at the speed of the wave. The new wave front at a later time is the envelope of the individual wavelets. The Gales 2017 G. Anderson Waves for Paddlers – slide 22 / 64 Huygens’ Principle Huygens’ Principle: Every point on a wave front can be considered as a source of tiny wavelets that spread out in the forward direction at the speed of the wave. The new wave front at a later time is the envelope of the individual wavelets. The Gales 2017 G. Anderson Waves for Paddlers – slide 22 / 64 Huygens’ Principle Huygens’ Principle: Every point on a wave front can be considered as a source of tiny wavelets that spread out in the forward direction at the speed of the wave. The new wave front at a later time is the envelope of the individual wavelets. The Gales 2017 G. Anderson Waves for Paddlers – slide 22 / 64 Huygens’ Principle Huygens’ Principle: Every point on a wave front can be considered as a source of tiny wavelets that spread out in the forward direction at the speed of the wave. The new wave front at a later time is the envelope of the individual wavelets. The Gales 2017 G. Anderson Waves for Paddlers – slide 22 / 64 Diffraction Diffraction: The bending of waves around obstacles into the shadow region. The Gales 2017 G. Anderson Waves for Paddlers – slide 23 / 64 Diffraction Diffraction: The bending of waves around obstacles into the shadow region. The Gales 2017 G. Anderson Waves for Paddlers – slide 23 / 64 Diffraction Diffraction: The bending of waves around obstacles into the shadow region. The Gales 2017 G. Anderson Waves for Paddlers – slide 23 / 64 Diffraction Diffraction: The bending of waves around obstacles into the shadow region. The Gales 2017 G. Anderson Waves for Paddlers – slide 23 / 64 Diffraction Diffraction: The bending of waves around obstacles into the shadow region. The Gales 2017 G. Anderson Waves for Paddlers – slide 23 / 64 The Great Wave The Wave Local Motion In A Water Wave Wavelength & Period, & Height Wave Speed & Dispersion Reflection, Refraction & Diffraction Combining Waves Combining Waves Lake Erie Principle of Superposition Constructive Interference Destructive Interference Clapotis Clapotis Harmonic Building Blocks Building Waves with Harmonics Kayak Cresting Wave Tall Waves in Deep Water Tallest Waves in The Gales 2017 G. Anderson Waves for Paddlers – slide 25 / 64 Deep Water Waves on Lake Erie, photo credit: Dave Sandford Waves on Lake Erie, photo credit: Dave Sandford Principle of Superposition Interference: When two waves travel through the same region of space at the same time they interfere. Principle of superposition: The amplitude of the resulting wave is the sum of the amplitudes of the two individual waves. x Amplitude The Gales 2017 G. Anderson Waves for Paddlers – slide 27 / 64 Principle of Superposition Interference: When two waves travel through the same region of space at the same time they interfere. Principle of superposition: The amplitude of the resulting wave is the sum of the amplitudes of the two individual waves. x Amplitude The Gales 2017 G. Anderson Waves for Paddlers – slide 27 / 64 Constructive Interference When peaks and troughs align, waves interfere construtively. A(x,t) = A1(x,t) + A2(x,t) Amplitude The Gales 2017 G. Anderson Waves for Paddlers – slide 28 / 64 Constructive Interference When peaks and troughs align, waves interfere construtively. A(x,t) = A1(x,t) + A2(x,t) Amplitude The Gales 2017 G. Anderson Waves for Paddlers – slide 28 / 64 Destructive Interference When peaks align with troughs, waves interfere destructively. A(x,t) = A1(x,t) + A2(x,t) Amplitude The Gales 2017 G. Anderson Waves for Paddlers – slide 29 / 64 Destructive Interference When peaks align with troughs, waves interfere destructively. A(x,t) = A1(x,t) + A2(x,t) Amplitude The Gales 2017 G. Anderson Waves for Paddlers – slide 29 / 64 Clapotis A standing wave caused by interference between an incident wave and the reflected wave from a nearly vertical shoreline. Full clapotis produces a standing wave which is twice the height of the incident wave. Image Credit: Rob Casey Image Credit: Alec Bloyd-Peshkin The Gales 2017 G. Anderson Waves for Paddlers – slide 30 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Clapotis The Gales 2017 G. Anderson Waves for Paddlers – slide 31 / 64 Harmonic Building Blocks First Harmonic λ1 = Fundamental Second Harmonic 1 λ2 = 2 λ1 Third Harmonic 1 λ3 = 3 λ1 Complicated wave shapes are built by superimposing sines, cosines and their harmonics. The Gales 2017 G. Anderson Waves for Paddlers – slide 32 / 64 Building Waves with Harmonics MWL As waves grow in height, harmonics are produced. Adding these harmonic waves results in waves with sharper crests and flatter troughs. The Gales 2017 G. Anderson Waves for Paddlers – slide 33 / 64 Tall Waves in Deep Water Tall waves in deep water are known as Stokes waves. MWL Figure 1: Linear (Airy) vs. Nonlinear (Stokes) solution for a sur- face wave. Note the steepening of the waves near the peak, and the flattening of the troughs. Vertical scale exagerated 2.5 . × In deep water, the maximum wave height is: H λ/7 max ≈ Whitecaps form when H = Hmax. The Gales 2017 G. Anderson Waves for Paddlers – slide 35 / 64 Tallest Waves in Deep Water x ct 1 η = Aλ cosh − 1 ,A = 1.108 λ − √3 sinh(1/2) ≈ ◦ ◦ 120 H ≈ λ/7 120 λ Maximum steepness: 30◦ • Maximum height: Hmax λ/7 • ≈ Whitecaps form when H = Hmax. • The Gales 2017 G. Anderson Waves for Paddlers – slide 36 / 64 Stokes & Cnoidal Wave Airy (linear) vs Stokes (nonlinear, deep water) H . λ/7 U = 10 Vertical Relief 2× Cnoidal (nonlinear, shallow water) H . d/2 U = 100 Vertical Relief 4× The Gales 2017 G. Anderson Waves for Paddlers – slide 37 / 64 By Michel Griffon - Own work, CC BY 3.0 The Great Wave The Wave Local Motion In A Water Wave Wavelength & Period, & Height Wave Speed & Dispersion Reflection, Refraction & Diffraction Shoaling and Breaking Combining Waves Shoaling and Breaking Breaking Wave Pic Shoaling Breaking Waves Breaking Waves: Two Limits Surfing Three Types of Surf Breaks Point Break Point Break Point Break Reef Break Reef Break The Gales 2017 G. Anderson Waves for Paddlers – slide 39 / 64 Group Velocity Image Credit: Andrew Schmidt Shoaling Waves slow down, decrease in wave- length, and increase in height when entering shallow water. Vertical Scale 3X Wave height 5X λ = cT The Gales 2017 G. Anderson Waves for Paddlers – slide 41 / 64 Breaking Waves As waves enter shallow water they slow down, bunch together, build in height, and break. Breaking conditions: H 1λ (deep water) • ≈ 7 d 1.8H (shallow water) • ≈ Image Credit: Scott Fairty How a wave breaks depends on the wavelength and the steepness of the ocean or lake floor. The Gales 2017 G. Anderson Waves for Paddlers – slide 42 / 64 Breaking Waves: Two Limits Spilling breakers: ocean/lake floor with a gradual slope. • Plunging breakers: ocean/lake floor with a sudden depth • change. Reef, sandbar, ... The Gales 2017 G. Anderson Waves for Paddlers – slide 43 / 64 Three Types of Surf Breaks Beach Break Waves breaking in shallow water on a sandy bottom. Big storms can move sand and change these breaks. e.g., Trestles in California. Point Break A surf break where diffraction amplifies waves at headlands. Wave refraction can give you long runs. e.g., Rincon in California. Reef Break Shallow reefs, typically farther offshore than other breaks and the surrounding water is deeper. e.g., The Pipelien in Hawaii. The Gales 2017 G. Anderson Waves for Paddlers – slide 45 / 64 Rincon Point, California Kuda Huraa, Maldives The Trestles, Orange County Waves breaking on the Great Mesoamerican Reef, c Mike Beck, the Nature Conservancy Reef Break, Brazil The Great Wave The Wave Local Motion In A Water Wave Wavelength & Period, & Height Wave Speed & Dispersion Reflection, Refraction & Diffraction Group Velocity Combining Waves Shoaling and Breaking Group Velocity Wave Sets and Group Velocity Surfing Sorted Waves Phase and Group Velocity Waikiki Beach Regimes Stokes Drift The Gales 2017 G. Anderson Waves for Paddlers – slide 51 / 64 Wave Sets and Group Velocity Why do waves come in sets? • How can understanding group velocity make me • a better paddler in the surf zone? The Gales 2017 G. Anderson Waves for Paddlers – slide 52 / 64 Sorted Waves When waves arrive from distant storms, dispersion sorts them into groups of waves with similiar wavelengths. shorter, longer, ← storm slower faster waves waves Long sorted waves, free of chop, are known as swell. The Gales 2017 G. Anderson Waves for Paddlers – slide 54 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Phase and Group Velocity The Gales 2017 G. Anderson Waves for Paddlers – slide 55 / 64 Regimes 1.0 = Hλ <–dispersive non-dispersive–> U d3 ) 0.8 Waves Break! Williams/Fenton H/d 0.6 Nelson H/d = 0.55 b b 7 U U / = 25 = 40 0.4 = 1 H/λ StokesTheory CnoidalTheory 0.2 Wave height/depth ( 0 vg 3 0 Deep = 1 Very Shallow 2 10 vp 4 10 10 Wavelength/depth (λ/d) The Gales 2017 G. Anderson Waves for Paddlers – slide 57 / 64 The Great Wave The Wave Local Motion In A Water Wave Wavelength & Period, & Height Wave Speed & Dispersion Reflection, Refraction & Diffraction Stokes Drift Combining Waves Shoaling and Breaking Group Velocity Stokes Drift Driftwood Local Motion In A Water Wave Stokes Drift Stokes Drift Ratio of Stokes Drift to Wave Speed Video Clips The Gales 2017 G. Anderson Waves for Paddlers – slide 58 / 64 Local Motion In A Water Wave In deep water, waves oscillate in circles. The radius decreases with depth. The Gales 2017 G. Anderson Waves for Paddlers – slide 60 / 64 Local Motion In A Water Wave In deep water, waves oscillate in circles. The radius decreases with depth. The Gales 2017 G. Anderson Waves for Paddlers – slide 60 / 64 Local Motion In A Water Wave In deep water, waves oscillate in circles. The radius decreases with depth. The Gales 2017 G. Anderson Waves for Paddlers – slide 60 / 64 Local Motion In A Water Wave In deep water, waves oscillate in circles. The radius decreases with depth. The Gales 2017 G. Anderson Waves for Paddlers – slide 60 / 64 Local Motion In A Water Wave In deep water, waves oscillate in circles. The radius decreases with depth. The Gales 2017 G. Anderson Waves for Paddlers – slide 60 / 64 Local Motion In A Water Wave In deep water, waves oscillate in circles. The radius decreases with depth. The Gales 2017 G. Anderson Waves for Paddlers – slide 60 / 64 Local Motion In A Water Wave In deep water, waves oscillate in circles. The radius decreases with depth. The Gales 2017 G. Anderson Waves for Paddlers – slide 60 / 64 Local Motion In A Water Wave In deep water, waves oscillate in circles. The radius decreases with depth. The Gales 2017 G. Anderson Waves for Paddlers – slide 60 / 64 Local Motion In A Water Wave In deep water, waves oscillate in circles. The radius decreases with depth. The Gales 2017 G. Anderson Waves for Paddlers – slide 60 / 64 Stokes Drift Larger circles above • Smaller circles below • Net motion to the right The• Gales 2017 G. Anderson Waves for Paddlers – slide 61 / 64 Stokes Drift The Gales 2017 G. Anderson Waves for Paddlers – slide 62 / 64 Deep Water Animation: Deep Water Ratio of Stokes Drift to Wave Speed 0.20 2 πH 4πz/λ Stokes 7 uL/v e ≈ λ λ/ 0.15 ∼ 2 H πH cosh 2kd uL/v 2 sinh2 2 λ kd = d/ ≈ H 1 0.10 ≫ dk shallow breaking wave 0.05 Cnoidal Deep water Steep breaking surf Stokes drift/wave speed 0 0 0.05 0.10 0.15 wave height/wavelength Example: Ten second swell in deep water (λ 156 m, Hmax 22 m), ≈ ≤ T v (3 knots) 30 knots ≈ seconds ≈ The Gales 2017 G. Anderson Waves for Paddlers – slide 63 / 64 Video Clips Breaking wave video: Side view. • Breaking wave video: From below. • FloWave Exhibition • Standing Waves • The Gales 2017 G. Anderson Waves for Paddlers – slide 64 / 64