Waves and Nearshore Circulation

Waves

wave number wave angular frequency

wave steepness relative water depth

Dispersion Relationship

Wave length decreases with decreasing depth

Approximate solution of Fenton & McKee

Go to Wave Calculator

Orbital Motions of Waves

Velocity Profiles

Wave Energy and Energy Flux

Wave Energy Flux

Dynamic Pressure

Look at another bunch of calculators, including wave particle motions

Wave Shoaling

12

Shoaling

Shoaling Coefficient, Ks

Wave Refraction

Where is crest?What are arrows?

Planform

Refraction

Refraction

Wave Diffraction

Calculable: Mathematically; parabolic modeling includes depth changes

Huygen’s Principle

Diffraction Diagram

Wave Breaking

Wave Models

REF/DIF (Kirby & Dalrymple)

RCPWAVE (Ebersole)

CGWave (Panchang)

FUNWAVE (Wei & Kirby)

SWAN (Holthuijsen)

WAVEWATCH III (Tolman)

Breaker Types

Surf Similarity Parameter

Dally, Dean, Dalrymple (1985)

Breaking Waves and Turbulence

Matsunaga (1994), Li and Dalrymple (1998)

Low Frequency Motions: Surf Beat

cross-shore motion only

Linearized long wave equations

cross-differentiate:

For h=m x

Edge Waves: alongshore dependency

Laguerre Polynomials

Edge Waves

Field Observations

Huntley, Guza, Thornton (1981)

Rip Currents, Tang and Dalrymple (1985)

Mean Quantities

Time Average

Depth Average

Depth and Time Average

equal to 0?

Mass Flux

H= 1 m, T= 6 s, h = 5 mE= 1090, C= 6.35, M=171 kg/m-sec

Momentum Flux

caligraphic M, not M (momentum, not mass)

Set-down and Set-up

offshore

inshore

Nearshore Circulation

Numerical models of these equations exist:

SHORECIRC (U Del)

Longshore Current

Longuet-Higgins (1970)

with mixing

Shear Waves

Ozkan-Haller and Kirby, 1999

Oltman-Shay, Howd, Birkemeier, 1989

Boussinesq ModelsSorenson et al. (1998) noticed that wave model

predicted currents

Chen et al. (1999)Haller’s rip current test

Variation in longshore wave height

Rip Currents

Simple Model of Rip Current

sand bar

rip rip incident waves

Dalrymple, 1978

Rip Current Types

Wright & Short,1984

Wright & Short,1984

Palm Beach,AustraliaArgus images

(Ranasinghe et al. 2004)

FUNWAVE: CUSPS

FUNWAVE: Hole

Synchonous Intersecting Wave Trains