Wave Shoaling Schematic

Changes that occur when a wave shoals (moves into shallow water):

In deep water = profile of swell is nearly sinusoidal.

Enter shallow water, waves undergo a systematic transformation.

Wave velocity and wave length decrease while the wave height increases.

Only wave period remains constant.

Wave Shoaling – L & C

Deep water - L, C depend only on period

Shallow water - L, C depend only on the water depth

Summarize regions of applications of approximations

Behavior of normalized variables.

PinPoutOutside the surf zone

Pin = Pout Wave energy flux is conserved

Ecn = constantEcn = E∞c∞n∞

∞=((1/2n)(C ∞ /C))1/2

Wave Shoaling – H

Explains why orthogonally directed waves increase height during shoaling

Direct compensation for slowing of individual waves and need to maintain constant wave energy flux

Waves convert a significant fraction of their kinetic energy to potential energy

Wave Shoaling – Steepness (H/L)

Straightforward consequence of combined shoaling behavior of H & L.

Steepness initially decreases upon entry to intermediate water depth, then rapidly increases until instability condition associated with wave breaking.

Wave Refraction Photos

Wave Refraction: Wave Crests vs. Wave Rays

Wave crests are the line segments that connect the peaks (or troughs) of a wave field. The crests are visible to the observer.

Wave rays are the lines orthogonal (perpendicular) to the wave crests, which represent the direction of wave propagation

Wave Refraction Wave Refraction - Point Reyes

c = (gh)1/2

Snell’s Law

)sin()sin(

)sin()sin(

2

2

1

1

∞∞

=

=

αα

αα

cc

cc

Wave Refraction

Wave Refraction: Energy flux per unit length of wave crest

Energy flux per unit length of wave crest is not necessarily conserved

Can lead to a decrease in wave height during the shoaling and refraction process.

Wave Refraction - La Jolla Canyon

2211)()( sEnCsEnC =

2/12/1

2

1⎥⎦⎤

⎢⎣⎡

⎥⎦⎤

⎢⎣⎡=

∞∞∞

ss

cc

nHH

€

Kr =s∞

s

⎡ ⎣ ⎢

⎤ ⎦ ⎥

1/ 2

€

=cos(α ∞)

cos(α )

⎡

⎣ ⎢ ⎤

⎦ ⎥

1/ 2

Combined Refraction and Shoaling

Effect of Shoaling

H = 2 mT = 10 sothogonal angle of incidence

Effect of Shoaling and Refraction

H = 2 mT = 10 s

compare:orthogonal wave vs. refracting wave

Modeling refraction - wave rays

H = 2 mT = 10 sα= 270˚

Modeling refraction - wave rays - double period

H = 2 mT = 20 sα= 270˚

bathymetry (in feet) focusing waves

“Jaws” Surfing Reef, Maui

Model simulations of individual waves - not time averaged.

Wave Diffraction

Lateral translation of energy along a wave crest.

Most noticeable where a barrier interrupts a wave train creating a "shadow zone". Energy leaks along wave crests into the shadow zone.

Also by analogy to light, Huygen's Principle explains the physics of diffraction through a superposition of point sources along the wave crest.

Wave Diffraction- Barcelona

Modeling with SWANRef/Diff numerical simulation of shoaling and refraction - monochromatic (not spectral - boo.)

SWAN - used here at UF (spectral - yay.)