Ocean Waves

- what is a wave?

- wave characteristics

- ocean surface gravity waves

Geography 104 - “Physical Geography of the World’s Oceans”

Readings (Ocean Waves):Text Chapter 10 (pgs 190 - 217)Reader pgs. 231 – 242 (wave related material)

What is a wave?“In its simplest scientific form, a wave is

an expression of the movement or progression of energy through a medium.” (Chamberlin and Dickey)

“A wave is a disturbance that propagates through space and time usually with transference of energy.” (Wikipedia)

Ocean Wave Characteristics- propagating disturbance

- characteristic length scale (wavelength)

- characteristic time scale (period)

- low frictional losses – thus able to travel long distances

- energy transport (not water transport like currents*)

- oscillatory (or cyclical) flow

- weak interaction with other waves

- movement depends on wave period and water depth

- many types of waves in the ocean

Types of ocean surface waves- waves need a generating mechanism, and a restoring force

- at ocean surface, disturbing force is wind

- capillary waves (wavelengths < ~1cm) are restored primarily by surface tension (of interest for remote sensing of the ocean)

- surface gravity waves exist at air-sea interface and are restored by gravity

- internal gravity waves (not wind driven) exist at density interfaces beneath the ocean’s surface and are restored by gravity

internal and surface waves

internal waves from space

Fig. 10.6

Types of wave motion- progressive waves oscillate uniformly and

travel (progress) without breaking

particles move back and forth in direction of wave motion; examples: sound waves, pressure waves

particles move back and forth in direction perpendicular to wave motion; occurs primarily in solids

particles move in “orbitals” with both “back-and-forth” and “side-to-side” movement; need interface to exist; surface gravity waves

Fig. 10.9

ocean surface waves

wave crests

wave crest

wavelength

wavelength

wave movement

90°

motio

n of w

ave crests

changing wave crests

Fig. 10.4

Fig. 10.5

Definitions: (do on board)- crest- trough- amplitude- height- wavelength- wave period- wave frequency- wave steepness- phase speed (Equation 10.1)

Ocean Waves (con’t)

- wave (phase) speed of deep, intermediate, and shallow water waves

- Stokes drift or wave drift

- group speed (1/2 the phase speed in deep water)

- wave generation (should have been #1)

- wave interference (should have been #2)

- dispersion

Geography 104 - “Physical Geography of the World’s Oceans”

Readings (Ocean Waves):Text Chapter 10 (pgs 190 - 217)Reader pgs. 231 – 242 (wave related material)

wave speed depends on water depth (h) relative to wavelength (L)

deep water: h > 0.5Lspeed determined by L or T (not h); cg = 0.5c

shallow water: h < 0.05Lspeed determined by h (not L,T); cg = c

intermediate water: 0.05L < h < 0.5Lspeed determined by h and L or T;

most surface gravity waves near shore are in intermediate water depths (more complicated math)for L = 220 m (T = 12 sec.) h between 11 -> 110 m

tanh (“tanch”) hyperbolic tangent function

x < 0.5 tanh(x) = x

x > ~2 tanh(x) = 1

wave speed vs. water depth

c =√(gL/2π) tanh(2πh/L)

L

= √gL/2π

wave speed for various wavelengths and water depths

deep water waves

L/2

- little motion below depth = 0.5L - orbit diameters decrease rapidly with depth to ~4% of surface

orbit diameter at surface = H

- phase speed = c = (gL/2π)1/2

- depth condition: h > 0.5L or L/2

shallow water waves

- phase speed = c =√g h- depth condition: h < 0.05L or L/20

- phase speed = c =√(gL/2π) tanh(2πh/L)- depth condition: L/20 < h < L/2

intermediate or transitional waves

Stokes Drift or Wave Drift – slight movement of water in the direction of wave propagation due to wave orbitals that are not exactly closed. Greatest near surface where orbital diameters are largest.

group velocity cg - deep water

waves travel in “trains”

individual waves in front of train constantly die, and are replaced by new waves at rear of train

crests appearat rear of group

crests disappearat front of group

group velocity cg - deep water

crests appearat rear of group

crests disappearat front of group

cg = group speed = ½ c

c = speed of individual wave

cg = group speed = ½ c

Fig. 10.18movement of individual waves through a wave group can be observed by throwing a rock in a still pond

wave development and evolution

surface gravity waves are generated by wind

wave generation is typically in deep water

wave spectrum

wave height is controlled by three factors:- wind speed- duration (length of time wind blows)- fetch (length of ocean over which the wind blows)

fully developed sea - result of sustained winds over a fetch- energy input by wind is lost by wave breaking (some energy into surface current generation) and propagation of energy from the region of generation

wave formation - fully developed sea

wind

time increasing

fully developed sea:energy input of wind = energy loss by breaking & wave propagation away from storm center

Fig. 10.16

fully developed sea when wave steepness exceeds 1/7 (H/L)

as wind blows wave steepness changes

Fully developed sea

Wave conditions in storm center

Fig. 10.17

wave energy exists in various frequencies (waves of varying periods) as wind is not constant

wave interference & the sea surface

wave interference & the sea surface

wave interference & the sea surface

sea surface profile

Fig. 10.11.a

wave interference

two wave trains - different wavelengths & heights

Fig. 10.11

idea of wave energy spectrum: waves of different characteristics (L,T,f) all exist at once

wave energy and direction spectra from data at Harvest platform (SBC)

Energy ~ H2

Fig. 10.19

wave generation by wind

dispersion – waves with longer T and L will travel faster. Dispersion is the separation of waves that travel with different speeds.

waves approaching Southern California coast

period (s)

waveht. (ft)

Surfline wave model on web

waves approaching Southern California coast

waveht. (ft)

Surfline wave model on web

wave rays

wind product used to force the Surfline wave model

Global distribution of wave height

Wave Refraction and Focusing

wave refraction – bending of a wave in response to its non-uniform encounter of shallow water

wave refraction causes wave crests to align with lines of constant water depth (isobaths) and can alter the distribution of energy along a wave

wave focusing – convergence of wave energy

wave refraction

wave refraction

wav

e ra

ys

surf zone

wave refraction: headlands and embayments

wave rays

wave refraction: headlands and embayments

wave rays

equal energy offshore

wave refraction: headlands and embayments

wave rays

lower wave energy

equal energy offshore

wave refraction: headlands and embayments

wave rays

lower wave energy

higher wave energy

equal energy offshore

Fig. 10.21

Wave Reflection

wave reflection – when a wave encounters a vertical boundary it is reflected

wave reflection, when combined with energy of the non-reflected wave can significantly increase wave height

Fig. 10.22

wave reflection off a jetty toward the beach

wave reflection: “The Wedge”

The Wedge, Newport Harbor

Wave Diffraction

wave diffraction – transfer of energy laterally along the crest of a wave

can result in dramatic change in wave direction

Fig. 10.23

wave diffraction at the end of jetty

lateral energy transfer

modeling wave refraction in Southern California

wave breaking

- winds constantly add wave energy to the ocean- but, ocean wave energy doesn’t increase continuously- wave breaking is the mechanism to remove wave energy- formally, wave breaking is dissipation of energy- wave breaking -> turbulence -> heat- wave breaking occurs when depth is sufficiently shallow- region of wave breaking is called the surf zone

wave breaking

c = sqrt(gh) in shallow water ; c = L/T for all waves

1) as h decreases, c decreases, L decreases, H increases2) H/L (steepness) increases3) breaking when H/L ≥ 1/7

wave breaking criteria: 1. steepness is large – H/L ≥ 1/7 2. or, depth is shallow – h ≤ 1.3 H

(crests move faster than troughs)

plunging breakers – steep beach for abrupt change in c

wave breaking

wave breaking – rip current

a net onshore transport of water occurs in the surf zone- crests moving faster than troughs- white water from breaking waves

net shoreward flow must be balanced

tsunamis

tsunami - Japanese word translates to “harbor wave”

Great Wave off the Coast of Kanagawa, by HokusaiImage often used in tsunami literature is misleading as tsunamis don’t typically manifest themselves as large breaking waves

tsunamis

- an extreme shallow water wave- caused by vertical displacement of the seafloor - not “tidal waves” as often assumed

tsunamis

- tsunami wavelength, L = ~200 km- L / 20 = 10 km- average ocean depth, h = ~4 km- h < L/20 => shallow water waves

- tsunami wave speed c = sqrt(gh) = ~200 m/s = 447 mph

- tsunami period, L/c = ~1000 sec = 16.67 minutes

- tsunami amplitudes (typically a few meters)

- tsunamis are highly energetic because L is large- tsunami “run-up” (decreasing h) causes damage

2004 Sumatra Tsunami

- magnitude ~9.2, the second largest earthquake ever recorded on a seismograph had the longest duration of faulting ever observed, between 8.3 and 10 minutes. It caused the entire planet to vibrate as much as 1 cm (0.5 inches) and triggered other earthquakes as far away as Alaska.

- sudden vertical rise of the seafloor by several meters displaced massive volumes of water, resulting in a tsunami

- the total energy of the tsunami waves equivalent to ~20x1015 joules

receding water (wave trough) of tsunami

Readings (Ocean Waves):Text Chapter 10 (pgs 190 - 217)Reader pgs. 231 – 242 (wave related material)