Review. Oceanography Lecture 7. We have to continually be jumping off cliffs and developing our wings on the way down Kurt Vonnegut

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We ave to continually be jumping off cliffs and developing our wings on te way down Kurt Vonnegut Beware of te man wo works ard to learn someting, learns it, and finds imself no wiser tan before.

1 We ave to continually be jumping off cliffs and developing our wings on te way down Kurt Vonnegut Beware of te man wo works ard to learn someting, learns it, and finds imself no wiser tan before. [ ][ ] He is full of murderous resentment of people wo are ignorant witout aving come by teir ignorance te ard way. Kurt Vonnegut, "at's radle" Oceanograpy Lecture 7 Te surface of te Ocean: 1) Waves 1. Review. Waves: b. Wave motion: speed and energy c. Deep- & Sallow-water waves Review a. Introduction! Sediments are produced by te weatering (cemical and mecanical breaking down) of rocks into particles tat are ten moved by air, water, and ice.! Sediments can also be formed from te accumulation of sells or micro- and macro-debris of organisms.! Sediments can terefore consist of " Mineral particles " Fossil particles b. lassification: Sediments can be subdivided on te basis of:! Te size of te particles (grain( size)! Teir mode of formation (origin( origin)! Terrigenous sediments! Biogenous sediments! Autigenic sediments! Volcanic sediments! osmogenous sediments Review c. Factors tat control sedimentation! Relationsip between average grain size and energy of bottom currents! Erosion, Transport and Deposition (sedimentation) depend on velocity of current and grain size! Settling rate of suspended particles varies wit diameter (Stokes Law) d. Sedimentation in te Oceans Two major areas of sediment deposition on te basis of water dept i. Self sedimentation: : Sallow, close to terrigenous source (teoretical equilibrium) ii. Deep-Sea Sedimentation Two main sources: - External (terrigenous( mud and sand) - Internal (biogenic( particles, autigenic particles) Tree categories: - Bulk emplacement - Pelagic sediments - Autigenic sediments

A wave can be regarded initially as an ideal a sinusoidal wave (tou te ideal regular waves bears little resemblance to real waves observed at sea # irregular in form and

ydrological cycle A aracteristics: H: Heit ( x A) L: Wavelengt (from crest to crest) T: Period (time required for two successive crests to pass a point) : Dept of water

Ideal waves: : If some water is lifted up and allowed to fall back Sea level cange # Oscillation due to geological canges in te under te action of gravity, its inertia will

2 A wave can be regarded initially as an ideal a sinusoidal wave (tou te ideal regular waves bears little resemblance to real waves observed at sea # irregular in form and period) Sea level oncept of level: Geoid # level surface on wic te potential energy is everywere te same Sea level cange # Oscillation due to geological canges in te ydrological cycle A aracteristics: H: Heit ( x A) L: Wavelengt (from crest to crest) T: Period (time required for two successive crests to pass a point) : Dept of water column below mean surface level Adapted from Pinet 000 Sea level cange a. Ideal waves: : If some water is lifted up and allowed to fall back Sea level cange # Oscillation due to geological canges in te under te action of gravity, its inertia will cause it to oversoot ydrological cycle te equilibrium position. Pressure forces will ten pus it back up and oscillation will ensue. Energy can be transmitted at te interface (boundary) between two fluids of different densities resulting in progressive orbital waves Adapted from Garrison 00

regarded as! Progressive waves,, in tat energy is travelling trou, or across te surface of, te material (i.e. water)! Standing waves (i.e. plucked guitar strings) considered as te sum of two

3 All waves can be regarded as! Progressive waves,, in tat energy is travelling trou, or across te surface of, te material (i.e. water)! Standing waves (i.e. plucked guitar strings) can be considered as te sum of two progressive waves of equal dimensions but traveling in opposite direction (later ) Waves can result from periodic and non-periodic disturbance of te water surface: In te case of non-periodic disturbances, te water particles are displaced from an equilibrium position # restoring force acts to bring back equilibrium to te system ( flat( flat water level): " Gravitational force exerted by Eart " Surface tension (tendency of water molecules to stick togeter and present te smallest possible surface to te air) Water waves are affected by bot of tese forces: # Wen L! 1.7 cm # capillary waves # Wen L > 1.7 cm # gravity waves (main interest of oceanograpy!) A few waves: A case of temporal- and spatial-scales Waves are classified according to teir wave period Wind waves: As te wind blows # formation of ripples (capillary waves) As te wind increases in speed # waves become larger (gravity waves) Variety and size of wind-generated waves are controlled by four principal factors: Wind velocity Wind duration Unobstructed distance over wic wind blows (fetc) Original sea state a.anatomy of a wave Te ideal relationsip among wave properties. If one caracteristic can be measured, te oter two can be calculated.

ausing factors: Te relationsip is a direct one Wind Speed (km/) Fetc (km) Duration () Wave Heit (m) Wave Lengt (m) Wave Period (s) 0 5.8 0.33 10.6 3. 30 77 7 0.88. 4.6 60 660 7.5 5.1 89. 9.

4 ausing factors: Te relationsip is a direct one Wind Speed (km/) Fetc (km) Duration () Wave Heit (m) Wave Lengt (m) Wave Period (s) Altou te relationsip is a direct one One condition will always be limiting as to te maximum development of wave eit and period! e.g. Wind Speed: 30 kn Fetc: 00 nm Time: 40 rs H ~ 7 m T ~ 1 sec b. Wave motion: Speed and energy Tere are matematical relationsips linking te caracteristics of wavelengt (L), wave period (T) and wave eit (H) to wave speed and to wave energy. Wave speed (celerity) # speed = distance/time = L/T (time one wavelengt takes to pass a certain point) c. Wave motion: Speed Approximations 1) For > L/ (L < ) # Deep-water waves If x is larger tan ",, ten tan x ~ 1 tan ("/L) = 1 (witin 0.5%) gl tan(! )! L Wave speed can also be represented by te equation: gl tan(! )! L Were:! g = acceleration due to gravity! L = Wavelengt! tan = yperbolic tangent! = water dept gl or 1.5L! gt " or 1.56T Wavelengt (or period) is te only variable affecting te wave speed!

5 b. Wave motion: Speed Approximations 1) For > L/ # Deep-water waves c. Wave motion: Speed Approximations ) For < L/0 (L > 0) # Sallow-water waves If x is small, ten tan x ~ x tan ("/L) = ("/L) (witin 3%) gl tan(! )! L or 3.1 ircular motion of particles # Exponential decrease of pat wit dept! Te cange in pressure ( size( size of te orbit) is undetectable at a water dept! L/ (te wave base ) Or: = L/T = (( ) 1/ # L = 3.13 () 1/.T Te water dept is te only variable affecting te wave speed! b. Wave motion: Speed Approximations ) For < L/0 # Sallow-water waves c. Wave motion: Speed Approximations 1) For > L/ # Deep-water waves (L < ) ) For < L/0 # Sallow-water waves (L > 0) 3) For L/0<<L/ ( < L < 0) Elliptical motion of particles Exponential decrease of vertical pat wit dept Not of orizontal pat!

c. Wave motion: Speed Approximations Deep-water waves tat ave te longest wavelengt and greatest period, will arrive first in regions distant from te storm wic generated tem: Te separation of waves by

Wave motion: Group Speed Individual waves do not persist for long in te open Ocean. Tey usually only exist for as long as tey take to pass trou a group of waves. c.

6 c. Wave motion: Speed Approximations Deep-water waves tat ave te longest wavelengt and greatest period, will arrive first in regions distant from te storm wic generated tem: Te separation of waves by virtue of teir differing rates of travel (speed) is known as dispersion. For > L/ (L < ) # Deep-water waves gl! or 1.5L c. Wave motion: Group Speed Individual waves do not persist for long in te open Ocean. Tey usually only exist for as long as tey take to pass trou a group of waves. c. Wave motion: Group Speed Individual waves do not persist for long in te open Ocean. Tey usually only exist for as long as tey take to pass trou a group of waves. i.e. two sets of waves: in pase and out of pase If two sets of waves are interfering to produce a succession of wave groups, te group speed ( g ) is: 1x g = 1 + g = g = c. Wave motion: Speed Approximations Assume You ave a storm blowing at 30 knots (nautical mile = km) over a fetc of 100 nautical miles for 10 ours. 1) Wat is te longest wave period generated by te storm? ~ 7 seconds ) Wat is te longest wavelengt of te waves generated by te storm? 76.4 m 3) Wen will te energy of te waves reac a boat tat is 500 nautical miles away? ~5 rs

c. Wave motion: Group Speed Wave energy travels at te group speed (not at te pase speed of individual waves) g = p / For

) Examples: g = p 1) Mid-oceanic swell: > 3000 m; L = 10 m # L < p = 13.

Tsunamis Seismic waves created by sudden movements of te Eart s crust (Eartquake), volcanic activity, or mudslide event #

Sallow-water wave p = 3) Tsunamis reacing te coast: = 4000m; L = 00 km # L > 0 p = 00 m/s ( g = p # te energy is in te wave)

Te strongest eartquake measured 9.0 magnitude and is te fourt strongest tis century.

7 c. Wave motion: Group Speed Wave energy travels at te group speed (not at te pase speed of individual waves) g = p / For sallow-water waves te group speed (energy) is te same as te pase speed (te energy is in te wave!) Examples: g = p 1) Mid-oceanic swell: > 3000 m; L = 10 m # L < p = 13.7 m/s ) Mid-oceanic swell reacing te coast: = 5m # L > 0 p = 7 m/s d. Tsunamis Seismic waves created by sudden movements of te Eart s crust (Eartquake), volcanic activity, or mudslide event # disturbance of te wole water column! Sallow-water wave p = 3) Tsunamis reacing te coast: = 4000m; L = 00 km # L > 0 p = 00 m/s ( g = p # te energy is in te wave) Sumatra Tsunami On December 5, 004, a series of about 15 eartquakes occurred one after anoter along te west coast of Sumatra. Te strongest eartquake measured 9.0 magnitude and is te fourt strongest tis century. urrent estimates put te deat toll at about 34,000. Millions more are at risk from disease and starvation Bay of Bengal/ Indian Ocean littoral regions of Indonesia, Malaysia, Tailand, Myanmar, Banglades, India, Sri Lanka and Maldives. e. Refraction Refraction of waves in progressively soaling waters can be described by a relationsip similar to Snell s law (refraction of lit) Sallow-water wave 1 = 1 = 1 = 1

f. Breaking waves As a wave nears te sore, only te period remains constant!

constant! To conserve te wave energy # te amplitude increases until A > 0.35 L g.

Te water oscillates back and fort about a fixed point: Node.

8 f. Breaking waves As a wave nears te sore, only te period remains constant! Sallow-water wave T = Since is directly proportional to (() 1/ ) As decreases # decreases (so will L) to maintain T constant! To conserve te wave energy # te amplitude increases until A > 0.35 L g. Standing waves (Resonance) Standing waves do not move orizontally but remain stationary (Guitar string). Te water oscillates back and fort about a fixed point: Node. Te properties of a standing wave depend on te geometry of te basin. Te larger te container, te longer its caracteristic standing wave will take to oscillate. In an open basin (seice), L 4l 4l T p = = = #!" T = #!" l = T T 4 Tides (ap. 9) For Next Time

Chapter 10 Waves. wave energy NOT the water particles moves across the surface of the sea. wave form moves and with it, energy is transmitted

Chapter 10 Waves. wave energy NOT the water particles moves across the surface of the sea. wave form moves and with it, energy is transmitted Capillary Waves, Wind Waves, Chapter 10 Waves Anatomy of a Wave more like a real wave Tsunamis, Internal waves big waves huge waves rogue waves small waves more like a sine wave Wave direction Wave wave