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Welcome to Geosc040, March 31; Lecture 21
Waves, Tsunami & Tides
Pontoon
Little Big town
Sea of Love
The National
Waterfalls
TLC
Swim
Jack's Mannequin
Thanks to Roman K & Kierstin E.
• Quiz 2 April 13. Calculators will be provided –but I
doubt you’ll need one
• On-line Assignments 10 and 11 due next week.
• Extra Credit Letter accepted until 11pm April 6
Read about the Ocean
My Job in Geosc040
100 Thomas is a big room. Talking is distracting to
your neighbors…
Don’t chat during lecture slides
Wait for clicker questions
Wind Generates Ocean Waves
Capillary waves become gravity waves as their wavelength exceeds 1.74
centimeters. These wind-induced gravity waves (wind waves) continue to
grow as long as the wind above them exceeds their speed.
Wind Waves
• Waves “break” when
oversteepened, thus the
“whitecaps” observed in
strongly wind-driven seas
• Observations suggest
that maximum wind waves
have L ≈ 800 meters; this
is equivalent to T of nearly
23 sec and S about 36
m/sec (or 130 km/hr).
Whew!!
--the highest, confirmed windwave height is about 34
meters!! Ugh!
Three Main Factors in Wave Generation by Wind
•1) Wind strength
(avg. or persistent wind velocity)
•2) Wind duration
(time that wind blows in one general direction)
•3) Fetch
(distance
over which
wind blows
uninterrupte
d in one
direction)
w
L
SWL
c
S
SWL
n
Wave
Definitions
H
d
DEFINITIONS
L= wavelength [meters]
S= Wave speed
[meters/sec]
T= wave period, time for
one wavelength to
pass [seconds]
d= water depth [meters]
Wavelength L
For deep water waves, we can describe the
relationship between wave length, wave
period and wave speed. We need to use a
few simple equations.
1) S = L / T, 2) S = 1.56 T, 3) L =1.56 T2
(S is speed in m/s, T is period in sec, and L is wavelength in m.)
Wave size and period. What happens at the beach?
Are waves all the same or is there a big one every
so often?
At a typical beach, say
along the outer banks,
this is what the wave
heights look like in a day
At a typical beach, say
along the outer banks,
this is what the wave
heights look like in a day
Wave height at
the beach
Most waves have a period
between 1 and 10 seconds
For deep water waves, that
means a speed between
1.56 m/s and 15.6 m/s
Recall: S = 1.56 T
Today’s Clicker Questions
A. I will receive full credit for answering 80% or more of the questions
B. I will receive no credit if I answer less than 80% of the questions
C. If there are 10 questions and I answer at least 8 of them I’ll get
full credit for today (100%); If I answer 7 or fewer questions, I will
receive no credit for today.
D. If I answer the question correctly I’ll get a bonus point, up to a
maximum of 105% for today’s in-class exercise
E. All of the above (this is the correct answer, choose E!)
Extra credit letters are worth up to 5% of my final course
grade, and:
A. are due Apr 6th and will be subject to electronic plagiarism
checking via Turnitin.psu.com. Letters will be checked
against everything on the web and previous papers
submitted for this and other classes
B. must be submitted as a file named with MY NAME. For
example if my name were Jane Doe, myfile would be
named: DoeJane_geosc040.docx or DoeJane_geosc040.pdf
C. are submitted via Angel Dropbox by uploading my file. I
will not copy the text of my letter and paste it into the
Angel page.
D. All of the above
E. I do not intend to submit an Extra Credit Letter
Wave Diffraction
Waves bend!
Diffraction
Wave Interference
Waves can “interfere” with one another
Constructive interference means that waves interact to build crests or
troughs higher or deeper than those of the original waves
Destructive interference means that waves cancel one another out
Such interactions produce characteristic patterns or “beats” --every fourth,
fifth, sixth (etc.) wave is larger than the other waves in the group. Surfers
learn how to capitalize on these patterns
Wave Interference
This has a really cool analog in sound and acoustics
https://academo.org/demos/waveinterference-beat-frequency/
Wave Interference
Waves can “interfere” with one another
Constructive interference means that waves interact to build crests or
troughs higher or deeper than those of the original waves
Destructive interference means that waves cancel one another out
Such interactions produce characteristic patterns or “beats” --every fourth,
fifth, sixth (etc.) wave is larger than the other waves in the group. Surfers
learn how to capitalize on these patterns
Wave Interference
Waves can “interfere” with one another
Constructive interference means that waves interact to build crests or
troughs higher or deeper than those of the original waves
Destructive interference means that waves cancel one another out
Such interactions produce characteristic patterns or “beats” --every fourth,
fifth, sixth (etc.) wave is larger than the other waves in the group. Surfers
learn how to capitalize on these patterns
Wave Diffraction
Three Main Factors in Wave Generation by Wind
•1) Wind strength
(avg. or persistent wind velocity)
•2) Wind duration
(time that wind blows in one general direction)
•3) Fetch
(distance
over which
wind blows
uninterrupte
d in one
direction)
Wave Generation by Wind
How Big is Big?
• Steepness of a wave flank does not exceed about 120 degrees
• A “rule of thumb”: H/L is a ratio of 1/7 (remember this!)
• A wave with L=156 m in our example above can have H≤22 m!
Wavelength L
Wave Height H
Wave Generation by Wind
How Big is Big?
• Steepness of a wave flank does not exceed about 120 degrees
• A “rule of thumb”: H/L is a ratio of 1/7 (remember this!)
• A wave with L=156 m in our example above can have H≤22 m!
Wavelength L
Wave Height H
Wind Waves
• Waves “break”
when oversteepened,
thus the
“whitecaps”
observed in strongly
wind-driven seas
Big Waves Travel in
Packs!
Wave Train
Swells: An example
of long-period
swells outrunning
swells of shorter
period
Wave Train!
The package of
waves (train)
moves slower than
individual waves
Wave Train!
The package of waves (train)
moves slower than individual waves
Big Waves Travel in
Packs!
Wave Train
Think of the Peloton
https://en.wikipedia.org/wiki/Peloton
Predicting Storm Impact at Beaches and at Sea
wave trains
travel at a rate
of 1/2 the
velocity of
individual waves
Wave Train!
The package of
waves (train)
moves slower than
individual waves
wave trains travel at a
rate of 1/2 the velocity
of individual waves
Come on Baby Take the Wave Train
Direction of Wave Train
Travel
4
3
2
5
5
6
4
6
7
6
2
3
5
3
4
5
1
4
2
3
• An individual wave does not persist long distances across
the ocean--wave trains form (waves travel as groups)
--the front waves continually die out because of the energy required
to “spin up” water through which they pass
--orbital motion remains after wavetrain passage and waves are added
to back of train to replace waves lost at front (individual waves last
only as long as it takes to travel through the wave train)
--because of this, wave trains travel at a rate of 1/2 the velocity of
individual waves (whoa! even though individual waves obey the
equations we have studied).
My Job in Geosc040
100 Thomas is a big room. Talking is distracting to
your neighbors…
Don’t chat during lecture slides
Wait for clicker questions
Types of Waves Defined in terms of Water Depth
Only some of the molecules in the water column
are involved in a deep-water wave…
Shallow-Water Waves
• Speed is related to water depth d: S =(g d)1/2
• Waves are slower in shallower water:
d=10 m, s=10 m/s; d=5 m, s=7 m/s; d=1 m, s=3.2 m/s
Wavelength (L) and speed (S) decrease while period T remains constant
S = L/T
piru.alexandria.ucsb.edu/~tierney
Wave Sets in Shallow Water
Note: increase in wave height and more peak
shaped waves as they shallow near beach
Shallow-Water Waves
• Speed is related to water depth d: S =(g d)1/2
• Waves are slower in shallower water:
d=10 m, s=10 m/s;
• d=5 m, s=7 m/s;
d=1 m, s=3.2 m/s
Wavelength (L) and speed (S) decrease while period T
remains constant
S = L/T
piru.alexandria.ucsb.edu/~tierney
Speed (or Celerity) of Shallow-Water Waves
• Speed is related only to water depth d
(not L or T as in deep-water waves)
• S = (g d)1/2
thus, waves move slower in shallow water
• At the shore the celerity of the base of a wave is slower
than the wave crest (friction with the bottom slows the body
• In words-- the crest moves somewhat faster than the body
of a wave, and the wave “breaks” (when H=0.75d)
• So a 3 meter wave breaks in 4 meters water depth
• The slope of the bottom locally determines whether a
“breaker” plunges (e.g., a “tube”) or spills (plungers
characteristic of steep slopes, spillers of gradual slopes)
Shallow-Water Waves
• Speed is related to water depth d: S =(g d)1/2
• Waves are slower in shallower water:
Wave Sets in Shallow Water
constant period & wavelength wave set approaching coast
Note: increase in wave height and more peak
shaped waves as they shallow near beach
•
•
•
•
Speed (Celerity) of Shallow-Water Waves
Speed is related to water depth d
Waves are slower in shallower water
Wave “breaks” when H = 0.75 d
A 3 meter wave (H) breaks in 4 meters water depth (d)
Reason for Concern
When and Why Do
They Occur and How
Can We Protect
Coastal Regions?
Tsunami are Shallow
Water waves!
What Causes Tsunami?
• Any event that causes displacement of large
amounts of water including:
– Earthquakes and associated seafloor uplift or
depression
– Landslides or submarine slides/slumps
– Volcanic eruptions
The resulting water motion creates a wave trough
or crest that then moves in all directions away
from the event--a tsunami
Tsunami
Tsunami means
“harbor wave.”
They are caused by
reverse or normal
faults that rupture
in the shallow ocean
crust.
Waves can travel at
800 km/hr in the
open ocean. Once
the waves reach
shallow shorelines,
they are slowed
down and the water
“piles up” forming
large amplitude
waves.
The shorelines around the Atlantic Ocean are at much smaller risk for tsunami damage than those
of the Pacific Ocean because the major faults in the Atlantic Ocean are transform faults, which do
not move vertically. (No vertical motion = no tsunami) An exception was the Lisbon earthquake of
1755, which caused tsunami damage on the east coast of the U.S., but, as we will see, volcano
collapse & undersea landslides could be an issue.
How Fast Do Tsunami Travel?
• Tsunami are “shallow-water” waves, even while traveling
over the deep ocean! [Why is this?]
• Shallow-water waves travel at velocities proportional to the
square root of the gravitational constant times the water depth
(yup, S=(gd)1/2)
• So, if the average depth of the ocean is 3.8 km, a tsunami
travels about 695 km/hr. For comparison, most normal windgenerated waves travel about 55 km/hr in deep water (a little
faster than a car on Beaver Avenue).
• In the deeper parts of ocean basins (the Pacific averages 4.8
km deep), tsunami could travel 800 km/hr.
• Tsunami waves are “refracted” (change directions) as their
velocities increase or decrease with changes in ocean depth.
Damage from Tsunamis
• Hilo, Hawaii, 1960
• Anchorage, Alaska,
1964
Andaman-Nicobar Earthquake
• Magnitude 9.0
• Dec. 26 2004
The December 26th Tsunami
• Model simulation of
the tsunami. For
eastern Indian Ocean
only.
-red is the crest
-blue is a trough
Simulation from
Delft Hydraulics