naval architecture & marine engineering university of michigan – college of engineering the...
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Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
The Marine Environment
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
Features of the Oceanic Cross-Section
• Wide and Shallow Aspect Ratio: 1 : 1000
• Stresses at Surface, Bottom, and Edges are most important
4000 - 6000 km4 - 6 km
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
Incident Solar Radiation
Temperature varies from Equator to the Poles Water and Air are heated unevenly
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
Wind Fields of the Earth
Uneven heating produces major wind
fields of planet
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
From Air to Water
• When the wind blows across the sea surface, momentum is transferred from the wind to the sea.
97% => currents
3% => surface waves
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
General Ocean Circulation
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
Ocean Wave Heights
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
The total energy of the surface wave field is enormous...
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
Energy Spectrum of the Sea Surface
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
Statistics of the Sea Surface
• Wave heights and associated periods (frequencies) within a storm follow a Rayleigh distribution.
• The “Significant Wave Height”, Hs is defined as the average of the 1/3rd highest apparent wave heights in a sample.
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
The Rayleigh Distribution
Hs
H1/10
H1
H/Hrms
HrmsfH
Highest wave in 1,000 waves = 1.90 Hs
Highest wave in 5,000 waves = 2.15 Hs
Highest wave in 10,000 waves = 2.23 Hs
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
The Energy of a Wind Generated Sea
The distribution of waves within a storm is a random process.
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
For all practical purposes, the heights of waves are a function of how hard the wind blows, how long it blows
for, and how much sea room there is … Force 12 winds (73 mph) over Lake Michigan would generate waves of 35 feet after 10 hours or so, but the waves couldn’t get any bigger than that because of the fetch … A gale blowing across a
thousand miles of ocean for 60 hours would generate significant waves of 97 feet, peak wave heights would be more than twice that. Waves that size have never been
recorded, but they must be out there. It’s possible that they would destroy anything in a position to measure them.
Sebastian Junger “The Perfect Storm”
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
Wind Generated Waves
The characteristics of the wind generated sea surface depends on:
• Wind speed• Wind Duration• Fetch Distance
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
Storm Wave Formulae
This can be expressed by the following formula for a fetch limited sea.
Where U10 is the wind speed measured at 10 meters above the water surface, x is the fetch distance in meters and g is the gravitational acceleration. Based on the JONSWAP Spectrum.
This is one example of many possible formulations.
Significant Wave Height
Dominant Period
Hs = 0.0016g-0.5 U10 x0.5
T = 0.286g-0.67 U100.33
x0.33
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
Feature Presentation
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering http://perfectstorm.warnerbros.com
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
There’s a certain amount of denial in swordfishing. The boats claw through a lot of bad weather, and the crews
generally just batten down the hatches, turn on the VCR, and put their faith in the tensile strength of steel.
Still, every man on the sword boat knows there are waves out there that can crack them open like a coconut.
Oceanographers have calculated that the maximum theoretical height for wind-driven waves is 198 feet; a
wave that size could put down a lot of oil tankers, not to mention a seventy-two foot sword boat.
Sebastian Junger “The Perfect Storm”
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
How does a “Perfect Storm” form?
http://perfectstorm.warnerbros.com/cmp/flash-thestorm-fr.html
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
The Perfect Storm From Shore
• Dateline, October 31, 1991 -• Outer Banks, North Carolina• Hurricane Grace is offshore and cruising north• Battering the coast with waves in excess of 20 ft
and storm surges washing over the islands...
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
The Perfect Storm Gathers
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
From Shore to Sea
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
Unfortunately for mariners, the total amount of wave energy in a storm doesn’t rise linearly with
wind speed, but to its fourth power. The seas generated by a forty knot wind aren’t twice as
violent as those from a twenty knot wind, they’re seventeen times as violent. A ship’s crew
watching the anemometer climb even ten knots could well be watching their death sentence.
Sebastian Junger “The Perfect Storm”
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
Automated Buoy Network
http://www.ndbc.noaa.gov/Maps/NovaScotia.shtml
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
Recorded Measurements
Period (s) Sig wave (m) Max wave (m)
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
Wave Profile at Maximum Steepness
L
H
H/L = 1/7
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
R/V Laurentian 80 feet in length
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
Vessels in Waves
http://perfectstorm.warnerbros.com/cmp/flash-effects-fr.html
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
Hs
H1/10
H1
H/Hrms
HrmsfH
How Big of a Wave Should Be Expected?
Hs = 15 m = 50 ft
Hmax = 32 m = 105 ft
At Breaking H/L = 1/7 => L=735 ft
Highest wave in 5000 waves = 2.15 Hs
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
Design Considerations for the Marine Environment
• Expected Environmental Considerations• Financial Constraints• Professional Engineering Responsibility
• Present Use• Unanticipated Use• Future Use
Naval Architecture & Marine EngineeringUniversity of Michigan – College of Engineering
Homework
• Choose an NDBC bouy and plot a history of (at least) the wave height and wind speed.
• Using the fetch limited sea formulas provided – Choose an offshore location
– Choose a wind speed
– Calculate• Significant wave height
• Dominant period
• Highest wave expected in 1000 waves
• How often this wave should be expected to occur