Naval Architecture & Marine Engineering University of Michigan – College of Engineering The Marine Environment

Naval Architecture & Marine Engineering University 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 km km

Naval Architecture & Marine Engineering University of Michigan – College of Engineering Incident Solar Radiation Temperature varies from Equator to the Poles Water and Air are heated unevenly

Naval Architecture & Marine Engineering University of Michigan – College of Engineering Wind Fields of the Earth Uneven heating produces major wind fields of planet

Naval Architecture & Marine Engineering University 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 Engineering University of Michigan – College of Engineering General Ocean Circulation

Naval Architecture & Marine Engineering University of Michigan – College of Engineering Ocean Wave Heights

Naval Architecture & Marine Engineering University of Michigan – College of Engineering The total energy of the surface wave field is enormous...

Naval Architecture & Marine Engineering University of Michigan – College of Engineering Energy Spectrum of the Sea Surface

Naval Architecture & Marine Engineering University 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”, H s is defined as the average of the 1/3 rd highest apparent wave heights in a sample.

Naval Architecture & Marine Engineering University of Michigan – College of Engineering The Rayleigh Distribution HsHs H 1/10 H1H1 H/H rms H rms f H Highest wave in 1,000 waves = 1.90 H s Highest wave in 5,000 waves = 2.15 H s Highest wave in 10,000 waves = 2.23 H s

Naval Architecture & Marine Engineering University 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 Engineering University 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 Engineering University 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 Engineering University of Michigan – College of Engineering Storm Wave Formulae This can be expressed by the following formula for a fetch limited sea. Where U 10 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 H s = g -0.5 U 10 x 0.5 T = 0.286g U x 0.33

Naval Architecture & Marine Engineering University of Michigan – College of Engineering Feature Presentation

Naval Architecture & Marine Engineering University of Michigan – College of Engineering

Naval Architecture & Marine Engineering University 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 Engineering University of Michigan – College of Engineering How does a “Perfect Storm” form? sh-thestorm-fr.html

Naval Architecture & Marine Engineering University of Michigan – College of Engineering The Perfect Storm From Shore Dateline, October 31, 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 Engineering University of Michigan – College of Engineering The Perfect Storm Gathers

Naval Architecture & Marine Engineering University of Michigan – College of Engineering From Shore to Sea

Naval Architecture & Marine Engineering University 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 Engineering University of Michigan – College of Engineering Automated Buoy Network

Naval Architecture & Marine Engineering University of Michigan – College of Engineering Recorded Measurements Period (s)Sig wave (m)Max wave (m)

Naval Architecture & Marine Engineering University of Michigan – College of Engineering Wave Profile at Maximum Steepness L H H/L = 1/7

Naval Architecture & Marine Engineering University of Michigan – College of Engineering R/V Laurentian80 feet in length

Naval Architecture & Marine Engineering University of Michigan – College of Engineering Vessels in Waves

Naval Architecture & Marine Engineering University of Michigan – College of Engineering HsHs H 1/10 H1H1 H/H rms H rms f H How Big of a Wave Should Be Expected? H s = 15 m = 50 ft H max = 32 m = 105 ft At Breaking H/L = 1/7 => L=735 ft Highest wave in 5000 waves = 2.15 H s

Naval Architecture & Marine Engineering University 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 Engineering University 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