8.1: Waves
- Page ID
- 558
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)In their simplest definition, waves can be described as energy and water. Every wave has a crest, which is the highest point of a wave, followed by a trough, the lowest point of a wave (NOAA). As seen in the diagram below, the distance between two waves is the wave length.
Figure: Anatomy of a wave. source: noaa
Waves can be caused by a number of things, such as: earthquakes, volcano eruptions and landslides but the most common ones are surface waves caused by winds (CoastalCare). When wind blows across the surface of the water, this creates friction between the air and the water causing a wave to form (NOAA). As the wave forms, it becomes easier for the wind to grip the water, creating larger waves. The size of the wave can depend on three things: wind strength, wind duration, and fetch. Fetch is the uninterrupted distance over which the wind blows with very little change in wind direction (NOAA). Larger waves are created by longer duration of winds; the stronger the winds, the higher the waves and the greater the fetch, the bigger the waves become (CoastalCare). As a wave approaches the shore, the wave direction can be changed due to the contour of the land (NOAA).
Rogue Waves
Rogue waves were originally thought to be a myth to cover the mistakes of sailors that wrecked at sea, but rogue waves are just regular waves of unusual height. Rogue waves occur when there are large swells that come from multiple directions and combine together to make one large wave (NOAA). There are three main characteristics of a rogue wave:
- Their height is greater than twice the size of surrounding waves,
- They often come unexpectedly from directions other than prevailing wind and waves, and
- They are unpredictable. (NOAA)
A rogue wave was seen in 2005 when a 70-foot wave crashed into a norwegian cruise ship. The average height of waves were approximately 30 feet that day before the rogue one struck causing damage to this ships hull (NOAA).
What Causes Waves to Break?
When waves break on the beach or shoreline it is because of the decreasing water depth that the wave has to work with as it approaches the shore. When a set of waves approach the shore they begin to interact more with the bottom than they did in the deep ocean. This causes waves to slow down and bunch together, while the time between crests(period) remains the same. (Coastalcare.org) As this happens the wave height begins to increase while the wave continues to slow down via interaction with the sea floor. Eventually the top of the wave will be moving faster then the bottom and will cause the top to topple over the front, also called the break. (surfing-waves.com)
Waves can also break in the open ocean. This is caused by the same above water process as a shore break and happens when the top of the wave is moving faster than the bottom part of the wave. However, in the open ocean there is no interaction with the bottom causing this. For a wave to break in the ocean the winds forming it need to be strong enough to cause the wave to reach a height at which the water in different parts of the column are moving at different speeds due to gravitational interactions. If this happens then the wave can suffer a typical break just as seen on the shoreline. (marineinsight.com)
Awavebreakingoff theNorthShoreofOahu,Hawaii(www.surfingnews.com/wpconte...-surf-spot.jpg)
References:
coastalcare.org/educate/waves/
www.surfing-waves.com/waves/h...aves_break.htmhttp://oceanexplorer.noaa.gov/edu/le...ing_waves.html
www.marineinsight.com/marine/...-of-sea-waves/
Tsunamis
Tsunamis are extremely large waves that can sometimes reach heights of over a 100 feet. These types of waves are caused from disturbances along the ocean floor from underwater landslides, volcanic activity, or earthquakes (National Geographic). They can have devastating impacts in the regions where tsunamis can occur. In the deep ocean, tsunami waves can appear to only be about a foot high and can travel at very high speeds of about 500 miles per hour (NOAA). As the wave approaches shore however, they slow down
and begin to gain energy and height. The trough reaches shore first, creating a vacuum effect, sucking the water away and exposing the shore line (National Geographic). This can actually be the first warning sign that a tsunami is approaching and it could arrive within 5 minutes. Knowing the signs of an approaching tsunami can help drastically reduce the damage.
Tsunamis are very large waves that can potentially reach 100 feet or more. Earthquakes, landside, volcanic eruption or meteorite can cause tsunamis and they occur along plate boundaries, this due to underwater disturbance. The waves are outward in all directions from where the tsunami originates. The topography of the coastline and ocean floor has a major significance to the size of the wave. The tsunami run up describes the height above sea level that the tsunami reaches. The process is very interesting, first the waves feel the bottom and then the wave becomes steeper and the wave then breaks. There can be more than one wave and the one after it may be larger than the one before. This is an example of a small tsunami at a beach resulting in a bigger wave a few miles away.
Tsunamis are known to be very dangerous even if they may not damage the coastline it hits. According to the International Tsunami Information Center it is said that the most destructive tsunamis have occurred along the coasts of California, Oregon, Washington, Alaska and Hawaii.
According to the North-Eastern Atlantic and Mediterranean Tsunami Information Centre, the wavelength is a factor, which depicts tsunamis from wind waves, (tsunami wavelength considered longer than a wind wave wavelength, it can be more than 200 km long). The wavelength is linked closely to the sea depth. As sea depth decreases, the wavelength decreases. And at the same time, the height of the wave increases.
Image:NOAA