Ocean School

Physical Science – Oceanography – Waves and Swells

Waves Descriptors:
Wave length (L): distance from crest to crest.
Wave height (H): difference from bottom of trough to top of crest
Wave amplitude (A): distance wave moves above or below water level (H/2)
Wave steepness: ratio of wave height to wave length (H/L)
Period (T): time for a complete wave to pass a point
Frequency (F): number of waves passing a point per second (1/T)
Phase velocity (C): speed with which a wave crest moves through the water C = L / T
Group velocity (Cgp): speed at which the wave energy moves forward
Particle velocity (V): speed at which the individual water molecules move within the wave.
Significant wave height (HSig) and period: average of highest third of waves.
Wave Ray: line perpendicular to a wave crest pointing in the direction the wave is traveling. Wave energy moves in the direction of the wave ray.

Wave Formulas for Deep Water:
Phase Velocity: C = 5.12 T (feet/second) (waves with longer periods move faster)
Wave Length: L = 5.12 T 2 (feet) (waves with shorter periods have shorter wave lengths)
Total Energy Transmitted by Wave: E = ½ pi 2 m F 2 H 2 (m is mass of moving particle)
Intensity of a Wave: I = 26024 H 2 F (watts / m 2 )

Types of Waves:
Wave Classification by Water Depth:
Deep water waves: generally have a symmetrical shape like a sine wave, unless compressed by high winds. In water where the depth > ½ L Statistics for wave height: 40% are less than 3.3’, 40% 3.3-13’, 10% 13-19’, 10% are higher than 19’. Extreme wave heights: 112’ (recorded in 1933 by the USS Ramapo in the Pacific), 100’ (south of Sable Island during the Halloween Gale of 1991), 135’ (in the Bass Strait south of Australia during the 1998 Sydney to Hobart Yacht Race). Highest theoretical height: 200’ (never measured).
Shallow water waves: have an asymmetrical profile with a steep, high crest and a wide trough. In water where the depth < ½ L. Statistics: the highest measured (storm-generated) shallow-water wave was 133’ (Tillamook Rock, Oregon)

Wave Classification by Generating Forces:
Wind-generated waves: Generated by transfer of energy from wind to water.

Storm waves (also called sea): Have high steepness. Irregular. Average wave length: Atlantic 325-500’, Pacific 600-650’, Antarctic Ocean 650-800’.
Swells: Storm waves that move out of the weather system which generated them. Have low steepness. Average wave length: 1000+’, maximum length: Atlantic 2700’, Pacific 3300+’

Breaking waves (surf): waves that have gotten too steep and are now converting their energy into water movement. Statistics: the highest measured breaking wave was 195’ (Unst Light, Shetland Islands).

Rogue waves (non-negotiable waves or freak seas): Very steep waves with an extremely deep trough (hole in the ocean). May be far bigger than the other waves in a system. Caused by several waves or waves and swells superimposing their crests. Frequently occur in groups of 3 (the 3 sisters) which travel across ocean basins and shoal at the continental shelf edge (600’) Generally exceed the stress rating of ships, sinking them.

Langmuir cells: convection (rotating) cells under the water surface with the axis of rotation parallel to the wind direction. Adjacent cells rotate in opposite directions, creating alternate convergence and divergence zones on the water surface. Convergence zones are visible through surface material accumulation. Play an important role in mixing and nutrient/gas transport.

Internal waves: form underwater at the boundary of water of different densities (SEE WATER). C less than in surface waves but H greater. Even ‘break’. Over their troughs slow-moving surface slicks composed of plankton, sediment, or pollutants can be observed.

Landslide surges: caused by large amounts of rock or ice dropping into the ocean due to earthquakes or glacial movements. Highest recorded: 1,640’ (Lituya Bay, Alaska, 1958), caused by 40 million cubic yards of rock falling from 3,281’.

Tsunamis: caused by submarine movements such as earthquakes, submarine landslides (slumping), or volcanic eruptions. Period generally 15 min, wave lengths up to 700 miles, speed over 350 knots, wave height only a few inches in deep water. Height increases as the wave breaks against the coast, reaching greater heights than wind-generated waves.

Seiches: standing waves which form in an enclosed area of water due to long-period waves (such as landslide and storm surges) sloshing back and forth and superimposing. The characteristics of the standing wave are determined by the length and depth of the enclosed area (which can be as big as an entire ocean basin).

Wave Classification by Period:
Capillary waves: Vibrations in the water surface caused by wind. The energy in capillary waves is so low that surface tension flattens them out when the wind stops. Period <1/10s, maximum height 0.68’’.

Gravity waves: self-propagating waves which only stop when they collapse into themselves (break). Period >1/10s – 5min, usually 20s – 5min.
Standing / stationary waves: caused by refection of gravity waves (see below). Wave does not move forward but water surface moves up and down. Period 30s – 5min. Called edge waves when moving parallel to shore and surf beat when moving on/off shore.

Long period waves: caused by seiches, tsunamis, and tides (SEE TIDES). Period 5min – 24+h.

Wave Generation:
Wind forms a small area of capillary waves in a diamond-shaped pattern on the water (Cat’s Paw). Because of the polar nature of water (SEE WATER), water has a skin on the surface which is actually strong enough to float small objects like metal needles. Wind causes this skin to vibrate. If the wind is stronger than 6 knots it then pushes against the capillary waves and turns them into real gravity waves. The bigger the gravity waves get the bigger a surface they present for the wind to push against, which is why wave height increases exponentially with wind speed, and total wave energy therefore increases to the forth power. Wind of a certain speed generates a wide variety of waves with different wave heights and periods (wave spectrum). Wind speed and duration (how long the wind blows over a certain area) determine wave height and period distribution of the waves within a storm. Fetch (how large the area is over which the wind blows) limits how large the waves can actually get before either running out of the storm system (waves move faster than weather systems, so this is the limiting factor on the open ocean) or into land. Fetch therefore also determines period, since it limits the duration of the force of the wind acting on a specific wave (the wind no longer acts on that wave when it runs out of the storm system or into land). If the fetch is large enough, what is called a fully developed sea state results. The waves are so large that any increase in height simply causes them to collapse due to gravity. The sea has reached equilibrium (maximum sea state). 90% of the maximum sea state is considered a fully developed sea state. While it takes about 3-5 days for the maximum sea state to develop, it only takes only 18-25 hours for a fully developed sea state to be reached. The larger the wind speed, the larger the fetch required for a fully developed sea state. For example a 60 knot wind will cause a fully developed sea state with HSig of 88’ after 25 hours as long as the fetch is at least 800 miles. Waves in the storm area are called storm waves or sea. In the storm waves have different periods or heights and move in different directions.
As waves move out of the area where the storm generated them they get sorted, with the faster, long-period waves moving ahead of the slower, short-period ones. Since they move out from the storm area in expanding circles, they become increasingly stretched out (wave rays diverge), decreasing in height and therefore reducing their steepness. They are now considered swells and propagate with almost no energy loss. They can move across whole ocean basins in that manner.

Wave Behavior:
Particle movement within waves: particles move in a circular orbit within the wave – up on the face of the wave, forward on the crest, down into the trough, and back through the trough. The circle is not perfect, and some water moves in the direction of the wave (mass transport). The diameter of the orbit gets smaller further down, reduced by ½ for every L/9. The speed of the particles also decreases further down. Below a depth of L/2 wave motion is no longer felt. This is the reason why a wave in water with a depth of less than L/2 starts to be influenced by the bottom.

High wind reduces the distance between crests, increasing steepness. Crests may be higher than troughs are deep. If H>L/7 the wave breaks.

Sediment transport and erosion: storm waves erode shorelines and move sediment offshore, swells tend to move sediment back onshore.

Shoaling: When waves start to feel the bottom (depth < ½ L), L decreases, but T stays the same. At a water depth between ½ L and 1/6 L phase velocity and wavelength decreases, and wave height also decreases. At a water depth of less than 1/6 L phase velocity and wavelength continue to decrease, but wave height now increases. As the water depth becomes less than 1/25 L, phase velocity is only determined by the water depth (d) (C=(g*d)1/2), while wave length still depends on the original period (L=(g*d)1/2 *T) (g is the due to gravity on earth: 32 feet / second2 ).The orbits of a shoaling wave are also influenced by the bottom. They become increasingly elliptical closer to the bottom and finally almost completely flat, moving landward under the crest of a wave and seaward under the trough. That is the reason why a wave will pull you out as it approaches and push you towards shore with its crest.

Breaking: Waves break in open water if they get too steep (see above) or when they reach the shore. Breaking occurs when the velocity of the upper part of the wave is higher than the velocity of the lower part. This can be caused by the wave touching bottom, the upper part being accelerated by the wind, or a faster wave superimposing itself on a slower one. There are several different ways in which a wave can break, depending on the shape of the bottom. When a wave breaks the energy contained in the wave is converted into water movement. The moving water on the face of a wave therefore has very significant force – up to 6 tons per square foot! An object in the water generally behaves as the water it displaces would have. This is why boats ride up and down non-breaking waves. However, when the wave breaks boats become part of the water moving down the face.

Spilling breaker: forms when waves get too steep in open water or on the shore when the bottom slope is less than 3 degrees and water depth is 1 – 1.2 H. The wave starts to break at its crest, with water running down its face, spreading the wave energy over a wide area. This form of breaker occurs most frequently. Boats caught in a spilling breaker get washed down the face and broken on or surf down the face.
Plunging breaker: forms when the bottom slope is between 3 and 11 degrees and the water depth is 0.9 – 1 H. The crest curves, forming a tube of air which is pulled underneath the wave. It frequently breaks out through the back of the crest, forming a fountain. If the slope is less than 7 degrees the wave will break twice in that manner: once offshore and once at the shore. If the slope is greater than 7 degrees the wave will only break against the shore. The wave energy becomes concentrated right under the break, which is why plunging are the most destructive. Boats caught in a plunging breaker become part of the tube.
Collapsing breaker: Forms when the bottom slope is between 11 and 15 degrees and the water depth is 0.8 – 1 H. A small air pocket develops, and the lower half of the wave collapses, but the wave is mostly reflected back out to sea.
Surging breaker: Forms when the bottom slope is greater than 15 degrees. The wave does not break, but surges up on shore and is then reflected back out. This creates standing waves.

Wave-induced currents: Breaking waves transport water towards the beach. Only some of that water returns flows back out underneath the incoming waves. Since waves usually impact the beach at a slight angle, the rest of the water moves along the shore in a longshore current. When the longshore current gets too strong it breaks through the incoming waves in a seaward rip current. The location of the rip current changes depending on wave height and period and beach and underwater topography (which also changes with the waves.

Storm surges: water piled against a coast by strong winds, raising the sea level gradually. Low barometric pressure is a contributing factor. Statistics: Highest recorded storm surges: Gulf Coast of US: 23’, Atlantic Coast of US: 5’ (Halloween Gale of 1991).

Reflection: Waves bounce back from a steep / vertical shore, forming a wave with the same period traveling back out to sea. The angle of impact equals the angle of refection, so a wave that comes from the right will be reflected to the left, and a wave that comes straight in will be reflected back on itself. In that case it overlaps perfectly with the next incoming wave. When its crest overlaps with the crest of the incoming wave, a crest is formed that is twice as high. When troughs overlap, a through is formed that is twice as deep. When a crest and a through overlap, they cancel each other out and no movement occurs. This pattern is called a standing wave. Interestingly enough, nodal points (points where there is no movement) exist in this standing wave at ¼ and ¾ L (and ever ½ L thereafter) away from the wall. Between those nodal points the standing wave oscillates, reaching 2H at the antinodes (the points halfway between the nodes). The water moves no longer in orbits but instead back and forth across the nodes and up and down under the antinodes.

Refraction: the bending of a wave as part of it touches bottom and slows down, resulting in the wave aligning itself parallel with the bottom contours. Wave rays diverge or converge during refraction, depending on which part of the wave slows down. For example a headland or submarine ridge when hit head-on by waves will cause convergence, while a bay or underwater canyon under the same circumstances will cause divergence. When wave rays diverge the wave is stretched out (less wave energy over a specific length of crest) and decreases in height. When wave rays converge the wave is compressed (more wave energy over a specific length of crest) and increases in height. Convergence results in erosion, while divergence results in sediment deposition.

Diffraction: the formation of a circular wave centered on the end of a narrow point sticking out parallel to the incoming wave crests (such as a breakwater). The wavelength of the circular wave is equal to that of the incoming wave. The circular wave spreads on the down-wave side of the obstruction. Directly down-wave of the point its height is 0.5H, and it drops to 0 in the shadow of the obstruction. Past the point the circular wave overlaps with the incoming wave, creating a series of lumps and holes moving along phase lines. The maximum height along the phase lines is 1.2H. In a harbor entrance formed by two breakwaters two diffraction pattern form and overlap, creating chaotic waves.

Currents: An opposing current shortens L. Convergence can occur in the center of the current, causing a concentration of wave energy and therefore extreme wave heights.

Trends due to Environmental Change:

Wave heights appears to be slowly increasing. This may be due to a drop in plankton abundance which may be related to pollution or increased UV radiation due to holes in the ozone layer. Plankton releases an oil-like chemical which forms a film on the surface (like oil) and inhibits the formation of capillary waves. Waves may be the least of our worries though since plankton generates a large amount of our oxygen. Global warming also seems to generate more extreme weather, which in turn generates higher waves.

Action:
What you can do:

Never build on barrier beaches. Barrier beaches naturally move.
Never artificially stabilize the shoreline on your property. Build further back.
When purchasing a large boat (sail or power) consider the most extreme conditions you could face where you want to use it and choose design criteria that would allow you to survive them. Unsinkable boats are manufactured both for sail and power.

What needs to be done globally:

Wave generators need to be explored as an alternative energy source.
Shoreline development in areas which can be affected by waves, especially barrier beaches needs to be stopped. Those areas are part of a dynamic, constantly shifting coastal system which cannot and should not be stabilized. Developments which are damaged by waves will cause significant environmental damage.
Beach armoring and stabilization needs to be stopped since it modifies natural wave-induced beach movement and current pattern, resulting in ecological damage and loss of marine and beach habitat. It is also extremely costly and at best temporary. Beach armoring is for example a definite factor in sea turtle population declines due to nesting habitat loss.
Harbor installations, especially refineries and chemical facilities must be designed so that they are above the highest level that can be reached by waves or tsunamis or are submersible.
Ship design criteria must be changed for ships carrying chemicals or oil to enable them to negotiate rogue waves.
Sipping lanes for oil and hazardous chemical transport must be internationally regulated so that they avoid areas where rogue waves are known to occur.

The Ocean School Action Map

Did you do a project at home that promotes renewable energy or opposes coastal development? Tell us about it and we will post it here. Our goal: red dots all over the map, all over the world!

Programs

Introduction

Wet Waves – 3h (K-4, family)
A classroom introduction to waves for kids and families. We’ll use a wave tank to see how waves are generated, what happens when they come close to a beach, and what happens to boats in waves.

All about Waves – 3h (5-12, adult)
A classroom program that explores the different types of waves, formation, wave behavior, wave-current interaction, and wave-landform interaction using a wave tank and mathematical models.

Exploration

Waves at the Beach – ½ day trip (5-12, family, adult)
We’ll measure wave period and wave height at the beach and see how waves change as they approach shallow water.

Extreme Waves – day trip (adult)
Now that we’ve learned how waves theoretically work, we’ll set out in kayaks to look at the different behaviors in real life on the ledges and cliffs. Where we can we’ll measure wave parameters, locate nodal points, and determine the water depth at which waves break.

Real Science

Coastline Monitoring – day trip (family, adult)
Are storms really getting more extreme? We will look at several beaches and determine if and why coastline erosion is occurring and if it seems to be increasing. Details soon.

Action Projects

Coastal Wave Erosion Monitoring – ½ day trip (family, adult)
As we paddle we’ll look for sections of shoreline modified by beach armoring. We’ll determine the impact of the structure on shoreline habitat and explore different more environmentally friendly solutions.

Further Reading

Fox WT. 1983 At the Sea’s Edge. Prentice Hall, New York

Junger S. 1997 The Perfect Storm. HarperCollins, New York

Dugard M. 1999 Knockdown. Pocket Books, New York

Links

NCEP Marine Modeling and Analysis Branch Products http://polar.wwb.noaa.gov/mmab/products.html

NOAA WAVEWATCH III http://polar.wwb.noaa.gov/waves/main_int.html

Integrated Publishing: Sea Surface Forecasting http://www.tpub.com/content/aerographer/14010/css/14010_127.htm

National Data Buoy Center (NDBC) Science Education Pages http://seaboard.ndbc.noaa.gov/educate/educate.shtml

Office of Naval Research Ocean in Motion: Waves http://www.onr.navy.mil/focus/ocean/motion/waves1.htm

Ocean World: Waves http://oceanworld.tamu.edu/students/waves/

Volvo Ocean Adventure: Ocean Zone: Waves http://www.volvooceanadventure.org/article.php/oz_5_wav.html

MarineWaypoints.com: Wind Scales http://www.marinewaypoints.com/marine/wind.shtml

APL Ocean Remote Sensing Ocean Wave Parameter Calculator
http://fermi.jhuapl.edu/wavecalc.html

Animated Waves http://members.aol.com/nicholashl/waves/waves.htm

Ocean Energy http://www.energy.ca.gov/development/oceanenergy/