Do you know why waves move the way they do?

Waves, what are they? A wave transfers energy from one place to another. Whether you're thinking of an ocean wave, a sound wave, or a light wave, they all essentially do the same thing. Waves get some kind of energy from point A to point B through whatever substance, or medium, they are in, be it water, air, or space. Waves oscillate the substance they are in to transfer that energy. What we're interested in for this article are how surface waves in water behave. We are going to demystify two wave things about waves:

• How and where they break
• How they can turn as the move towards the coast

Before we launch into it, let's check out a nice photo of waves. The photo is extra special because it shows some really neat effects of water waves bending light waves and causing bright light ripples in the water.

Nice picture of water waves and light waves interacting from http://oceanleadership.org/

You've probably already developed an intuition for how waves move just by watching. In fact, you might be much more of an expert than you think if you spend your time surfing, sailing, or just hanging out at the water! Experience counts for a lot here, so we'll try to weave a picture between good experience and science.

Let's start with wave breaking. Why do waves break? First, a good rule of thumb to remember is that waves slow down in shallow water. Taking it a step further, when the water is shallow enough, that slow down happens more at the bottom of the wave. The faster moving top of the wave tips over the bottom like a tipping glass of water. Lo and behold ... We have a breaking wave. While the physics is more complicated when you dig into the problem, that's the essential idea!

There is generally a depth of water where waves of a certain height will break.  This depth is cleverly called the "Depth of Breaking". A water depth of approximately one and a quarter (1.25) times the wave height causes a wave to break. So, a 10 ft wave will typically start to break in 12.5 ft of water. While there are a lot of things that can modify this ratio, such as a steep rock reef or very steep beach, its a good rule of thumb. The figure below gives us a conceptual picture of what's happening with waves breaking. You can see the wave marching towards the shore. As the water depth decreases, the wave slows down due to shoaling in the shallow water. When it hits the depth of breaking, the top keeps moving fast and tips over the bottom and we have a breaking wave.

As waves approach the shoreline they feel the bottom which slows them down and
eventually causes them to break at the "depth of breaking" in a depth of water
about 1.25 times the wave height.

The waves change direction by almost 90 degrees in the space of a quarter of a mile!

Curving waves, or wave refraction, is our next topic. Take a moment and look at the picture below. This is Rincon Point in Santa Barbara, California and produces one of the most famous right handed point breaks in the surfing world. Notice the waves at the top of the picture are parallel with the top of the picture frame and the wave at the bottom are facing the right side of the frame. The waves change direction by almost 90 degrees in the space of a quarter of a mile!

Nice aerial showing wave wrapping around the point at Rincon in Santa Barbara , CA. Image from http://www.travelgrom.com/.

So what's happening here? If we think back to our rule of thumb, waves slow down in shallow water, we can put together a picture of what's happening. When we extend this to long wave front, the wave will experience different water depths along its length as it approaches a coast. A point on the coast sticking out into the ocean, like Rincon, provides big depth differences in a small space. In the image below we see the waves coming in from the left and approaching a point.  The portion of the wave near the point hits a shallow water point earlier than the rest of the wave.

So what happens when these waves hit the shallower water near the point? They slow down and eventually break. The shallower bottom is almost like a hand pushing on waves and slowing them down, while in the deeper water the waves keep moving uninterrupted. I drew the  black arrows on the figure below to help visualize this slow down so we can see what happens. The shallower slower moving waves hang back while the waves at the top of the image in deeper water keep marching forward. The wave curves in response and causes the wave to turn, or wave refraction! 

The focusing and curving of energy at coastal points is why point breaks are often such amazing surf spots.  

When we pull this all together at a coastal point we get an interesting phenomenon called wave focusing. Let's marry up the figure above with the other half of a point and plot it out in the figure below. Now we have the waves curving in towards the point from both sides focusing the wave energy at the point. You can see the energy coming from both sides to make the waves bigger. The blue arrows showing wave direction help visualize this "focusing" of energy at the point. The focusing and curving of energy at coastal points is why point breaks are often such amazing surf spots.  

An important parting note is what we started talking about in the post about how sand moves around at the coast. The change in wave energy from the point to the adjacent beaches causes two interesting things to happen.  First, the focusing of energy will pick up sand and even erode cliffs where the energy is high. Second, the material moved at the point is carried down the coast to lower energy areas due to longshore transport. The sand creates our beaches, sand bars, and even fills our harbors as we discussed in the previous articles! Now you're starting to see a picture of how all of this works together.

Please help support our efforts by signing up for our newsletter on the right side of this page or on our website to get regular updates on the world of ocean science, ocean energy, surfing, and other fun topics. Or course you can get the BEST idea as to what the ocean is doing with your very own WaveClock. Great resources like Dean and Dalrymple (2002) provide the detailed wave mechanics behind these processes I have greatly simplified here. Check it out to dive in more.

Enjoy the the beach!
Craig

R.J. Dean and R.A. Dalrymple (2002). Coastal processes with engineering applications. Cambridge University Press. ISBN 0-521-60275-0. p. 96–97.

How does the sand get to the beach?!

Now we get to the fun stuff ... the beach! In the last post we explored how the sand gets to the coast from the mountains. We all know it's rivers, but it's a great process to explore. Then the sand hits that crazy area where currents, waves, and tides all interact. These competing forces move the sand around and get it to the place we are most often thinking about ... the beach.

I am going to take a step back a little, because we haven't really talked about what sand is. The particles that make up sand have an important characteristic that makes them sand and that's the size of the particles. The most common definition of sand is any particle that is larger than 63 microns (0.063 mm) in diameter according to whats called the Wentworth size scale. Now that's pretty small!  More commonly what we think of as nice "beach sand" is larger than about 200 micron (0.2 mm) in diameter. So, beach sand is essentially quartz sediment larger that about 200 microns in particle size.

Great, that's the size, but what is sand made of? Most commonly, sand coming from the land is made up of the mineral quartz. Straight from the dictionary, quartz is:

 A hard white or colorless mineral consisting of silicon dioxide, found widely in igneous, metamorphic, and sedimentary rocks. It is often colored by impurities (as in amethyst, citrine, and cairngorm). (Google, 2015)

However, that definition gives us some good insight into the sources of most sand. Much of our land on this planet is made up of some type of igneous, metamorphic, or sedimentary rock. When rain erodes these rocks over time, a lot of the sand ground out is made up of quartz. The ground up rock washes down gullies, hillsides, and other streams to the rivers and so on, to the coast.

One other big source of sand, in areas such as the pacific islands, is coral reefs. The reefs are made up primarily of a material called carbonate (another mineral like quartz). Interestingly, fish are a common way some reefs get broken up into sand. Parrot fish cruise along munching on the reef and grind it up into sand.  One parrot fish can produce up to 200 lb of sand a year (Thurman and Webber, 1984). That's a lot of sand!

One parrot fish can produce up to 200 lb of sand a year!

Suffice to say there are a few different sources of the sand grains. Now let's get down to it and talk about how it get's where it is going! We have a pile of sand on the coast where a river has dumped it out, parrot fish has pooped it all over, a cliff has eroded, or some other source has dumped it there. Once on the coast, the waves can start pushing this stuff around. We'll save a full wave mechanics discussion for future articles, but we are going talk about some of the important things the waves do at shorelines to move the sand.

There are two ways our sand can be moved by the waves:

• along the shore, called longshore transport, and
• on or off the shore, called cross-shore transport.

Longshore transport moves the sand in pretty exciting and phenomenal ways. I'm sure you've sat on the shore watching the waves come in and have probably noticed that they hardly ever come straight into the shoreline. If you can imagine, this is because of that angle the waves are often peeling along the beach. Think of that peeling like a push along the beach from the waves. That push is a real force expressed by the waves and is felt by the sand out there under the waves. The force moves our sand down the shoreline in ... you guessed it ... longshore transport.

... here in Santa Cruz, waves can push enough sand in the harbor mouth to fill in up to 15 ft of channel overnight during a storm!

Figure from the Santa Cruz Harbor showing how sand is
moved from the river down the coast to the Harbor and
beyond due to longshore transport (also called littoral drift).
Source: http://www.santacruzharbor.org/dredgeWhy.html

Longshore transport is typically the biggest way sand is moved out of the river mouth or delta to other areas along the coast. In fact, here in Santa Cruz, waves can push enough sand in the harbor mouth to fill in a 15 ft deep channel overnight during a storm!

When you look at the figure below, imagine a river has dumped sand on the left side of the picture (upcoast direction). The waves coming in from offshore are also coming from the left slightly and moving to the right (blue arrows show the wave direction). The pushing from the waves moves the sand to the right (downcoast direction). The black arrows point in the direction of the steady march of sand due to longshore transport.

Waves coming into the coast from the upper left push to the right along the beach. Sand gets picked up by the waves and moved along that direction. The movement along the shore is called Longshore Transport.

If the sand is just pushed along the shoreline how does any sand get onto the beach? When the waves move to the coast they create another force pushing to the beach. Just like longshore transport, the force of the waves pushing into the beach creates a cross-shore transport of the sand.

In the summertime, when the waves are smaller, the sand piles up on the beach with each wave and slowly builds up. Over time that sand builds to a happy status quo called the equilibrium profile. The equilibrium profile typically has a nice berm with a flat beach behind it.  This is where we set our towels down, throw up some volley ball, and roast ourselves in the sun while enjoying a frosty cold beverage. Those gentle waves push the sand higher and higher up the beach with each tide.  The sand eventually builds us a summer beach profile as shown in the figure below. 

Cross-sections showing summertime and wintertime beach formation and sand movement. Smaller waves in the summer typically bring sand to the beach, while large winter waves move sand offshore into sand bars.

The whole sand dynamic on the beach does somersaults in the wintertime.

You're well aware that things liven up quite a bit in the wintertime. The weather gets cooler, the sky darkens, and the wind starts brewing in the ocean. The winds build up big waves that get bigger ... and bigger .. until we have big storm waves breaking along our nice calm summer beach. Those waves, as you'd expect, pack a much bigger punch when they slam onto the sand. They pick up the sand in all that turbulent mess and pull it off the beach. The assault pulls the sand out to deeper, somewhat calmer, water where it forms a new underwater sand bar. The figure above shows how our nice summer berm was cut away by the waves and moved to the winter sand bar. 

In Santa Cruz County at Manresa Beach, the winter sand bars cause the waves to break offshore and give us some fantastic surfing conditions when the conditions are right. That's what inspired the invention of the WaveClock, to see the waves and tide out there in real time. We've got a number of them up on Etsy ready to go now, or order a custom one on the website. Also, don't forget to sign up for our free newsletter on the left of this page to keep up with what's going on in the ocean world!

This article describes pretty ideal world stuff. Some beaches may have no sand in the summertime and lots of sand in the winter depending on the waves, sources of sand, and the type of coast (such as cliffs or offshore reefs). Also there are rip currents, offshore canyons, rocky points, and other coastal features that can modify the movement of all this sand. In the next articles we will explore sediment budgets (yeah sediment has a budget too!) and wave mechanics to develop a deeper understanding of how all these things play together on the coast.

Happy Exploring!
Craig Jones

Reference
Thurman, H.V; Webber, H.H. (1984). "Chapter 12, Benthos on the Continental Shelf". Marine Biology. Charles E. Merrill Publishing. pp. 303–313.

Where in the hell do our beaches come from? Sand on the brain ...

View of the Homochitto River.
Source: Google Earth, Imagery Date: 4/9/2013

I was flying across Mississippi last week, looked down on a river, and was struck by the white sand bars shining brilliant through the green forests. Going on Google Earth it took a few minutes to find out what river I was looking at, but I found it. The image here shows the tortuous path of the Homochitto Rive. The white sand pops through the green-forested terrain outlining its path as it flows eventually to the Mississippi River.  To me, an engineer/scientist who has been looking at water bodies for most of my career, it truly floored me the amount of sand in this river.  Certainly, this river has no problems there!

Sand is an important, sometimes critical resource, in coastal communities.

Anyone living near the coast can likely relate to a local beach or coastal region where sand or a lack thereof, is a problem for local communities. Sand is an important, sometimes critical resource, in coastal communities. It can provide a resource in the form of a thriving tourist industry to lay it’s blanket down and support a local economy. It also provides an important protective barrier in regions ravaged by periodic hurricanes. Sand is akin to a band-aid protecting the tender shoreline from the ravages of storm waves.

The high value of sand, and its management throughout the world, had me reflecting on the importance of what I saw abundantly in the Homochitto River from above and what we desire so deeply the coasts. If we take a brief journey from the hillsides, fields, and mountainsides where this sand originates, we can follow it through the river, down to the coast, and eventually to the deep ocean. 

The river itself provides the true punch of the mighty force to deliver this precious gold (figuratively and literally) from the mountains to the coast. Most of us know, or can certainly surmise, that most of the sand and mud we see flowing in a river comes from upstream. What we well understand is that scouring, erosion, and removal of soil and rocks from upstream bring sediment (sand and mud) downstream. Leonardo Da Vinci pondered these problems in the 15^th and 16^th century while watching the complex course of water flowing through local rivers (Graf, 1984).  We'll hear a bit more from him in a bit.

All this “stuff” transports downstream through the river like a conveyor belt. Of course, some of this material rains out in deposits along the river’s course during this journey. Where does it rain out? Rivers twist and turn, and like a freeway zooming with cars, the water speeds up and slows down. Slowing down along the inside of turns and speeding up on the outside of turns. Sediment drops out in the slower flow and is picked up and moved through the faster flow. Where the sediment drops out and builds up on the inside of the turns “point bars” are formed.  Where sediment picks up and the water cuts away at the riverbanks are features called “cut banks”.

Point bars form on the inside of river bends where the
water slows down and drops out sediment.

An interesting little rule of thumb as true today as in Da Vinci’s time is an observation he noted (Simons and Sentruk, 1992):

Where water has the least movement, the bottom will be of the finest mud or sand, where the water has a stronger current the shingle is larger.

What he is saying is that where the water is moving slow the sand and mud drop out of the river flow, and where it is fast the “shingle” (or material the river bottom is made up of), is larger. We see this in rivers that have cobblestones and boulders where it is fastest flowing. Pretty cool physics in action!

What struck me looking at this river from the airplane is no just that there is sand, there is a TON of sand on the point bars visible from 30,000 ft in the air.

Why do we care about this and why are you laboring through my long-winded explanation? If we go back to that picture of the Homochitto River we see sand. What struck me looking at this river from the airplane is no just that there is sand, there is a TON of sand on the point bars visible from 30,000 ft in the air. The blatant display of sand by this river is unique. It’s not easy to go to Google Earth and look for lots of rivers around that appear as brilliant with sand. To me, that means there is TONS and TONS more sand making it downstream that we don't see. Downstream to the coast!

What happens to all of this sandy gold when it hits the coast? It can hit an estuary, think San Francisco or Chesapeake Bay, it can form a delta like the Mississippi River, or it can tumble full bore into the ocean. The interaction of the fresh water and salt water in these zones form many fields of science, but it is sufficient to say that the sand makes it to the coast eventually.

If we think about that sand going from a pretty swift flowing river to the big deep slow moving coastal current, we can imagine all that sand dropping out like it did on the point bars. At this point (no pun intended), the waves start to take over. Similar to the high and low speeds in the river, big waves pick up the sand and move it around, while smaller waves allow that sand to drop out. We all know that these waves vary in size daily, monthly, yearly, and by location and depth of water. The movement and fate of sand along the coast is amazing topic I am going to save for our next article titled “Now I am at the beach, where do I go?” or something equally satisfying!

Sign up for our newsletter and keep up with our comings and goings on this page and at The WaveClock. Order your very own WaveClock there to see the ocean in real-time and really know how that sand is moving. Email us anytime at contact@thewaveclock.com

All the best!
Craig Jones

References

U.S. EPA (2014, February 5^th) WATERS Data. Retrieved from http://water.epa.gov/scitech/datait/tools/waters/tools/waters_kmz.cfm

Graf, W. (1984) Hydraulics of Sediment Transport. Water Resource Publications.

Simons, D. and F. Sentruk (1992) Sediment Transport Technology: Water and Sediment Dynamics. Water Resource Publications.

How to know what ocean wave measurements really show?

You are sitting out on the pier one day watching the waves roll by (not quite a song lyric, but you have the image). Each wave slowly rolls under your feet. You see the water rise and fall along the barnacle covered piling. You definitely have a sense of which direction that wave is moving. The top of the wave is a few feet above the bottom of the wave.  That's your wave height. It takes about ten seconds between the peak of two waves. So, that's your wave period. Wave height is how high the wave is from crest to trough and wave period is the time between those troughs and crests. Simple right?

Description of ocean waves from the Coastal Data Information Program (CDIP).

But wait ... it took 10 seconds for the first one to pass, 12 seconds for the next one, which was a foot higher, and then a bunch of smaller waves that are moving faster. This is not quite as straightforward as the single height and period we see coming from NOAA or other information sources.

The reason, as anyone who watches the ocean for any time knows, is that the surface is a mix of waves of different lengths, heights, and directions all mixing together. An average condition, sometimes referred to as the sea state, does emerge, but all those waves jumble together. So, what measurements are the buoys giving us? The buoys measure the vertical motion of the sea surface and compile all of those height measurements into what's called an energy spectrum. The energy spectrum is the amount of wave energy (which is the height of a wave squared) split up into frequencies (frequency = 1/period). There are many reasons energy spectra are used to describe ocean waves, but primarily they provide scientists and engineers an easy way to compile complex information resulting from measuring the sea surface.

It helps to break down a single spectrum to better comprehend it. The figure below shows a spectral measurement from a NOAA wave buoy. The spectra is essentially the "raw" data coming out of a wave measurement buoy. It is compilation of the wave data over 20 minutes. The plot shows the energy (that's roughly our wave height squared) on the Y-axis, frequency on the bottom X, and period on the top X.

Image of the Monterey Bay NOAA NDBC buoy 46042 spectral wave energy. 

The wave spectra has a dominant or peak period that we see from the NOAA measurements. That's the easiest part to pick out. It's just the peak along that little spectrum and is about 10 seconds or at a frequency of 0.1 Hertz on this plot. Another one we see from the NOAA buoys is the average period. It is the average period of all of the waves over a time period. However, in my opinion the dominant period usually tells us what we are interested in, but it can miss longer period swells like a good south swell in Hawaii or California. That's where we may look for a second peak in the higher periods (lower frequencies) in the spectra.

Then there is also the height, but that expresses as energy in the spectral plots. How do we get a wave height from this? Fortunately, we can easily calculate a significant wave height form the spectra. It's the average of the highest one third (highest 30%) of the waves measured in a 20 minute time period. The way we do this mathematically is we sum up the area under the spectra, take the square root, and multiply it by 4.

The wave heights and periods are all essentially based on the vertical motion of the buoy. If you are more interested in the math definitely dig in here: NOAA Wave Measurement Description

Wave directions are determined from either the horizontal moving or tilting of the buoy.  Think of an object floating on the sea surface.  As a wave moves past, the object moves forward then backward as the wave moves past. Also, its going to tilt forward and backward along the face and back of the wave. The measurements of these motions are also compiled into what's called a directional spectrum. It is similar to an energy spectrum, but it tells us which direction the waves are coming from over a 20 minutes period. AND .. if there are two swells in the water, it will measure both of the directions and be able to discern the height spectra of each.

Below is a directional spectrum from a CDIP buoy in Monterey Bay. Think of these plots like a compass with each direction representing where wave energy is coming from. Now instead of a line spectrum like the previous graph, we have colors to represent our higher (red) and lower (blue) wave energy. The plot shows the most wave energy (red) coming from about 300 degrees (west-northwest). We can also see some wave energy from the southerly direction. We have a little bit of south swell in the water.

Directional spectra from CDIP buoy in Monterey Bay.

Amazing stuff and maybe a little more complicated than most people thought, but now that you're in the know, share the knowledge!

Check out the WaveClock for up to date wave information right on your desk, living room, bedside, or anywhere you have a good WiFi connection! Sign up for our newsletter for more information. Latest designs available on Etsy.

What is the WaveClock?

Think of a classic nautical clock.  We get time, temperature, barometric pressure, and humidity in a classic analog format that's been in use for generations.

But many of us from surfers, ocean enthusiasts, fishermen, boaters, and anyone interested in the coast want to know what the waves and tides are doing and more importantly what the conditions are right now!

Lucky for us, NOAA maintains thousands of stations throughout the United States and outer coastal waters that measure the real-time wave and tide conditions continuously. All of that information is made available through internet connected data bases.

Welcome in the WaveClock! By connecting through your WiFi, the WaveClock is easily programmed through the smartphone app to the nearest NOAA wave buoy and tide station to display that data on an intuitive analog interface.

So what? 

We can look all this up on our smartphones, computers, tablets, or whatever and see what's going on. The big difference is that an analog interface is easier to read! It updates all by itself every 15 minutes and shows you exactly what's happening out there without messing around with any other devices. First thing in the morning, when you get home for a lunch break, after work or school, whenever you walk into your house! Also, we're working hard to make the coolest designs and even offer custom clocks just for you so it just looks plain awesome in your room.

So, check out the WaveClock. See our website www.thewaveclock.com and our Etsy store with our current stock ready to ship.

We've designed and developed the newest device to show you the ocean now. Pleasure Point Design has worked hard to perfect the design and displays. Everything is manufactured in the USA and the WaveClock is built right here in Santa Cruz, California.

Drop us an email with any questions or suggestions support@thewaveclock.com.

Thanks!
Craig Jones and The WaveClock Team