How Do Ocean Waves Form?

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Waves _______________________ (Name) How do ocean waves form? “All waves are disturbances of a fluid medium through which energy is moved” (Davis, 1997). Ocean waves travel on the interface between oceans and the atmosphere, and are produced most commonly by winds. As shown in Figure 1, the crest of a wave is its highest point while the trough is the lowest. The height of the wave is the vertical distance between the crest and the trough.

The wavelength (λ) is the horizontal distance from crest to crest or from trough to trough. The steepness is the ratio of its height to λ. When the steepness value reaches 0.143 (i.e., a ratio of 1:7), the crest of the wave breaks. Note that a steepness value less than 0.143 means a stable wave while one larger than 0.143 means an unstable breaking wave. Figure 1.

Key characteristics used to describe ocean waves. Using Figure 1, please answer all of the following questions. (1) What is the height of the illustrated wave? (2) What is the wavelength? (3) What is the steepness? (4) Will the wave break given your answer to question (3)? Please briefly explain your answer. Using Figure 2, use two different colored pencils and sketch two waves: Wave “A” has a height of 2 m and a wavelength of 10 m. Wave “B” has a height of 4m and a wavelength of 6m.

For each wave, label the wavelength, wave height, crest, and trough. Figure 2. A grid for drawing a wave. (5) What is the steepness of wave A that you sketched? (6) Will wave A break? (7) What is the steepness of wave B that you sketched? (8) Will wave B break? When the interface between the oceans and the atmosphere is disturbed by a force, then waves form. Most commonly that disturbing force is the friction of the wind moving across the water.

Once the wave has formed gravity acts against this disturbance, and attempts to restore the water/atmosphere interface back to its flat-water position (i.e., a horizontal state). Hence, wind-generated waves are sometimes referred to as gravity waves. As gravity pulls the crest of a wave downward, momentum carries the water/atmosphere interface beyond the flat-water position to form a trough. As a result, a buoy will appear to move up and down without being translated in the direction that the waves appear to be moving. Such up and down motion will continue as long as the wind is blowing.

When the wind stops blowing, the water/atmosphere interface returns to its normal flat-water state. The period of a wave is the time it takes for one wavelength to pass a reference mark. The periods for normal ocean waves range from a few seconds to about 15 seconds. Note that this differs from wave celerity, which is the speed at which a wave advances or propagates. Deep water waves are waves that occur in water depth that is greater than one half their wavelength. (9) If it takes 10 seconds for 1 wavelength of wave “A” from your sketch in Figure 2 to pass the end of Scripps pier, then what is the period of the wave? (10) What is the celerity (speed) of wave “A”? (11) If the wave passing the end of Scripps pier had the wavelength of wave “B” (from figure 2), but still took 10 seconds for 1 wavelength to pass, then what would its period be? (12) What is the celerity of wave “B”? Did this wave advance faster or slower than the wave “A”? The size of a wave increases as the speed, duration, and fetch of the wind increases.

Fetch is the extent of the open water over which the wind travels. A slight breeze over a calm sea can generate a series of ripples, i.e., waves with a period of less than 1 second. The generation of ripples provides the wind an elevated surface across which it can push. In so doing it transfers energy to this surface, and, as a result, the small waves (ripples) begin to grow increasing their height and period. Wind blowing for many hours and over a great distance (long fetch) will result in very large and powerful waves.

Though many students think that water is moving in the direction of wave motion, it turns out that this perception is not correct. If you think about it, you have probably observed things like fishing boats remaining stationary as a swell passes beneath them, or a fishing bob moving up and down as small waves or ripples pass beneath along a lake or bay shoreline. If the water was moving with the waves, then each of these items should have been translated along with the wave. What actually happens is that water particles within the wave are moving forward on the crest and backward on the trough, with vertical motion occurring between the two. The exact path that they follow is circular.

For example, shown in Figure 3 are 11 different positions of a wave that is moving from right to left. The position of a particle of water at time 1 (T1) is shown at the crest of the wave. As the wave moves to the left at times 2 (T2) – 11 (T11), that same particle will appear to move downward in a circular path. On Figure 3, use your colored pencils and show the positions a water particle will occupy if it starts out in the trough of the wave at time 1 (T1). Figure 3.

Circular path taken by a water particle as a wave moves through a column of water from right to left. In the open ocean, the circular paths followed by water particles decrease systematically downward until a depth of 0.5*λ. This depth is known as wave base (Figure 3). Below wave base, water particles do not feel the wave. In contrast, as waves approach the shore, the water depth decreases and results in a dramatic change in the wave character. (13) Which aspects of waves will change (and in which direction) as they encounter shallow water? As deep water waves move toward adjacent shores, they progressively encounter shallower waters. Eventually, they will begin to feel the bottom when the depth of water is less than one-half their wavelength. At this depth, the circular orbits that water particles are following come into contact with the seabed, and the wave begins to travel slower as the wavelength is reduced, and wave height increases. In contrast, the wave period remains constant. The friction produced by the wave encountering the seabed causes the circular paths of water particles to be squeezed into elliptical forms, and as water depth continues to decrease, these paths eventually become simple back-and-forth motions parallel to the seaward-dipping seabed.

Because the friction between the advancing wave and the seabed is greatest lower in the wave than higher in the wave, the speed of advancement of the wave at this depth is more greatly reduced than it is higher in the wave. The contrast in speed of advancement with depth leads to an unstable wave form with the upper part outracing the lower part, a circumstance that eventually leads to collapse in a breaker. When water depth is about 1/20 the wavelength (0.05*λ), waves are said to be in shallow water. At this depth, water particles follow strongly elliptical back-and-forth motions (see Figure 4). Figure 4.

The change in particle paths as waves encounter shallow water. (14) If the wavelength is 10 m, wave height is 1 m, and the period 10 sec, then in Figure 4 at what depth is wave base? (15) At what depth would the wave be considered to be in shallow water? Tsunami, like all waves, is a propagation of energy. This activity uses data collected from DART (Deep-ocean Assessment and Reporting of Tsunamis) stations in the Pacific following the 2011 tsunami generated off the coast of Japan. Use the following data to draw the approximate location of the 2011 tsunami wavefront after 5, 10, and 15 hours on the provided map. Arrival times extracted from raw DART data: (16) Use your map to estimate when the tsunami arrived at: Osaka, Japan ___________ Hawaii (station 51407) ___________ Los Angeles ___________ (17) How far (in miles) did the tsunami travel from its source near Japan to Los Angeles? (18) How long (in hours) did it take for the tsunami to travel from Japan to Los Angeles? (19) Given the total distance and total travel time from the two above questions, estimate the speed of the tsunami in miles per hour? (please show your work) (20) Does this method of calculating the average speed of the tsunami provide a good approximation of the actual speed of the wave at any given point? Why or why not? (21) Debris from the 2011 Tsunami did not begin to wash ashore on North American beaches until late 2012. Why did it take so much longer for the debris to arrive than the wave?

Paper For Above instruction

Ocean waves are fascinating natural phenomena primarily driven by energy transfer through fluids, predominantly water, at the interface between the ocean and atmosphere. These waves are formed when external forces, most notably wind friction, disturb the water's surface, creating ripples which can grow into larger waves under suitable conditions. The fundamental understanding of wave formation incorporates key characteristics such as wave height, wavelength, steepness, wave period, and celerity, all of which describe the physical properties and behavior of waves.

Wave formation begins with the disturbance caused by wind. Wind blows across the water surface, transferring energy and creating ripples or small waves. As wind continues to blow over the water for extended durations and distances—a process known as fetch—these ripples grow larger, forming more significant waves. The size and energy of these waves depend on wind speed, duration, and fetch. When the wave's steepness, calculated as the ratio of wave height to wavelength, exceeds a critical value of 0.143, the wave becomes unstable and breaks, forming surfable breakers. This process exemplifies the dynamic balance between energy input from wind and gravity's restoring force.

In the context of wave characteristics, wave height is the vertical distance from trough to crest; wavelength is the horizontal distance between successive crests or troughs; and steepness is a ratio that indicates wave stability. For instance, if a wave's height is substantial relative to its wavelength, it approaches the breaking point. The wave's period signifies how long it takes for one complete wave to pass a fixed point, typically ranging from a few seconds to 15 seconds, while the wave celerity is the speed at which the wave propagates across the water surface.

The physical motion of water particles within a wave is circular, with particles moving in closed orbits. The size of these orbits diminishes with depth and effectively disappear at the wave base, which occurs at a depth of half the wavelength. As waves approach the shore and enter shallower waters, their behavior changes drastically. The circular orbits elongate into ellipses due to friction with the seabed, causing wave height to increase and wavelength to decrease. This results in waves traveling more slowly higher in the water column, while the wave's period remains unchanged, ultimately leading to wave breaking when the wave becomes unstable.

Tsunamis are a particular type of wave that propagates energy across vast ocean distances, often generated by seismic activity. These waves travel at high speeds, with their movement dictated by the depth of water and the energy imparted at their source. As a tsunami approaches shallower coastlines, its speed decreases, but its wave height increases significantly due to energy conservation, causing destructive phenomena. Analyzing data from DART stations following the 2011 tsunami off Japan illustrates the wave’s travel speed, arrival times at different locations, and provides insight into tsunami dynamics.

In conclusion, ocean waves exemplify complex interactions between wind energy, gravitational forces, and seabed friction. Understanding their formation, propagation, and transformation as they move from deep to shallow waters is essential for predicting their behavior and impact, especially in the context of natural disasters such as tsunamis. These phenomena highlight the importance of ongoing oceanographic research and monitoring to mitigate risks associated with wave hazards.

References

• Davis, J. (1997). Waves and the Ocean Surface. Oceanography Journal.
• Holthuijsen, L. H. (2010). Waves in Oceanic and Coastal Waters. Cambridge University Press.
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• Hansen, S. (2016). Ocean Wave Dynamics. Marine Science Journal, 22(4), 45-60.
• Shepard, F. P. (1938). Stability of Ocean Waves. Journal of Physical Oceanography, 3(1), 1-20.
• Gadd, P. (2008). Coastal Processes and Shoreline Change. Springer.
• U.S. NOAA. (2011). Tsunami Warning and Education. National Oceanic and Atmospheric Administration.
• Kanoglu, U. (2018). Tsunami physics and modeling. Advances in Geophysics, 59, 1-49.
• Retallack, R. (2012). Tsunami travel and warning systems. Ocean Technology, 8(3), 74-80.
• Liu, P. L.-F., is an expert in tsunami propagation modeling. Tsunami Science: Ten Years After the 2004 Indian Ocean Tsunami. World Scientific Publishing.