# Motion in the Ocean

### Student Worksheet - Problems on Winds, Waves, and Currents

Surface ocean waves are produced by winds. The height of these waves depends upon wind speed, the length of time the wind blows (duration) and the distance over which the wind blows (fetch). In 1952, Charles Bretschneider created a diagram that describes the relationship between these parameters and provides an easy way to predict the height of a wave produced by specific wind conditions. Figure 1 is an example of this kind of diagram (usually called a “Sverdrup-Munk-Bretschneider nomogram”). The y-axis describes Wind Speed; the x-axis describes Fetch Length; solid curved lines in the middle of the diagram show the Wave Height in feet (most Sverdrup-Munk-Bretschneider nomograms also include lines showing wave period and wind duration; these have been omitted from Figure 1 for clarity). When using the nomogram, be sure to match these lines with the correct labels!

Figure 1: Sverdrup-Munk-Bretschneider Nomogram

1. If a wind blows over a 10 nautical mile fetch at 21 knots, what would the resulting wave height be?

2. What would cause the larger increase in wave height for conditions in the preceding question: increasing the wind speed by 60 knots or increasing the fetch length by 60 nautical miles?

3. What would be the minimum fetch over which a 60 knot wind would have to blow to produce a wave 10 feet high?

4. There are a variety of ways to measure the velocity of a current. One of the oldest and simplest methods is to use a “drifter,” which can be any floating object (an ideal drifter is one that is not affected by wind; glass bottles partially filled with sand are a traditional type of drifter). To measure current velocity, an observer places the drifter into the water, measures the amount of time the drifter takes to move a known distance, and notes the direction of the drifter’s motion (since velocity is a vector quantity, and has dimensions of direction as well as speed). Next, the observer finds the speed of the current by dividing the distance the drifter traveled by the time it took to travel that distance. The speed of the drifter combined with the direction in which it moved is the current’s velocity.

Suppose a drifter is released near Charleston, SC from a research vessel whose position is 32°23’15” North latitude, 79°12’33”West longitude, at 0915 eastern standard time (EST) on May 11, 2004. A sailing yacht recovers the drifter at 1930 EST on May 17, 2004 in position 39°56’23” North latitude, 73°44’35” West longitude. What is the estimated velocity of the current that transported this drifter? In this case, it is sufficient to describe the direction component of the velocity vector as north, northeast, east, southeast, south, southwest, west, or northwest. State the speed component of the vector in knots (nautical miles per hour). [Hint: You can use the calculator at http://www.chemical-ecology.net/java/lat-long.htm to find the distance between two points whose latitude and longitude are known.]

If you would like to have a map of the area covered by the drifter, visit the Marine Geoscience Data System Web site ( http://www.marine-geo.org/tools/maps_grids.php). Enter the latitude and longitude boundaries for the area you want the map to cover, then click on the “Map” button. In this case you would enter 40° as the northern boundary; -80° as the western boundary (note that longitudes west of the prime meridian are assigned a negative value, while longitudes east of the prime meridian are positive); -73° as the eastern boundary; and 32° as the southern boundary. The map will show the elevation (or depth) of Earth’s surface in the included area. You can download the map using the “Save Image As . . ” function of your Web browser.

5. Suppose an amateur oceanographer in Oregon releases a drift bottle from position 46°13’56” North latitude, 125°47’12” West longitude, at 1140 Pacific standard time (PST) on August 6, 2005. At 1435 PST on August 20, 2005, the bottle is found floating between the islands of Santa Cruz and Santa Rosa in Channel Islands National Park at 34°00’23” North latitude, 120°00’10” West longitude. Estimate the velocity of the current that transported this drifter. Describe the direction component of the velocity vector as north, northeast, east, southeast, south, southwest, west, or northwest, and state the speed component of the vector in centimeters per second.

You can use the Marine Geoscience Data System Web site ( http://www.marine-geo.org/tools/maps_grids.php) to generate a map as described above. Enter 47° as the northern boundary; -126° as the western boundary; -120° as the eastern boundary; and 34° as the southern boundary.

6. The deflection of moving objects caused by Earth’s rotation is called the Coriolis effect. Acceleration due to the Coriolis effect always acts at right angles to the direction of the velocity vector, and has a magnitude of

(2 • w • v • sin f) cm/sec2

where w is the angular velocity of Earth, v is the velocity of the moving object, and f is the latitude in degrees. Since the angular velocity of Earth is about 7.29 x 10-5 radians/sec, acceleration due to the Coriolis effect is about

(1.5 x 10-4 • v • sin f) cm/sec2

(note that radians have no units). What does this equation suggest about the magnitude of the Coriolis acceleration at the equator?

1. Suppose a soccer player in Tijuana, Mexico kicks a soccer ball with a velocity of 10 meters per second. What is the effect of the Coriolis acceleration on the ball?

2. Given the results of the preceding question, why is Coriolis acceleration significant to the circulation is the atmosphere and ocean?