Ocean Waves & Tides: Sixth Grade Science
Ocean water is in perpetual mechanical motion, energized by wind-driven surface waves and astronomical gravitational tides generated by the Moon and Sun.
The Mechanics of Wind-Driven Ocean Waves
Surface waves are disturbances that travel across the ocean's surface, transferring mechanical kinetic energy derived from atmospheric winds. It is crucial to understand that an ocean wave represents energy traveling through water—the water itself does not travel across the ocean! As a wave passes in deep water, individual water molecules move in closed vertical circular loops called orbital paths:
- At the crest, water molecules move forward.
- In the trough, water molecules move backward.
- The diameter of the circular orbit decreases with depth, vanishing at a depth equal to half the wavelength (the wave base, depth = λ / 2).
- Submarines cruising below the wave base experience completely calm, motionless water, even during roaring surface hurricanes.
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| ORBITAL WAVE MOTION IN DEEP WATER |
| |
| Direction of Wave Energy Travel =====================================> |
| |
| Crest Crest |
| ( O ) ( O ) |
| / \ / \ |
| ( o ) ( o ) Circular orbital loops |
| \ / \ / shrink with depth |
| ( O ) ( O ) |
| Trough Trough |
| ----------------------------------------------------------------- |
| Wave Base (Depth = λ / 2): Zero wave motion below this line! |
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Factors Determining Wave Size
The height and energy of wind-driven ocean waves depend on three physical variables:
- Wind Speed: Faster winds transfer more kinetic energy via friction to the water.
- Wind Duration: How long the wind blows continuously across the water surface.
- Fetch: The uninterrupted horizontal distance of open water over which the wind blows without changing direction. Ocean storms with vast fetch across the Pacific generate towering ocean swells.
Breaking Waves in the Surf Zone
When a deep-water swell approaches the shallow coastline and water depth drops below the wave base:
- The circular orbits of the water molecules touch bottom and drag against the seabed.
- Friction flattens the circular orbits into squashed horizontal ellipses.
- The wave slows down, its wavelength shortens, and water piles upward, increasing wave height.
- Eventually, the wave becomes too steep to support itself (when the wave height-to-wavelength ratio exceeds 1:7); the wave crest outruns the dragging bottom, curls over, and crashes forward as a breaking wave (surf).
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| WAVE TRANSFORMATION IN SHALLOW WATER |
| |
| DEEP WATER SHALLOW SURF ZONE |
| Crest Curls & Breaks! |
| Wave energy moves freely /\ / |
| Circular orbits / \ / |
| ~~~~~~~~~~~~~~~~~~~~~~~ / \_/ |
| \ / |
| \ Friction / |
| \ with Sea / |
| \ Bed / |
| =====================================+=============================== |
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Tides: Astronomical Gravitational Forces
Tides are the daily periodic rising and falling of sea level along coastlines, caused by the gravitational attraction exerted upon Earth's oceans by the Moon and the Sun. Although the Sun is 27 million times more massive than the Moon, the Moon is 390 times closer to Earth; because gravitational tidal forces diminish with the cube of distance (1 / d^3), the Moon's tidal pull is roughly twice as strong as the Sun's.
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| SPRING VERSUS NEAP TIDE CYCLES |
| |
| SPRING TIDE (Extreme Highs & Lows; Maximum Tidal Range) |
| Sun, Moon, and Earth align in a straight line (Full Moon & New Moon). |
| Gravitational pulls reinforce each other! |
| |
| [ SUN ] ---------------> [ MOON ] ---------------> [ EARTH ] |
| |
| NEAP TIDE (Moderate Highs & Lows; Minimum Tidal Range) |
| Moon is at a 90-degree right angle to the Sun (First & Third Quarter). |
| Gravitational pulls cancel each other! |
| |
| [ MOON ] |
| ^ |
| | |
| [ SUN ] ---------------> [ EARTH ] |
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Spring Tides Versus Neap Tides
- Spring Tides: Occur twice a month during the New Moon and Full Moon phases when the Sun, Moon, and Earth align along a straight line (syzygy). The gravitational pulls of the Sun and Moon reinforce each other, producing extreme tidal bulges: exceptionally high high tides and exceptionally low low tides (maximum tidal range).
- Neap Tides: Occur twice a month during the First Quarter and Third Quarter moon phases when the Moon and Sun pull at right angles (90 degrees) relative to Earth. The Sun's gravitational pull counteracts a portion of the Moon's pull, producing moderate, mild tides: lower-than-normal high tides and higher-than-normal low tides (minimum tidal range).
Exercises and Solutions
Exercise 1: Calculating Wave Properties and Wave Base. A ocean swell rolling across the open Pacific has a wavelength of 160 meters and a wave period of 10 seconds. (a) Calculate the speed of the wave in meters per second; (b) Calculate the depth of the wave base beneath which submarine passengers will feel zero wave motion; (c) If a nuclear submarine is cruising at a depth of 60 meters, will the crew experience rolling wave turbulence from this swell?
Solution 1: (a) Wave speed is wavelength divided by period: v = λ / T = 160 meters / 10 seconds = 16.0 meters per second. (b) The wave base depth is half the wavelength: Depth = λ / 2 = 160 meters / 2 = 80 meters. (c) Yes, the submarine will experience rolling wave motion. Because the submarine is cruising at 60 meters depth, it is operating above the 80-meter wave base, placing it inside the lower orbital motion zone of the passing wave swells. To reach completely calm, undisturbed water, the submarine must dive deeper than 80 meters.
Exercise 2: Predicting Tidal Ranges Based on Lunar Phases. An ocean shipping captain needs to navigate a massive container ship into a shallow tidal harbor that has an underwater sandbar obstacle. The ship has a deep draft and requires the absolute maximum possible high tide depth to clear the sandbar safely. (a) Should the captain schedule the ship's arrival during a Spring Tide or a Neap Tide? Justify your answer; (b) Which two moon phases should the captain look for on the nautical calendar to time the arrival?
Solution 2: (a) The captain should schedule the ship's arrival during a Spring Tide. Spring tides produce the highest high tides of the monthly tidal cycle because the gravitational pulls of the Moon and the Sun align and combine constructively, pulling the tidal bulge to its maximum vertical elevation above sea level, providing the necessary clearance over the shallow sandbar. Neap tides produce weak, subdued high tides that might leave the ship stranded on the sandbar. (b) The captain should look for either the New Moon phase (when the Moon is between Earth and the Sun) or the Full Moon phase (when Earth is between the Sun and Moon), as both alignment phases produce maximum spring tides.