Waves and Water Dynamics

Waves and Water Dynamics

Wave Generation

• Disturbing Force: Most waves are generated by wind blowing across the ocean surface.
  • Atmospheric circulation transfers about 2% of its energy to the ocean surface.
• Fluid Interface Interaction: Waves can also form at interfaces between fluids of different densities.
  • Air-Ocean Interface: Like a boat on the surface.
  • Atmospheric Waves: Giant air masses with different densities interacting. These affect weather.
  • Internal Waves: Occur within the ocean due to density differences.
    • Associated with the pycnocline, where density changes rapidly with depth.
    • Low-density surface water sits above higher-density water which causes waves.
    • Larger than surface waves, reaching up to 100 meters (330 feet).
    • Can be generated by tides, turbidity currents, or ships.
    • Hazardous to submarines; can push them to crush depths.

Wave Basics

• Definition: Waves transfer energy through a medium (the ocean).
• Particle Motion: Water particles move up and down, back and forth, or in an orbital (circular) fashion.
• Energy Distribution: Wind-generated waves are most common. They can be plotted as a function of energy produced vs wave period. Tsunamis have long periods and release a lot of energy (but occur infrequently).

Types of Progressive Waves

• Progressive Waves: Oscillate uniformly and progress through the water without breaking.
  • Longitudinal
  • Transverse
  • Orbital
• Longitudinal (Push-Pull Waves): Compression and expansion, like clapping hands. Molecules compress and expand.
  • Travel through solids, liquids, and gases.
  • Example: Slinky attached to a wall.
• Transverse Waves: Particles move up and down (side-to-side), like doing the rope exercise at the gym.
  • Transmit through solids only (not liquids).
• Orbital Waves: Water particles move in a circular fashion (bobbing up and down).
  • Particles don't travel far, energy moves to next water molecule.

Wave Terminology

• Crest: The highest point of a wave.
• Trough: The lowest point of a wave.
• Still Water Level: Theoretical zero-energy level, halfway between crest and trough.
• Wave Height: Vertical distance between crest and trough.
• Wavelength: Horizontal distance between successive crests or troughs.
• Orbital Path: Circular movement of water particles; diminishes with depth.
• Wave Base: Depth to which wave energy affects water particles.
  • Calculated as wave base = wavelength / 2 .
• Wave Steepness: Ratio of wave height to wavelength ( steepness = height / wavelength).
  • If the ratio exceeds 1/7, the wave breaks.
• The wave period is the time for one wavelength to pass a fixed point. If you are anchored on a boat, it's the time it takes for the next wave crest to strike the boat.
• Wave Period (T): Time for one wavelength to pass a fixed point (crest to crest).
• Wave Frequency: Inverse of wave period ( frequency = 1 / T).

Particle Motion and Wave Base

• Particle Motion: Water particles move in circles, transferring energy.
  • The wave form (energy) advances, but the water remains relatively in place.
  • Analogy: Rubber ducky in a bathtub moves in an orbital pattern as waves pass.
• Wave Base: The extent to which the energy from the wave ineraction interacts with the water molecules. This can be calculated based on the wavelength. Say if a wavelength is 10 feet, the wave base is 5 feet ( wave base = wavelength / 2), meaning the wave will interact with particles 5 feet beneath the surface.

Wave Types Based on Depth

• Deep Water Waves: Occur when water depth is greater than the wave base.
  • All wind-generated waves in the open ocean are deep water waves.
  • Wave speed (celerity) is calculated as C = wavelength / wave period .
  • You can use the handy dandy chart to determine the celerity of a wave if you if you know the wavelength. Draw a straight line up to the period, and draw a line straight across to the graph.
• Shallow Water Waves: Occur when water depth is less than 1/20 of the wavelength.
  • The seabed interferes with orbital motion, flattening it.
  • Examples: Wind-generated waves in shallow areas, tsunamis, and tides.
  • Have a different equation to calculate the solarity or velocity of wave. This is because the ocean floor interferes with the water molecules.

Wind-Generated Wave Development

• Capillary Waves: Small, initial waves caused by wind stress.
  • Wavelengths less than 1.74 cm (0.7 inches).
  • Think ripples when blowing on your hot coffee.
• Gravity Waves: Larger waves formed as wind energy increases.
  • Wavelength exceeds 1.74 cm.
  • Pointed crests and rounded troughs.
  • Gravity aids in energy transfer.
  • Capillary waves are like the ripples in the pond when you throw a rock is radiates outwards.

Factors Affecting Wave Energy

• Wind Speed: Higher wind speed increases energy.
• Wind Duration: Longer duration increases energy.
• Fetch: The distance over which the wind blows adds more energy to the ocean.
  • Storm fetch blows across on the sea, and this causes high energy waves. Those waves move fasters than the storm itself, creating a swell.

Wave Height and Energy

• Wave Height: Directly related to wave energy.
  • Most waves are less than 2 meters (6.6 feet).
  • Breaking waves (whitecaps) occur when steepness exceeds 1/7 ratio.
• Beaufort Wind Scale: Describes sea surface appearance based on wind conditions.
  • Reference page 258 in the book.
  • Hurricane wind speeds have foam and spray, visibility is greatly reduced.
• Scientists use to have a theoretical maximum where waves do not exceed 60 feet. But this was proved wrong by the USS Ramapo after they faced waves up to 112 feet high.

Fully Developed Sea and Swells

• Fully Developed Sea: Equilibrium condition where waves can't grow larger because energy is lost through breaking (whitecapping). A fully developed sea is where the waters have the condition for the waves to grow no further.
• Conditions to create a fully developed sea is an increase wind speed, increase fetch, duration of the wind speed, average height of the waves itself and the wave period. This is not ideal to be traveling on a cruise ship at the moment.
• Swells: Uniform, symmetrical waves that travel outward from a stormy area.
  • Longer wavelengths and long crests transport energy far distances.
  • Swells form when waves move through a fully developed sea, they move faster and the waveforms are longer and symmetrical.

Wave Train

• Wave Train: A group of waves with similar characteristics moving in the same direction. Under ideal circumstances, a train wave is the group of waves will emerge one by one. A group of waves will have velocity. Under ideal condition. Not too complex. These circumstances are rarely found in the ocean. Wave train speed is slower, half the speed of one of the individual leading waves. This helps disperse the energy. Decay distance is the distance over which waves can change from choppy to uniform swell.

Wave Interference Patterns

• Wave Interference Patterns: Waves coming in from different directions and interacting with one another, a