6.1 Wave formation, propagation, and characteristics

Wave Formation, Propagation, and Characteristics

Waves are the ocean's primary way of moving energy from one place to another. Wind, earthquakes, and gravitational forces all generate waves, and each produces waves with distinct behaviors. Understanding how waves form, travel, and change gives you the foundation for topics like coastal erosion, tides, and tsunami dynamics.

Wave Formation and Characteristics

Process of Wave Formation

Most ocean waves start with wind. As wind blows across the water's surface, friction between the moving air and the water transfers energy into the surface layer. Three factors control how large those wind-generated waves become:

• Wind speed — faster wind pushes more energy into the water
• Wind duration — the longer the wind blows, the more energy accumulates
• Fetch — the uninterrupted distance over which the wind blows across open water. A longer fetch means bigger waves because the wind has more room to build them up.

Small ripples called capillary waves form first. Once the surface is roughened by these ripples, the wind can grip the water more effectively, building larger and larger waves.

Wind isn't the only wave-maker. Seismic activity on the ocean floor (earthquakes, volcanic eruptions, underwater landslides) generates tsunamis, and the gravitational pull of the Moon and Sun produces tidal waves (tides). These have very different wavelengths and behaviors compared to wind waves.

Wave Propagation and Energy Transfer

A wave moves energy through the water, but the water itself doesn't travel with the wave. Individual water particles move in roughly circular paths, returning close to their starting position after each wave passes. This is called orbital motion.

The energy in a wave exists in two forms:

• Kinetic energy from the motion of water particles
• Potential energy from water displaced above (crests) or below (troughs) the still-water level

In deep water, water particles trace circular orbits that shrink with depth. Below about half a wavelength, there's essentially no wave motion at all. In shallow water, the seafloor interferes with the circular motion, flattening the orbits into ellipses. This distinction matters because it changes how waves behave as they approach shore.

Wave Types and Properties

Types of Waves and Their Characteristics

Every wave can be described by three basic measurements:

• Wavelength ($\lambda$) — the horizontal distance from one crest to the next
• Frequency ($f$) — the number of wave crests passing a fixed point per unit of time
• Amplitude — the vertical distance from the still-water level to the crest (half the total wave height)

Wave steepness is the ratio of wave height to wavelength. When steepness exceeds roughly 1:7, the wave becomes unstable and breaks.

Waves are also classified by what generates them and by the water depth they travel through:

Based on water depth relative to wavelength, waves fall into three categories: deep-water waves (depth > $\lambda / 2$), transitional waves, and shallow-water waves (depth < $\lambda / 20$). The category determines which equations govern the wave's speed.

Wave Speed, Wavelength, and Frequency Relationships

The fundamental wave equation ties the three core properties together:

$c = \lambda f$

where $c$ is wave speed, $\lambda$ is wavelength, and $f$ is frequency. For a given wave speed, longer wavelengths mean lower frequencies, and shorter wavelengths mean higher frequencies. That's the inverse relationship between wavelength and frequency.

How you calculate wave speed depends on the water depth:

1. Deep-water waves — speed depends on wavelength, not on the bottom:

$c = \sqrt{\frac{g\lambda}{2\pi}}$

Longer deep-water waves travel faster than shorter ones. This is why, far from a storm, you see long-period swell arrive at the coast before shorter chop.

1. Shallow-water waves — speed depends only on water depth:

$c = \sqrt{gh}$

Here $g$ is gravitational acceleration ($9.8 \, m/s^2$) and $h$ is water depth. As the water gets shallower, the wave slows down. This is why waves bunch up and steepen as they approach shore, eventually breaking.

These relationships explain a huge range of ocean behavior, from why tsunami waves (extremely long wavelength) cross entire ocean basins at jet-plane speeds in deep water, to why surf breaks predictably near shore as depth decreases.