VIII. Ocean Waves

The previous chapter focused on waves that were fully deterministic, that is, could be fully predicted without any randomness. Here we turn our attention to non-deterministic, or random, waves as we recognize that the ocean is comprised of many different wave heights and frequencies. The ocean’s surface can be represented as the sum of deterministic waves, provided they act independently and interact minimally. Wind-generated waves vary irregularly over time and space, making it impossible to describe the sea based on individual waves. Instead, the sea surface must be treated stochastically. The statistical properties of waves can be assessed using frequency and probability domains. In deep water, wave heights follow a Gaussian distribution, while in shallow water, they deviate from this pattern but can still be described using theoretical probabilistic distributions. The sea can be classified into ten distinct sea states, increasing in severity with significant wave height.

Wind-generated waves consist of both capillary and gravity waves. Capillary waves are small ripples where surface tension acts as the restoring force, while gravity waves, also wind-driven, are primarily influenced by gravity. Gravity waves play a crucial role in affecting the movement and forces on offshore structures. Although capillary and gravity waves are caused by wind, other types of waves are produced by phenomena such as earthquakes, storms, and planetary motions.

Capillary waves develop on the ocean’s surface when wind speeds are very low. As these waves grow over time, their wavelengths and amplitudes increase until they transition into gravity waves, typically measuring in the centimeter range. Once they reach this stage, continued growth is driven by wind pressure on the steep slopes of the waves, along with shear stress from turbulent wind eddies and tangential surface stress from the air. Non-linear wave interactions also contribute to the formation of both smaller and larger waves. The generation of waves is influenced by how long the wind blows and the distance over which it travels, known as the fetch.

This chapter is a distillation of more detailed texts about ocean waves and the marine environment from the following:

• Taylor, G.I. Generation of Ripples by Wind Blowing Over a Viscous Fluid. In The Scientific Papers of G.I. Taylor, G K Batchelor, Ed. Cambridge, London, 1963, ch. 25, pp. 244-254.
• Jeffreys, H. On The Formation of Waves by Wind. Proc. Roy. Soc. London Ser. A 107 (1924), 189-206.
  Jeffreys, H. On The Formation of Waves by Wind II. Proc. Roy. Soc. London Ser. A 110 (1925), 341-347.
• Miles, J.W. On the Generation of Surface Waves by Shear Flows. Journal of Fluid Mechanics 3 (1957), 185-204.
  Miles, J.W. On the Generation of Surface Waves by Shear Flows Part 2. Journal of Fluid Mechanics 6 (1959), 568-582.
• Miles, J.W. On the Generation of Surface Waves by Shear Flows Part 3. Journal of Fluid Mechanics 6 (1959), 583-598.
• Sverdrup, H.U., and Munk, W.H. Wind, sea and swell. Theory of relations for forecasting. U.S. Hydrogr. Office, Washington 601 (1947).
• Pierson, W,J. Wind generated gravity waves. Advances in Geophysics (1955), 93-178.
• Apel, J.R. Principles of Ocean Physics. Academic Press, New York, 1987.
• Lamb, H. Hydrodynamics. CJ Clay and Sons, Cambridge, 1895.
• Mei, C. The Applied Dynamics of Ocean Surface Waves. John Wiley and Sons, New York, 1982.
• Phillips, O.M. The Dynamics of the Upper Ocean. Cambridge University Press, Cambridge, 1977.