Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

1 results

  • Chapter Four - Gravity Waves on Water

  • Johannes Falnes, Adi Kurniawan
  • Book:
    Ocean Waves and Oscillating Systems
    Published online:
    12 May 2020
    Print publication:
    28 May 2020, pp 62-120

  • Summary

    Chapter 4 introduces basic differential equations and boundary conditions for gravity waves propagating along a water surface. Assuming low wave amplitudes, equations are linearised. Then a quantitative discussion is given for harmonical (sinusoidal) waves propagating either on deep water, or otherwise on water of constant depth. Phase and group velocities are introduced, and then formulas are derived for the potential energy and the kinetic energy associated with a water wave. A closely related result is an important formula for the wave-power level, which equals the wave’s group velocity multiplied by the wave’s stored – kinetic + potential – energy per unit of sea surface. An additional subject is the wave’s momentum density. A section concerns real sea waves. Further, circular waves are mathematically described. Two sections of the chapter concern mathematical tools to be applied in Chapters 5–8 of the book. A final section considers water waves analysed in the time domain.