Author's home page | Contents | Next section | Manual

The Oceanic Tides Overview

The ocean tides are manifested by alternating vertical displacements of the sea surface coupled with periodic horizontal movements of the water called the tidal currents. The ocean tides are caused by the gravitational forces produced by the moon and the sun. More exactly, the origin of tides is related with the non-homogeneity of the lunar and solar gravitational fields over the extent of the globe.

This package of computer simulations offers some dynamic illustrations for the properties of tide-generating forces that arise on the earth due to the gravitational field of the moon (or of the sun).

The simulations of this package are implemented as Java applets. Java applets are run by web browsers (with Java plugin installed) under security restrictions to protect the user. In case you have Java 7 or Java 8 installed on your machine, trying to run Java applications generates a message:

  • Java applications blocked by your security settings.
As a workaround, you can use the Exception Site List feature of your operating system to run the applications blocked by security settings. Adding the URL of the blocked application (applet) to the Exception Site List allows the applet to run with some warnings.

Steps to Add URLs to the Exception Site list:

  • Go to the Java Control Panel (On Windows click Start, then Control Panel, and find Java there).
  • Click on the Security tab of the Java Control Panel.
  • Click on the Edit Site List button.
  • Click Add in the Exception Site List window.
  • Click in the empty field under the Location field to enter the URL.
  • Type in (or paste) the required URL that hosts the applet, namely
  • Click OK to save the URL that you entered.
  • Continue on the Security Warning dialog.
  • Reload the web page with the applet.

The applets are created with the help of Easy Java Simulations tool developed by Francisco Esquembre, professor of Murcia University, Spain.

A detailed theoretical background (with relevant math equations) for the phenomenon of ocean tides can be found in the paper A Dynamic Picture of the Oceanic Tides available in the pdf format (170 KB). You will need the Adobe Acrobat Reader program to read the manual or to print out the hard copy (20 pages).

The simulations show the tidal forces in the geocentric reference frame that rotates together with the earth making one revolution during a day. We assume for simplicity that the celestial body creating these forces (the moon or the sun) occurs in the equatorial plane of the earth. Its distance from the earth is certainly much greater than shown in the simulation. This means that its image on the screen shows correctly only the direction toward the source body.

The program shows also the stationary tidal wave generated by these forces in a simplified model of the earth covered everywhere by the water envelope of equal depth. The amplitude of this wave is exaggerated in the simulation in order to make visible the peculiarities of the phenomenon.

The gravitational force of the moon exerted on any body on the surface of the earth is much smaller than the gravitational force of the sun. However, the earth is much closer to the moon than to the sun. Therefore the non-homogeneity of the lunar gravitational field is considerably greater than that of the solar field. It occurs that the moon-induced tides are more than twice greater than the sun-induced tides.

To better understand the properties and time variation of the tide-generating forces, and of the tidal wave produced by these forces, we recommend studying successively the sections listed in the Contents.


  1. Global picture of tidal forces and the force at a fixed point
  2. Time variations of tidal forces at different fixed points
  3. Rotating tidal forces as mutually orthogonal oscillating forces
  4. Two systems of oscillating forces
  5. Standing waves driven by the oscillating forces
  6. Both oscillating waves and the circulating tidal wave
  7. The tidal wave over resonance
  8. Tidal friction and the phase delay

Back to top

Author's home page | Contents | Next section | Manual

The Oceanic Tides Overview