In deep water waves, individual particles are translated and rotated in a vertical plane about a horizontal axis. This means that as a wave passes through a body of water, the particles of water that make up the wave's motion experience both horizontal and vertical displacements, as well as rotational movement.

Explanation:

Translation of particles:
- When a wave passes through a body of water, the particles of water that make up the wave's motion are displaced horizontally and vertically.
- This horizontal and vertical displacement of particles is referred to as the translation of particles.
- The particles move in a circular or elliptical path as the wave passes through them.
- The magnitude of the horizontal displacement decreases with depth, while the magnitude of the vertical displacement increases with depth.

Rotation of particles:
- In addition to the translation of particles, deep water waves also cause rotational movement of the individual water particles.
- The particles rotate in a vertical plane about a horizontal axis.
- This rotational movement is due to the elliptical or circular motion of the particles caused by the wave passing through them.
- The rotation of particles is more pronounced near the surface and decreases with depth.

Importance of understanding particle motion:
- Understanding the translation and rotation of particles in deep water waves is important in various fields, including coastal engineering, offshore structures, and marine ecology.
- The translation and rotation of particles influence the behavior and impact of waves on coastal structures, such as breakwaters, seawalls, and jetties.
- The movement of water particles also affects sediment transport and erosion processes along coastlines.
- In marine ecology, the motion of particles in waves plays a role in the distribution and movement of plankton, larvae, and other marine organisms.

Conclusion:
In deep water waves, individual particles are not only translated horizontally and vertically but also rotate in a vertical plane about a horizontal axis. Understanding particle motion is crucial for various applications in coastal engineering, offshore structures, and marine ecology.