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frequency (f),which is the reciprocal of the period,

wave elevation (η) which represents the instantaneous elevation of the wave

from the still water level (SWL) or the mean water level (MWL),

horizontal water particle velocity ( x), which is the instantaneous velocity

along x of a water particle,

vertical water particle velocity ( y), which is the instantaneous velocity along

y of a water particle,

horizontal water particle acceleration (ax), which is the instantaneous

acceleration along x of a water particle, and

vertical water particle acceleration (ay), which is the instantaneous acceleration

along y of a water particle.

A wave creates a free surface motion at the mean water level acted upon by

gravity. The elevation of the free surface varies with space x and time t. The
simplest and most applied wave theory is the linear wave theory. It is also called

small amplitude wave theory or Airy theory. For the linear wave theory, the wave
has the form of a sine curve.

Stokes' second-order wave provides two components for the wave kinematics.
the first one at the wave frequency and the second one at twice the wave

frequency. The relevant formulas for the two components are shown in table 3.4.

The second-order component is smaller than the first-order contribution. The wave

profiles from the two components combine to provide a steeper crest and shallower

trough.

Fifth-Order Stokes Wave Theory is applicable for deep-water high waves. As

the name implies, the fifth-order theory comprises five components in a series

form. Each component is generally an order of magnitude smaller than the

previous one in succession.

Current is a common occurrence in the open ocean. The current at the sea

surface is mainly introduced by the wind effect on the water, variation of

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