Oceanography

Linear Theory of Ocean Surface waves

The ocean surface wave can be described quantitatively as follows.Surface waves are inherently nonlinear: The solution of the equations of motion depends on the surface boundary conditions.

By assuming that the amplitude of waves on the water surface is infinitely small so the surface is almost exactly a plane. To simplify the mathematics, one can also assume that the flow is 2-dimensional with waves travelling in the x-direction. We also assume that the Coriolis force and viscosity can be neglected.

With these assumptions, the sea-surface elevation ς of a wave traveling in the x direction is :

With

Σ = a sin (kx - ?t)

Where ? is wave frequency in radians per second, f is the wave frequentcy in Hertz(Hz) k is wave number, T is wave period, L is wave-length, and where we assume, as stated above, that k a = o (0)

The wave period T is the time it takes two successive wave crests or troughs to pass a fixed point. The wave-length L is the distance between two successive wave crests or troughs at a fixed time.