Waves on the ocean surface are visible to us all, however, less obvious are the subsurface dynamics generated by these waves. As explained in Wave types and characteristics, expressing waves in simple mathematical terms as sine and cosine functions, is beneficial when analyzing their characteristics and behavior. However, when observing a body of water it is clear that waves are not in fact uniform and have quite a bit of variability. At any given time the sea surface is composed of different types of waves the surface is in general irregular in both time and space. As a manufacturer of Doppler instruments, Nortek’s wave measurement solutions approach the problem from below the surface. A major advantage of such subsurface measurements is that the instrumentation is located safely below the surface where the risk of loss by vessel collision, vandalism, or theft is reduced.
Orbital velocities
Beneath the surface, waves generate an orbital motion as they pass a point (Figure 1). When a wave propagates past a point it creates local currents below the surface in a clockwise direction. These currents are special in the sense that they are changing direction, so that the water particles below the crest of the wave moves in the direction of propagation, while the water below the trough moves in the opposite direction. This cyclical motion constructs a circular path in deep water and is often referred to as a wave’s orbital velocity.
The ability to measure the orbital dynamics from below allows us to interpret the waves on the surface by use of linear wave theory, and estimate many of the wave parameters that are commonly used to describe a sea state. An important detail to understand about orbital velocities is that they attenuate exponentially with increased depth and shorter wavelength. In other words, particle velocities and their orbital dimensions decrease with increasing distance below the surface and wave energy will only propagate to a certain depth and consequentially the energy cannot be seen or measured below this depth. This means that short waves in deep water do not have an orbital velocity signal that penetrates to the bottom, since higher frequency waves attenuate more quickly with depth. Thus there exists a tradeoff between the depth of the measurement location and the ability to measure the higher frequency waves. This is also true for the dynamic pressure (discussed in the next section), since it is largely dependent on the presence of orbital velocities.
A wave is said to be a deep water wave when the total water depth is greater than half the wavelength (\(D>L/2)\). The orbital motion for deep water waves is circular and of diminishing diameter with depth. Conversely, a wave is considered a shallow water wave when the total water depth is less than 1/20 of the wavelength (\(D<L/20)\). The orbital motion for shallow water waves is elliptical at the surface getting progressively flatter with depth. A the bottom, all motion is strictly back and forth. When the wave is at a depth less than \(L/2\) but greater than \(L/20\) it is a transitional wave.
Dynamic pressure
Another important property when measuring waves is the dynamic pressure. It is largely dependent on the presence of orbital velocities and this means that similarly to the orbital velocities the dynamic pressure signal from waves experiences attenuation as a function of depth and wavelength. The dynamic pressure is at maximum under the wave crest. The rate of decrease with depth is well understood and modeled by linear wave theory. This allows us to measure the pressure near the bottom, and to rescale the measurement to obtain the wave elevation spectrum at the surface by use of transfer functions.
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