Comprehensive Manual32
© 2018 Nortek AS
Orbital Velocities
When a wave propagates past a point it creates local currents below the surface. These currents are
special in the sense that they are changing direction, whereby the crest of a wave will have the
affected water below it moving in the direction of propagation, and the affected water below the trough
moving in the opposite direction of the propagation, as illustrated in the figure below. This cyclical
motion constructs a circular path in the water column and is often referred to as a wave’s orbital
velocity. The orbital velocity produced when a wave passes is the basic mechanism for obtaining
information about the waves on the surface, by use of linear wave theory. This provides the means to
estimate the directional wave parameters that are commonly used to describe the sea state.
Figure: Description of the orbital velocities beneath a w ave as it
propagates. Note that the orbital velocity attenuates w ith depth.
An important detail to understand about orbital velocities is that it attenuates exponentially with
increased depth and shorter wavelength. The wave energy will only propagate to a certain depth; and
the energy cannot be detected below this depth. This means that:
Short waves in deep water do not have an orbital velocity signal that penetrates to the bottom. The
depth limit is related the the Wavelength (L), and is typically at depth L/2.
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 exactly why we are both depth and frequency limited
when measuring waves. See example in next section.
Pressure
Another important property when measuring waves is the dynamic pressure. It is largely dependent
on the presence of orbital velocities and this means it also 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, to rescale the measurement to obtain the wave elevation spectrum at the
surface, by use of transfer functions. The pressure data is thus used for the non-directional wave
estimates.
2.1.8.1 Processing Method
The instrument samples pressure and measurements of orbital velocities, but the resulting time
series of raw measurements is not particularly useful from a practical standpoint. The wave data
therefore needs to be processed to yield the relevant wave parameters that can broadly, yet
accurately, characterize the sea state.
The PUV analysis provides an accurate estimate of the wave elevation spectra in addition to the
direction and the directional spreading. The dynamic pressure measurement provides a means of
estimating all the non-directional wave parameters, while the combined P, U, and V measurements
allow for estimating the directional wave parameters.
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