The Doppler effect is the apparent change in frequency of a wave when a wave source moves with respect to an observer, or when the observer itself moves relative to the wave source. The Nortek instruments use the Doppler effect by transmitting a short pulse of sound ("ping") of known frequency into the water, listening to the return signal and measure the change in frequency of the signal. The difference in frequency between the transmitted and received pulses is proportional to the velocity of the water. The emitted sound pulse does not reflect from the water itself, but from small suspended particles. These particles are typically phyto- or zooplankton, suspended sediment, or small air bubbles. The scattering materials float passively in the water and it is assumed that they move with the same speed as the water - the measured velocity of the particles is the velocity of the water surrounding the particle. This is a key assumption for the Doppler approach to measure water velocity. The sound pulse scatters in all directions when it hits the particles. Most of the sound continues forward, but a small amount is reflected back to the source. The instrument relates the change in frequency to a relative velocity of the scattering particle compared to the instrument. Only changes in the distance between the instrument and the scattering material (radial motion, along the path of the acoustic pulse) can be measured since this is the only motion that affects the Doppler shift. That means that the instrument does not consider the velocity perpendicular to the beam at all. The instrument then performs onboard signal processing by comparing the transmitted wave with the received wave. The relative velocity can be calculated using equation 2.
| \( V = \frac{F_{\text{Doppler}}}{F_{\text{source}}} \times \frac{C}{2} \) | (2) | |||
| \(V\) | - | current velocity \( [\frac{m}{s}]\) | ||
| \( F_{\text{Doppler}}\) | - | change in received frequency (the Doppler shift) \( [Hz]\) | ||
| \( F_{\text{source}}\) | - | frequency of the transmitted sound wave \( [Hz]\) | ||
| \(C\) | - | speed of sound \( [\frac{m}{s}]\) | ||
From equation 2 one can see that:
- If the backscattering particle is moving away from the instrument so that the frequency of the reflected pulse decreases, the Doppler shift and hence the velocity of the particle is negative.
- If the distance between the transducer and the scattering target decreases, i.e. the particle is moving towards the instrument, the frequency of the reflected pulse increases and the Doppler shift and the velocity is positive.
- If the scattering particle and the instrument stay at a fixed distance from one another, there is no Doppler shift.
In order for the instrument to be able to calculate the Doppler shift the emitted sound needs a known transmit frequency. Nortek instruments range from the so-called narrowband instruments, which transmit a pulse of near-constant frequency, to more advanced broadband instruments which sweep frequencies from low to high in its emitted signal. The signal that is emitted from a so-called broadband instrument is referred to as a chirp and a series of chirps are put together to form one transmit pulse, or ping. The difference between the highest and lowest frequency signal component is referred to as the instrument's bandwidth.
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