# On the Variation of Turbulence in a High-Velocity Tidal Channel

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## Abstract

**:**

^{−1}were recorded with maximum flow speeds of 3 ms

^{−1}in the absence of significant wave activity. The velocity fluctuations and turbulence parameters show the presence of large turbulent structures at each location. The easternmost profiler located in the wake of a nearby headland during ebb tide, recorded flow shielding effects that reduced velocities to almost zero and produced large turbulence intensities. The depth-dependent analysis of turbulence parameters reveals large velocity variations with complex profiles that do not follow the standard smooth shear profile. Furthermore, turbulence parameters based on data collected from ADCPs deployed in a multi-carrier frame at the same location and time period, show significant differences. This shows a large sensitivity to the make and model of ADCPs with regards to turbulence. Turbulence integral length scales were calculated, and show eddies exceeding 30 m in size. Direct comparison of the length scales derived from the streamwise velocity component and along-beam velocities show very similar magnitudes and distributions with tidal phase.

## 1. Introduction

^{−1}) was demonstrated in [8]. This identified the effects of Doppler noise and its implications on turbulence parameters. The Doppler noise is created as a byproduct of the velocity calculation, where a phase difference for the Doppler shift occurs for multiple returns within a spatially determined cell [9]. More recent studies quantifying turbulence in tidal channels compared the velocities between a bed-mounted ADCP and an ADV [10,11]. These studies presented a standardised metric, adopted from the wind energy industry, to quantify tidal turbulence; this is known as the turbulence intensity. The turbulence intensity can be calculated using the velocity fluctuation minus the Doppler noise. If the noise is not accounted for, the instantaneous measurements from ADCPs can overestimate the value of the standard deviation calculated from velocity. This produces higher turbulence values for the same corresponding location. The noise can be described as white noise, where it is distributed evenly across all frequencies. The effects of this noise can be mitigated by averaging; this can either be done in time, where instantaneous velocity fluctuations are averaged over a number of minutes, or in space, where velocity fluctuations can be averaged across the vertical profile. This, however, is not a viable solution when considering turbulence measurements. The quantification of the Doppler noise was improved in [12]; this applied a polynomial least square regression method to extend the inertial range to the high-frequency end of the velocity spectrum, lowering the noise floor. Additional methods for correcting instrument noise were presented in [13]. These use either a Noise Auto-Correlation (NAC) or Proper Orthogonal Decomposition (POD) approach to determine and remove noise. In the case of the NAC method, the noise level is calculated based on the velocity spectrum, restricting the noise reduction to the frequency domain. However, the POD method is capable of reducing noise over the spectrum and within the time domain, providing a more flexible output. In addition, these methods may be more suitable for reducing noise in the presence of waves.

## 2. Data Collection and Methodology

#### 2.1. Sensor Deployment

#### 2.2. Basic Data Processing

## 3. Data Analysis and Results

#### 3.1. Flow Characteristics

#### 3.2. Depth Profiles

^{−1}with only a small increase towards the surface. The ebb tide shows very small velocities for the lower part of the water column, and this changes after 13 m upwards, where the velocity increases gradually towards the surface. The SP3 sensor shows a much more conventional shear profile, which experiences a smooth curve from the seabed to the surface, where flow speeds continually increase. The velocity profiles presented provide further details of the flow characteristics around the Fall of Warness. These measurements are key to fully understanding the following analysis of turbulence parameters.

#### 3.3. Turbulence Intensity

#### 3.4. Turbulence Kinetic Energy

#### 3.5. Turbulence Spectra

^{−5/3}in each sub-figure as defined by Kolmogorov’s model [32], this highlights the gradient of the energy cascade from the inertial sub-range. More recently, the description of the −5/3 turbulence energy cascade has been shown to under predict the gradient of the turbulence energy cascade [33]. However, as this study provides measurements for comparisons with other field sites, this study will maintain to use the more conventional −5/3 cascade as this provides a better comparison with existing literature. The majority of the spectra show a measured gradient much lower than the −5/3 gradient. The results compare well between the SE and SP3 sensors in terms of magnitude and distribution of the energy with frequency. The low-frequency part of the spectrum shows no presence of surface gravity waves, which would be represented by an increased PSD in the region of 0.3 to 0.05 Hz. The lower sample rate of the SP3 and SE RDI Sentinel sensor show less noise variation than both Signature sensors, producing a smoother plot. The SP1 sensor records a much larger turbulence velocity spectrum for the ebb tide, indicating larger turbulence variations, with a heavy weighting toward lower frequencies. The results of the turbulence spectra reflect the conclusion shown in the Turbulence Kinetic Energy results displayed in Figure 7. This shows larger magnitudes of turbulent features for the SP1 sensor, specifically during the ebb tide, where there is an increase in low frequency flow components.

#### 3.6. Reynolds Stresses

#### 3.7. Integral Length and Timescales

_{i}) describes the duration of the largest turbulent features. This is calculated using the integration of the autocorrelation function (${R}_{uu}$) of the velocity fluctuation based on the method presented in [15]:

#### 3.8. Length Scales and Homogeneous Assumption

## 4. Discussion

## 5. Conclusions

^{−1}at 150° and ebb velocities of 1.2 ms

^{−1}at 315° are present within the channel. The SP1 sensor, close to the easterly landmass in Figure 1, experiences flow interference midway through the flood tide that persists into the ebb tide, this provides much lower velocities with a wider directional variation.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Sensor deployment locations for the Fall of Warness measurement campaign with the bathymetry provided by UK Hydrographic Office.

**Figure 3.**Left: Average flow velocity vectors over 10 min in the streamwise coordinate system for the SE—Signature 500, SP1—Signature 1000, SE—Sentinel V50 and the SP3—Workhorse. Right: Average flow direction (degrees) and velocity (m/s) for the same sensors at a 10 min interval. With the start date time of the 13 July 2016 11:00:00 am. All data provided is taken 10 m above the seabed.

**Figure 4.**Average peak flood and ebb flow profiles for each sensor for three tidal phases, where blue indicates flood tide and red indicates the ebb tide. The values for the u and speed component of the ebb tide have been inverted to illustrate different flow direction.

**Figure 5.**Turbulence intensity. Left: ${I}_{u}$ based on 10 min windows for each sensor. Right: Turbulence intensity for the first three peak velocity flood and ebb tides, where the flood is positive (blue) and the ebb tide has been made negative (red).

**Figure 6.**Turbulence kinetic energy. Left: TKE based on 10 min windows for each sensor. Right: TKE for the first three peak velocity flood and ebb tides, where the flood is positive (blue) and the ebb tide negative (red).

**Figure 7.**Average turbulence velocity spectra for each sensor during the peak flood (blue) and ebb (red) tide at 10 m from the seabed. The individual spectra for three instances are shown in grey for each sensor during the peak flood and ebb tide. The grey dashed line is included in each subplot to indicate the −5/3 gradient of Kolmogorov’s turbulence energy cascade.

**Figure 8.**Reynolds stresses depth profiles for streamwise uw and transverse vw velocity components, where the flood tide is shown in blue and the ebb tide in red.

**Figure 9.**Integral time (blue) and length scales (red) for the streamwise velocity components. Based on measurements 20 m above the seabed for all sensors. The average velocity for each sensor is shown in grey.

**Figure 10.**The time (left) and length (right) integral scales presented in time and water depth for all sensors. Colour scale units are presented in seconds for the left column of subplots and meters for the right column of subplots.

**Figure 11.**Streamwise, beam 1 and 3 length scales, 13 m above the seabed for both SE co-located sensors. The shaded area indicates length scales shorter than the length over which the homogeneity approximation applies for the given distance from the sensor.

Sensors | Location | Beams | Transmitting Frequency | Beam Angle | Sample Frequency | Vertical Cell Size | Depth |
---|---|---|---|---|---|---|---|

Signature 500 | SE | 5 | 500 kHz | 25° | 4 Hz | 0.5 m | 37 m |

Signature 1000 | SP1 | 5 | 1000 kHz | 25° | 4 Hz | 0.5 m | 37 m |

RDI Sentinel 600 | SE | 4 | 600 kHz | 20° | 2 Hz | 0.75 m | 37 m |

RDI Sentinel 600 | SP3 | 4 | 600 kHz | 20° | 0.5 Hz | 1 m | 44 m |

Sensor Location | Mean | Standard Deviation | ||||
---|---|---|---|---|---|---|

Pitch | Roll | Yaw | Pitch | Roll | Yaw | |

SE (Signature 500) | 1.73° | −4.93° | 232° | 0.07° | 0.08° | 0.04° |

SP1 (Signature 1000) | 0.53° | 0.21° | 164° | 0.13° | 0.09° | 0.37° |

SE (RDI Sentinel 600) | −0.92° | −0.50° | 233° | 0.32° | 0.36° | 0.60° |

SP3 (RDI Sentinel 600) | −0.48° | 3.11° | 160° | 0.45° | 0.38° | 40.81° |

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**MDPI and ACS Style**

Greenwood, C.; Vogler, A.; Venugopal, V. On the Variation of Turbulence in a High-Velocity Tidal Channel. *Energies* **2019**, *12*, 672.
https://doi.org/10.3390/en12040672

**AMA Style**

Greenwood C, Vogler A, Venugopal V. On the Variation of Turbulence in a High-Velocity Tidal Channel. *Energies*. 2019; 12(4):672.
https://doi.org/10.3390/en12040672

**Chicago/Turabian Style**

Greenwood, Charles, Arne Vogler, and Vengatesan Venugopal. 2019. "On the Variation of Turbulence in a High-Velocity Tidal Channel" *Energies* 12, no. 4: 672.
https://doi.org/10.3390/en12040672