# Wave Buoy Measurements at Short Fetches in the Black Sea Nearshore: Mixed Sea and Energy Fluxes

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area General Description

#### 2.2. Wave Buoy Data

#### 2.3. Auxiliary In Situ and Reanalysis Data

#### 2.3.1. Anapa Weather Station

#### 2.3.2. Wind Reanalysis Data

#### 2.3.3. Wave Model Data

#### 2.4. Theoretical Background of the Data Analysis

#### 2.4.1. Similarity Approach by Kitaigorodskii [42] for Analysis of Wind–Wave Coupling

#### 2.4.2. Theory of Wave Turbulence for the Analysis of Wind–Wave Coupling

## 3. Results

#### 3.1. Utrish Buoy Time Series for Nearshore Wave Dynamics

#### Directionality of Wind and Waves as a Key Feature of Wave Dynamics

#### 3.2. Conventional Analysis of Wind Speed, Wave Heights, and Periods as Essential Physical Parameters

#### 3.3. Theory of Wave Turbulence for Wind–Wave Coupling Diagnostics

#### 3.3.1. The Equilibrium Range in the Wave Spectra Measured Using the Buoy

#### 3.3.2. Energy Flux in the Spectral Equilibrium Range

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The research area. (

**a**) The general features of the study area and its location within the Black Sea boundaries. (

**b**) The bathymetry at the buoy location. S1 and S2 are the buoy locations at different experiment stages (see Section 2).

**Figure 2.**Buoy time series. Height (

**a**) and zero-crossing period (

**b**) recorded by the buoy. The vertical line shows the beginning of the stage II.

**Figure 3.**Wind and wave directions. (

**a**) Wind speed and direction at the Anapa station. (

**b**) Wind speed and direction from NCEP/CFSRv2. (

**c**) Buoy wave heights and directions. (

**d**) Wave model heights and directions.

**Figure 4.**Wind directions from the Anapa station and from NCEP/CFSRv2. Left—stage I, right—stage II. (

**a**,

**b**) Comparison of all data with ${H}_{s}>0.25$ m. (

**c**,

**d**) Comparison for winds higher than 4 m/s.

**Figure 5.**Wind directions from the Anapa station vs. buoy wave directions. (

**a**,

**b**) Spectral peak wave direction. (

**c**,

**d**) Mean-over-spectrum direction. (

**e**,

**f**) Spectral peak wave direction for winds higher than 4 m/s. (

**g**,

**h**) Mean-over-spectrum direction for winds higher than 4 m/s. Left—stage I, right—stage II. Circles in panel (

**a**) illustrate a possible sequence of wave system conversion: (1) purely wind-driven waves generated along a dominating wind direction (close to the diagonal of the scatter plot); (2) swell as a possible result of the wind-driven system after a switching wind direction.

**Figure 6.**Wind directions from NCEP/CFSRv2 vs. buoy wave directions. Left—stage I, right—stage II. (

**a**,

**b**) Mean wave directions for all data. (

**c**,

**d**) Wave spectral peak directions for all data. (

**e**,

**f**) Mean wave direction for winds higher than 4 m/s. (

**g**,

**h**) Wave spectral peak directions for winds higher than 4 m/s.

**Figure 7.**(

**a**) Spectral component directions vs. spread from buoy data. (

**b**) Peak wave directions measured by buoy vs. wave model data.

**Figure 9.**Wave age vs. pseudo-age, ${H}_{s}>0.25$ m, no wind speed restrictions. Left column—stage I, right—stage II.(

**a**,

**b**) Buoy measurements with the wind speed scaling from Anapa station. (

**c**,

**d**) Buoy measurements with the wind speed scaling from NCEP/CFSRv2. (

**e**,

**f**) Wave model data with with the wind speed scaling from NCEP/CFSRv2.

**Figure 10.**Wave age vs. pseudo-age, ${H}_{s}>0.5$ m, wind speed ${U}_{10}>4$ m/s. Left column—stage I, right—stage II. (

**a**,

**b**) Buoy measurements with the wind speed scaling from Anapa station. (

**c**,

**d**) Buoy measurements with wind speed scaling from NCEP/CFSRv2. (

**e**,

**f**) Wave model data with with the wind speed scaling from NCEP/CFSRv2.

**Figure 11.**Period of measurements 1 February 2020 11:43:00–1 February 2020 16:13:00 (${H}_{s}\approx $ 1.88–2.10 m). (

**a**) Buoy frequency spectra $E\left(\omega \right)$. (

**b**) Bottom panel—compensated dimensionless spectra with the wind from NCEP/CFSRv2 scaling $E\left(\omega \right){\omega}^{4}/\left(g{U}_{10}\right)$, horizontal line corresponds to estimates of ${\alpha}_{4}=0.0045$ of Bjorkvist et al. (see, e.g., [43]).

**Figure 12.**Period of measurements 3 June 2021 19:44:00–4 June 2021 00:14:00 (${H}_{s}$ = 2.58–2.94 m). (

**a**) Buoy frequency spectra $E\left(\omega \right)$. (

**b**) Compensated dimensionless spectra with the wind from NCEP/CFSRv2 scaling $E\left(\omega \right){\omega}^{4}/\left(g{U}_{10}\right)$, horizontal line corresponds to estimates of ${\alpha}_{4}=0.0045$ of (see, e.g., Bjorkvist et al. [43]).

**Figure 13.**Scatter density plot (normalized by the distribution maximum) of the wind speed from NCEP/CFSRv2 vs. the retrieved one. Cluster 1 of the probability excess correspond to the validity of the wind speed retrieval algorithm [93]. Cluster 2 can be treated as the effect of wave system conversion, see Figure 5a and the corresponding comments.

Stage | Coord. | Depth, m | Fetch, m | Dates | Data Type | Number of Records |
---|---|---|---|---|---|---|

1 | 44.7191 N, 37.4343 E | 18 | 600 | 31 January 2020–21 February 2020; 17 July 2020–2 October 2020; 27 October 2020–18 February 2021 | wave height, zero-crossing period, spectra | 11,143 |

2 | 44.716 N, 37.428 E | 42 | 1500 | 15 March 2021–17 June 2021 | wave height, zero-crossing period, spectra | 4569 |

Wave Motion Sensor | Precision | 1–2 cm, all directions (1$\sigma $) |

Periods | 1.6–20 s | |

Wave data | Resolution | 1 cm (north 2 cm, LSB “north” is GPS data gap indicator) |

Range | −20 ± 20 m | |

Rate | 1.28 Hz | |

Reference | WGS84 | |

Spectral data | Frequency resolution | 0.005 Hz below 0.10 Hz and 0.010 Hz above frequency range 0.025–0.60 Hz |

Direction resolution | $1.5\xb0$ | |

Direction range | 0–360° |

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## Share and Cite

**MDPI and ACS Style**

Rybalko, A.; Myslenkov, S.; Badulin, S.
Wave Buoy Measurements at Short Fetches in the Black Sea Nearshore: Mixed Sea and Energy Fluxes. *Water* **2023**, *15*, 1834.
https://doi.org/10.3390/w15101834

**AMA Style**

Rybalko A, Myslenkov S, Badulin S.
Wave Buoy Measurements at Short Fetches in the Black Sea Nearshore: Mixed Sea and Energy Fluxes. *Water*. 2023; 15(10):1834.
https://doi.org/10.3390/w15101834

**Chicago/Turabian Style**

Rybalko, Aleksandra, Stanislav Myslenkov, and Sergei Badulin.
2023. "Wave Buoy Measurements at Short Fetches in the Black Sea Nearshore: Mixed Sea and Energy Fluxes" *Water* 15, no. 10: 1834.
https://doi.org/10.3390/w15101834