# Modeling of Hydrodynamics and Dilution in Coastal Waters

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Mixing Process and Dilution

#### 2.1.1. Near-Field Dilution

#### 2.1.2. Far-Field Dilution

_{p}= −ln(0.1)/T

_{90}

_{p}is the decay rate of pollutant, D

_{x}, D

_{y}, D

_{z}are turbulent diffusion coefficients in x-, y-, z- directions, respectively, S

_{s}is the concentration at the farthest point of near-field region (pollutant source). The decay rate k

_{p}is a function of T

_{90}, that is the disappearance time of 90% of the microorganisms. The value of T

_{90}depends on the season: in summer it is equal to at least 1.5 h in the Aegean Sea and the Mediterranean Sea and 2 h in the Black Sea, and is greater in winter when can reach 3–5 h.

## 3. Study Field

## 4. Wind and Wave Climate

## 5. Current Pattern

_{a}= 1028 kg/m

^{3}. The temperature of sea water, salinity, and density were taken as constant in the numerical model. The steady state circulation patterns at the surface and bottom layers under the shear forcing of wind blowing from WSW, WNW, and NE at 10 m/s are shown in Figure 8, Figure 9 and Figure 10.

## 6. Modeling of Pollutant Transport

## 7. Results and Discussion

_{90}was taken as 1.5 h in summer and 2.5 h in winter in numerical modeling.

## 8. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

${g}^{\prime}$ | Buoyant gravitational acceleration |

${\rho}_{0}$ | Effluent density |

${\rho}_{a\left(z\right)}$ | Vertical ambient distribution |

${\rho}_{ref}$ | Reference density |

C | Pollutant concentration |

D_{x} | Turbulent diffusion coefficients in x-direction |

D_{y} | Turbulent diffusion coefficients in y-direction |

D_{z} | Turbulent diffusion coefficients in z-direction |

k_{p} | Decay rate of pollutant |

S_{s} | Concentration at the farthest point of near-field region (pollutant source) |

u | Velocities in s (axial) direction of the buoyant jet |

v | Velocity in r (transverse) direction of the buoyant jet |

bac | Bacteria |

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**Figure 1.**Geographical location of the study area in Edremit Bay [36].

**Figure 2.**Wind rose based on hourly wind measurements for 1970–2016: (

**a**) Ayvalık Meteorological Station; (

**b**) Edremit Meteorological Station; and

**(c)**wind rose based on wind predictions with 6 h intervals for 2000–2016 from European Centre for Medium Range Weather Forecast (ECMWF) operational archive for coordinates of 39.50 °N–26.90 °E [33].

**Figure 3.**Correlations of wind velocities (m/s) between: (

**a**) Ayvalık Meteorological Station and ECMWF operational archive for coordinates of 39.50° N–26.90° E; (

**b**) Edremit Meteorological Station and ECMWF operational archive for coordinates of 39.50° N–26.90° E [33].

**Figure 4.**Fetch distances according to directions [33].

**Figure 5.**Wave roses [33].

**Figure 7.**Current roses: (

**a**) sea surface layer and (

**b**) bottom layer from ECMWF for 2012–2016 for coordinates 39.50° N–26.90° E [33].

**Figure 8.**Current pattern: (

**a**) sea surface layer and (

**b**) bottom layer, for wind blowing from WSW with speed 10 m/s at the steady state [33].

**Figure 9.**Current pattern: (

**a**) sea surface layer and (

**b**) bottom layer, for wind blowing from WNW with speed 10 m/s at the steady state [33].

**Figure 10.**Current pattern: (

**a**) sea surface layer and (

**b**) bottom layer, for wind blowing from NE with speed 10 m/s at the steady state [33].

**Figure 12.**The effect of wastewater discharge on near-field dilution [20].

**Figure 13.**Effect of current velocity on near-field dilution [20].

**Figure 14.**Distribution of the pollutant cloud caused by the wind blowing from WSW at: (

**a**) 10 m/s and (

**b**) 2 m/s [33].

**Figure 15.**Distribution of the pollutant cloud caused by the wind blowing from WNW at: (

**a**) 10 m/s and (

**b**) 2 m/s [33].

**Figure 16.**Distribution of the pollutant cloud caused by the wind blowing from NE at: (

**a**) 10 m/s and (

**b**) 2 m/s [33].

**Table 1.**Exceedance time interval and the probability distribution of significant wave heights (H

_{s}) of ECMWF data for 2000–2016 [33].

Direction | Distribution Equation | 1 h/year | 5 h/year | 10 h/year |
---|---|---|---|---|

H_{s} (m) | H_{s} (m) | H_{s} (m) | ||

WNW | H_{s} = −1.11 − 0.268ln(p(H)) | 1.3 | 0.9 | 0.7 |

W | H_{s} = −0.714 − 0.225ln(p(H)) | 1.3 | 1.0 | 0.8 |

WSW | H_{s} = −0.708 − 0.283ln(p(H)) | 1.9 | 1.4 | 1.2 |

SW | H_{s} = −0.781 − 0.424ln(p(H)) | 3.0 | 2.4 | 2.1 |

SSW | H_{s} = −0.404 − 0.323ln(p(H)) | 2.5 | 2.0 | 1.8 |

S | H_{s} = −0.479 − 0.233ln(p(H)) | 1.6 | 1.3 | 1.1 |

SSE | H_{s} = −0.193 − 0.104ln(p(H)) | 0.8 | 0.6 | 0.5 |

**Table 2.**Wind velocities and occurrence frequency [33].

Wind Speed (m/s) | Wind Direction | Occurrence Frequency (%) | |||
---|---|---|---|---|---|

Summer | Winter | Spring | Autumn | ||

>10 | WSW | 0.006 | 0.005 | 0.006 | 0.003 |

>10 | WNW | 0.001 | 0.001 | 0.001 | 0.005 |

>10 | NE | 0.001 | 0.006 | 0.005 | 0.006 |

<2 | WSW | 98.5 | 97.2 | 98.5 | 98.6 |

<2 | WNW | 98.2 | 97.8 | 98.5 | 98.7 |

<2 | NE | 98.6 | 97.4 | 98.2 | 98.9 |

Total diffuser length | 117 m |

Depth of discharge | −15 m |

Pipe diameter of sea outfall | 0.56 m |

Diameter of diffuser port | 0.075m |

Number of ports | 40 |

Density of wastewater, ρ_{a} | 999 kg/m^{3} |

Average density of sea water, ρ_{0} | 1028 kg/m^{3} |

Initial coliform concentration, Co | 1 × 10^{6} bac/100mL |

Discharge of wastewater, Q | 250 L/s |

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**MDPI and ACS Style**

Inan, A.
Modeling of Hydrodynamics and Dilution in Coastal Waters. *Water* **2019**, *11*, 83.
https://doi.org/10.3390/w11010083

**AMA Style**

Inan A.
Modeling of Hydrodynamics and Dilution in Coastal Waters. *Water*. 2019; 11(1):83.
https://doi.org/10.3390/w11010083

**Chicago/Turabian Style**

Inan, Asu.
2019. "Modeling of Hydrodynamics and Dilution in Coastal Waters" *Water* 11, no. 1: 83.
https://doi.org/10.3390/w11010083