# Mesoscale Eddies in the Black Sea and Their Impact on River Plumes: Numerical Modeling and Satellite Observations

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Numerical Model

^{2}/s) allows the model to realistically reproduce numerous mesoscale and sub-mesoscale eddies and structures such as eddies, filaments, mushroom currents, and jets [3,28,69].

#### 2.3. Spectral Methods

#### 2.3.1. Fourier Transform

**V**(t) in a Cartesian coordinate system at a point with coordinates

**r**: {x, y, z}, at times t

_{i}= iδt, i = 1, 2, …, N, using the Fourier series:

**V**(t) is defined as ${\mathrm{S}}_{\mathrm{ij}}=\langle \widehat{{\mathrm{u}}_{\mathrm{i}}}\ast \widehat{{\mathrm{u}}_{\mathrm{j}}}\rangle $, where $\widehat{{\mathrm{u}}_{\mathrm{j}}}$ are the components of the vector ${\hat{\mathrm{V}}}_{\mathrm{m}}$; the asterisk (*) denotes the complex conjugation; the brackets denote the averaging over the ensemble, which due to the ergodicity hypothesis is replaced by averaging over the resolution bandwidth window [78].

#### 2.3.2. Wavelet Transform

_{0}(η):

#### 2.4. Lagrangian Particle Tracking Method

_{t}denotes the total number of time steps, and Δt is the time step. The advective movement of each particle within a grid cell is computed with the use of the linear interpolation of the velocity components for the corresponding Die2BS grid cell at the time step Δt.

^{−1}m/s that will cause an accumulation of particles in layers with weak vertical mixing. To avoid this, we use the so-called “consistent random walk” (CRW) approach for determining the vertical displacement of particles as ${\vartheta}_{3}={\mathrm{K}}_{3}^{\prime}\left(\mathrm{z}\right)\mathrm{\u2206}\mathrm{t}+{\mathsf{\gamma}}_{3}{\left[2{\mathrm{K}}_{3}\left({\mathrm{z}}^{\ast}\right)\right]}^{1/2}$.

## 3. Results

#### 3.1. Spectral Analysis of Eddy Kinetic Energy

^{−4}s

^{−1}, respectively. N is a characteristic magnitude for the Brunt–Väisälä frequency,$\mathrm{N}={\left(\frac{\mathrm{g}}{{\mathsf{\rho}}_{0}}\frac{\partial \mathsf{\rho}}{\partial \mathrm{z}}\right)}^{1/2}$, where g is the gravitational acceleration, $\mathsf{\rho}$ is the upstream density profile, ${\mathsf{\rho}}_{0}$ is a mean density, and z is the upward vertical coordinate). ${\mathrm{R}}_{\mathrm{d}}={\left(\mathrm{g}\left(\mathsf{\Delta}\mathsf{\rho}/\mathsf{\rho}\right)\mathrm{H}\right)}^{1/2}{\mathrm{f}}_{0}^{-1}$, where $\mathsf{\Delta}\mathsf{\rho}$ is the density difference between the stratified thickness of $\mathrm{H}$ and homogeneous layers.

^{−1},we may expect the periodicity of the generation of the topographic eddies within the range from ~23 to ~2.3 days.

#### 3.1.1. FT Analysis

#### 3.1.2. WT Analysis

#### 3.2. Caucasian Eddy Formation

#### 3.3. Development of an Isolated Eddy and Its Translation along the Caucasian Coast

_{0}in the period between days 305 to 365 (i.e., 10 September–31 December) of the model year 39. According to the prehistory of this event, at the beginning of day 305 (not shown), there were no young eddies developing along the Caucasian coast though the model revealed several short strips of anticyclonic vorticity (ζ/f

_{0}~−0.2) confined within narrow bands along the coast abeam of Novorossiysk, Tuapse, and Pitsunda.

_{0}reached the value of about −1.2, whereas in the center of A22 that equaled about −0.4. Note that there is no connection yet between the young eddy A11 and the Rioni eddy A22 approaching the Iskuria Cape. On days 322–327, eddy A11 increased in size, while A22 continued moving to the northwest to the Pitsunda Cape, providing a stable connection tying A22 and A11 eddies, though this tie was to weaken due to the dissipation of A22 when it passed over the Iskuria Cape, as is clarified by Figure 6 (days 332, 340, and 345). As A11 moved away from the place of origin, A22 gradually dissipated. By day 355, A22 almost disappeared; only weakened remnants of A22 are seen, whereas eddy A11 traveled the abeam of Tuapse and maximum ζ/f

_{0}equaled −0.4.

_{0}~−0.6.

_{0}dropped to 0.02.

_{0}in the core of A22 remained constant and equal to −0.4 until day 315 and began gradually decreasing as the eddy passed over the sill and decayed. The variation of vorticity at site A12 reflected effects of all processes: the short event of A11 generation lasting until day 310, the intrusion of A22 lasting until day 340, and an increase of vorticity appeared to cause by a new event of A11 generation.

## 4. Discussion

_{10}(C), corresponding to surface streamlines modeled for days from 310 to 365. Visual analyses of the particle distribution revealed that at the beginning of the particle experiment (day 310) all released particles followed the RC and stretched along the Caucasian coast as a narrow northwestward band pressed against the shore. Within the band, river discharges are clearly pronounced by red strips. This pattern was conserved until an eddy event, the prehistory of which predicted an anticyclonic meander in the coastal zone between the Pitsunda Cape and Tuapse. Once a near-shore eddy had been formed (the first signs appeared on day 315), the eddy behavior started to affect the nearby river plumes. It resulted in engulfing and capturing particles from river plumes into the eddy.

## 5. Conclusions

^{−1}, i.e., from 0.043 to 0.43 cpd that corresponds to the period from 23.3 to 2.3 days.

_{0}~−0.6. During the mature stage, the inner core of A11 had a radius of about 30 km and the core rotation was estimated to be about 12 days. The translation velocity of the eddy during this period was found equal to 2.3 km/day. During the decay stage, A11 underwent intensive decaying so that by day 365, the vorticity in the eddy core dropped to 0.2 and, 10 days later its value dropped to 0.02.

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Bathymetry of the study area in the northeastern part of the Black Sea. Yellow line indicates section northwest from Sochi; yellow numbers 1 and 4 indicate sites at the shelf and continental slopes, respectively, which are referred to in Section 3. The red line D denotes the characteristic horizontal dimension of the submarine ridge used in Section 3.1 for estimation of shedding frequency.

**Figure 2.**An example of online graphical output from the Lagrangian particle model illustrating particles captured by the Caucasian anticyclonic eddy (CAE). Yellow color indicates particles traveling in the open sea while magenta color denotes those stuck to the shoreline.

**Figure 3.**Spectra of kinetic energy, $\mathrm{KE}=0.5\left({\mathrm{U}}^{2}+{\mathrm{V}}^{2}\right)$, at the continental slope (Site 4, panel

**A1**) and shelf slope (Site 1, panel

**B1**). In the panel (

**A1**,

**B1**) in log–log coordinates, thin blue curves denote Fourier spectral densities while thick light-green and light-blue curves denote the mean Fourier spectral densities at 2 m and 167 m, respectively; thick blue curves in semi-log coordinates denote variance-preserving spectra (

**A2**,

**A3**,

**B2**,

**B3**). Frequency range with high level of coherence is shaded. The variable “ampl” is in units of J/m

^{3}.

**Figure 4.**Temporal variations of the kinetic energy density (KE) and the wavelet density (WD) of KE in the range of periods 1–100 days during the model year 39 at Sites 4 (left panel) and 1 (right panel). KE and WD are presented at two depths: 2 m (

**A1**,

**A2**,

**B1**,

**B2**) and 167 m (

**A3**,

**A4**,

**B3**,

**B4**). The white curve shows the time-integrated WD spectra integrated over time. At the right side of each wavelet diagram, the color scale indicates the intensity of the square of the KE. The right color scale denotes units of WD (J/m

^{3}); the 4-day series of KE and WD output corresponds to monthly/row points at the lower scales of KE and WD. The red lines in the shaded parts of the panels A1 and A3 indicate the appearance (at the row points around 2000) of a coherent eddy spanning the depths from the surface to at least to 167 m.

**Figure 5.**Snapshot of streamline structures and sea surface height (SSH) associated with the evolving of: (

**A**) eddy-chain marked by letters A; and (

**B**) the Caucasian anticyclonic eddy (0A1). The BAE and 0A2 denote the Batumi and Rioni anticyclonic eddies, respectively; 1 and 2 denote the Inguri and Rioni rivers, respectively. Magenta lines show isobars of 100, 300, 500, 750, 1000, 1250, 1500, and 1750 m. In the inset, solid lines show the conventional positions of the RC at the easternmost part of the Black Sea in summer (yellow) and winter (green). The yellow ring shows the conventional position of the BAE in the spring–summer period.

**Figure 6.**Sequence of vertical vorticity ζ normalized by f

_{0}at the depth of 50 m illustrates the generation and evolution of the CAE in the period of the transition of circulation from summer to winter of simulated year 39. Julian days are shown at the top. Magenta lines show isobars 500, 1000, and 1400 m. A11 and A22 denote the CAE and the Inguri–Rioni AE, respectively. F denotes coastal upwelling filaments. The inset in the panel ‘day 310’ shows streamlines of the RC abeam of the Iskuria Cape. The magenta star shows the site A12 where the generation of the CAE is triggered, while the white bar shows the submarine ridge nearest this site. In the panel, ‘day 310’ and numbers 1, 4 denote the sites used for kinetic energy spectra study (as in Figure 4).

**Figure 7.**MODIS Aqua optical satellite image snapshot (

**A**); and MERIS Envisat total suspended matter product (

**B**) illustrating entrainment of river plumes by isolated eddies at the study area on 7 December 2021 and 8 July 2010, respectively.

**Figure 8.**A sequence of planar distributions of particle concentration illustrating the influence of the isolated Caucasian anticyclonic eddy on the particle transport mimicking river plumes. In the panel ‘day 310’, Tuapse, Ashe, Mzymta, Bzyb, and Kodor river mouths are marked by numbers 1, 2, 3, 4, and 5, respectively. Julian days are shown at the top. Magenta lines show isobars 500, 1000, and 1400 m. The arrays D, in the panels ‘day 325’ and ‘day 330’, designate dipole structures.

**Figure 9.**Successive MODIS Terra/Aqua satellite images illustrating the capture of the chlorophyll-a rich river plume water by the Caucasian anticyclonic eddy on 26 May 2017 (

**A1**); and dragging it by the eddy along the coast on 13 June 2017 (

**A2**). The center of the eddy is marked by AC. River mouth locations are numbered as in the panel ‘day 310’ of Figure 8.

**Table 1.**The normalized vertical vorticity ζ/f

_{0}in eddies: Caucasian AE (A11), Batumi AE (A22), and at the site (A12).

Day | 305 | 310 | 315 | 322 | 327 | 332 | 340 | 345 | 355 | 365 |
---|---|---|---|---|---|---|---|---|---|---|

A11 | −0.0 | −0.9 | −1.2 | −0.8 | −0.8 | −0.6 | −0.6 | −0.6 | −0.4 | −0.2 |

A12 | −1.0 | −0.6 | −0.3 | −0.4 | −0.4 | −0.80.4 | −0.2 | −0.4 | −0.5 | −0.6 |

A22 | −0.4 | −0.4 | −0.4 | −0.3 | −0.3 | −0.3 | −0.2 | −0.2 | −0.1 | −0.1 |

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**MDPI and ACS Style**

Korotenko, K.; Osadchiev, A.; Melnikov, V.
Mesoscale Eddies in the Black Sea and Their Impact on River Plumes: Numerical Modeling and Satellite Observations. *Remote Sens.* **2022**, *14*, 4149.
https://doi.org/10.3390/rs14174149

**AMA Style**

Korotenko K, Osadchiev A, Melnikov V.
Mesoscale Eddies in the Black Sea and Their Impact on River Plumes: Numerical Modeling and Satellite Observations. *Remote Sensing*. 2022; 14(17):4149.
https://doi.org/10.3390/rs14174149

**Chicago/Turabian Style**

Korotenko, Konstantin, Alexander Osadchiev, and Vasiliy Melnikov.
2022. "Mesoscale Eddies in the Black Sea and Their Impact on River Plumes: Numerical Modeling and Satellite Observations" *Remote Sensing* 14, no. 17: 4149.
https://doi.org/10.3390/rs14174149