On the Hydrodynamic Geometry of Flow-Through Versus Restricted Lagoons

water

Article On the Hydrodynamic Geometry of Flow-Through versus Restricted Lagoons

Nikolaos Th. Fourniotis 1,2,*, Georgios M. Horsch 1 and Georgios A. Leftheriotis 1

1 Department of Civil Engineering, University of Patras, University Campus, 265 00 Patras, Greece; [email protected] (G.M.H.); [email protected] (G.L.A.) 2 Department of Civil Engineering, Technological Educational Institute of Western Greece, Megalou Alexandrou 1, 263 34 Patras, Greece * Correspondence: [email protected]; Tel.: +30-2610-996519

Received: 19 January 2018; Accepted: 17 February 2018; Published: 25 February 2018

Abstract: The classification of a lagoon as a restricted lagoon is shown to depend not solely on its geometry but also on the tidal hydraulics. By numerically simulating the tidal exchange of two lagoons of similar geometrical dimensions, the Nidova lagoon and the Papas lagoon, in Western Greece, subject to very similar tidal forcing, applied to the two tidal inlets in the first case and three in the second, very different residence times are found, namely 2.5 days for the Nidova and 25–30 days for the Papas lagoon. This large difference is attributed to the fact that whereas the Papas lagoon functions as a typical restricted lagoon, in which the water renewal is achieved by mixing in the lagoon of the tidal prism water exchanged within a tidal cycle, the Nidova lagoon functions as a flow-through system because of the differential arrival of the tide at its two tidal inlets. It is suggested that this way of enhancing the flushing rate of a lagoon be considered, whenever possible, when creating a new tidal inlet to the lagoon.

Keywords: ﬂow-through system; tidal inlets; residence time; coastal lagoon; MIKE 3 FM (HD & TR); MIKE 21 FM (HD)

1. Introduction Coastal lagoons are particularly important for fisheries and extensive or intensive aquaculture in many areas of the world, since marine fish species migrate towards lagoons, which provide favorable conditions for feeding and shelter [1]. Mediterranean lagoons, specifically, are important for aquaculture activities, and make a crucial contribution to the fishery economies in many countries. In Greek waters, important fishing and extensive aquaculture activities have been developed in the majority of lagoons (30 in the Aegean and 46 on the Ionian coast), occupying a total area of about 34,500 ha [2]. The fishery exploitation is based on traditional barrier fish traps. These are permanent entrapment devices and the catches are based on the species-specific inshore–offshore seasonal or ontogenic fish migration [3]. The majority of these extensive lagoon systems are located in western and northern Greece. The largest is the Messolonghi lagoonal complex located in western Greece, comprising six lagoons. The Messolonghi lagoon system covers about 15,000 ha [4] (p. 97), while the Papas lagoon (Araxos Cape, Achaia, Greece) has a mean size of 4500 ha [5]. In recent years many lagoon ecosystems have been affected by natural and mostly anthropogenic influences, e.g., hydrologic and hydrodynamic alterations, sources of pollution, sedimentation of tidal inlets/mouths, and regional infrastructure work. These changes gradually lead to alterations in the physical, chemical, and biochemical parameters of these complex ecosystems, which in turn may directly affect fish production and ecosystem dynamics [6,7]. The concentration of the corresponding substances in the lagoon ecosystems is generally dependent on hydrodynamic circulation and water renewal time, which are the crucial factors for decisions with regard to lagoon restoration design and

Water 2018, 10, 237; doi:10.3390/w10030237 www.mdpi.com/journal/water Water 2018, 10, 237 2 of 16 management actions, aiming at the improvement of environmental conditions and fishery exploitation. An innovative method of data analysis has been presented in recent studies, focusing on similar coastal basins in Southern Italy [8,9]. The aim of these studies was to interpret hydrodynamic processes associated with these water bodies by identification and evaluation of hydrodynamic and meteorological data. Among the physical parameters that affect the water quality of coastal lagoons, renewal of water has long been identified as a key parameter and has been made the basis of the early classification by Kjerfve [10] in choked, restricted, and leaky systems according to the degree of water exchanged with the adjacent coastal ocean. More recently, the water renewal time has been proposed as the basis for the classification of lagoons [11]. As a result of the importance of water renewal in lagoons, the creation of new artificial tidal inlets has been proposed and applied as a solution in several instances (see e.g., [12]). The question then arises: is the amount of water exchanged in each tidal cycle the basic parameter—with all other parameters kept constant—determining the flushing time? Or, to rephrase the question, are two lagoons of similar dimensions and under the same tidal forcing expected to have similar flushing rates, or is it possible to have widely varying differences in flushing rates? The answer is provided by a real-life example of two lagoons situated in Western Greece, of similar dimensions and under very similar tidal forcing, namely the Nidova lagoon, part of the complex of the wider Messolonghi lagoon, and the Papas lagoon, both communicating with the Gulf of Patras. The former has a flushing rate on the order of a few days and the latter of over a month. In what follows, we analyze why the former, having only two tidal inlets, does not behave as a typical, restricted lagoon, as one might expect from mere inspection of its geometry, because the hydrodynamics circumvent, so to speak, the topography and render the lagoon a flow-through basin, whereas the latter, having three tidal inlets, behaves like a typical restricted lagoon and, possibly as a result, suffers recurring dystrophic crises.

2. Materials and Methods

2.1. Description of the Study Areas The Nidova lagoon is embedded between the Messolonghi (south) and the Aetoliko (north) greater lagoons (Figure1a). The lagoon is approximately 1.5 km 2 in surface area, with a mean depth of 1.20 m and a maximum depth of 3 m at the western part of the basin. It is elongated in plan view, 2000 m long, approximately, with a perimeter of 5000 m. The lagoon communicates to the north with the deeper Aetoliko lagoon via arc stone bridges, while to the south it is connected to the Messolonghi lagoon by a dredged trench (i.e., an underwater channel that is deeper than its surrounding waters) approximately 50 m wide, 1000 m long, and 1–3 m deep at mean lagoon level. At the western part of the lagoon an embankment with a road on it exists, linking the city of Aetoliko with the Dolmas islet in the south, where the Waste Water Treatment Plant of Aetoliko City operates. This embankment precludes exchange of Nidova waters with the Messolonghi lagoon waters from the west, so that the exchange between Nidova and Messolonghi takes place exclusively south of Nidova. Tidal water enters from the Gulf of Patras to the Messolonghi lagoon from the south, and proceeds to Nidova through the dredged trench, while continuing to move into the Messolonghi lagoon, in parallel to the embankment up to the Aetoliko lagoon, and enters the Aetoliko lagoon through the arc stone bridges. The Nidova lagoon communicates with the Aetoliko lagoon (in the north) though the continuation of the arc stone bridges. During the last few years phytoplankton biomass blooms have formed in the restricted Nidova basin and cover almost the entire surface of the basin during the spring and early summer. The Papas Lagoon is embedded within the northwestern coast of the Peloponnese, adjacent to the Gulf of Patras (Figure1b). The lagoon is of elongated shape, with its main axis along the NW–SE direction. It is 5 km long, 1 km wide on average, and covers an area of about 6.2 km2 [13]. It is a deep water body, having a mean depth of 1.8 m and a maximum depth of 5 m. It is connected to the Gulf of Patras with three stable tidal inlets, the length and width of which lie within 160–260 m and 25–50 m, Water 2018, 10, 237 3 of 16

Water 2018, 10, x FOR PEER REVIEW 3 of 16 respectively.m, respectively. During During the winter, the winter, it is supplied it is supplied with fresh with water fresh by water a small by draining a small streamdraining discharging stream intodischarging the lagoon’s into southeastern the lagoon’s part,southeastern which borders part, which cultivated borders land cultivated [14]. land [14].

FigureFigure 1. 1.Upper Upper panel: General General map map of the of wider the wider area of area the Gulf of the of Patras Gulf ofin western Patras in Greece western (adapted Greece (adaptedfrom MIKE from C MIKE‐MAP, C-MAP, 2018, [15]). 2018, The [ 15open]). Theboundaries open boundaries have been marked have been with marked black lines. with Land black area lines. Landis given area isin givenyellow; in sea yellow; area is sea given area in isblue given and in white blue (blue and for white depths (blue < 50 for m depths and white < 50 for m depths and white > for50 depths m). Detail > 50 m).of the Detail areas of of the interest areas ofis given interest in isthe given lower in panel the lower for (a panel) the Nidova for (a) the lagoon Nidova (Google lagoon Earth, 12‐08‐2017) and (b) the Papas lagoon (Google Earth, 15‐07‐2016) [16]. The locations of tidal (Google Earth, 12-08-2017) and (b) the Papas lagoon (Google Earth, 15-07-2016) [16]. The locations of inlets are denoted with red circles. tidal inlets are denoted with red circles.

TheThe lagoon lagoon is is subject subject to to extensive extensive fish fish exploitationexploitation and and aquaculture. aquaculture. It Itis isnaturally naturally eutrophic, eutrophic, with no anthropogenic influences on the waterfront. Within the last 35 years, nine dystrophic crises with no anthropogenic influences on the waterfront. Within the last 35 years, nine dystrophic crises have been reported, followed by mass fish mortality and benthic fauna; these occurred during the have been reported, followed by mass fish mortality and benthic fauna; these occurred during the summer months of the years 1979, 1984, 1987, 1996, 1997 [17], 2004, 2010, and 2012 [18]. The summer months of the years 1979, 1984, 1987, 1996, 1997 [17], 2004, 2010, and 2012 [18]. The dystrophic dystrophic crises have been related to the decomposition of large beds of macro algae [14]. crises haveBoth been lagoons related are protected to the decomposition by the Ramsar of Convention, large beds of and macro the Nidova algae [ 14lagoon]. is also included inBoth the Natura lagoons 2000 are network. protected The by proper the Ramsar management Convention, of the andlagoons, the Nidova which is lagoon of primary is also importance included in theto Natura local fishermen, 2000 network. includes The plans proper for managementdredging operations, of the lagoons,creation of which inlets, is or of other primary infrastructure importance to localworks fishermen, in the area, includes with the plans aim of for improving dredging the operations, hydrodynamic creation circulation of inlets, and or otherwater infrastructure renewal of worksthese in ecosystems. the area, with the aim of improving the hydrodynamic circulation and water renewal of these ecosystems. 2.2. The Hydrodynamic Code and the Advection–Diffusion Code

Water 2018, 10, 237 4 of 16

2.2. The Hydrodynamic Code and the Advection–Diffusion Code The simulations presented herein have been performed using the commercially available CFD (Computational Fluid Dynamics) code MIKE21 and MIKE3 Flow Model FM (where FM stands for flexible mesh). The MIKE3 Flow Model FM has been used for three-dimensional flow simulation in the Messolonghi–Aetoliko lagoon. It is a modeling system developed by the Danish Hydraulic Institute (DHI), based on a finite volume and an unstructured mesh approach. The hydrodynamic module (HD) extracts numerical solutions from the three-dimensional continuity, momentum, temperature, salinity, and density equations. The momentum equations are used in the incompressible, Reynolds-averaged form of the Navier–Stokes equation (RANS), invoking the Boussinesq assumption and the hypothesis of hydrostatic pressure in the vertical. The turbulence closure is achieved using the Smagorinsky formulation for diffusion in the horizontal and the standard k–ε model in the vertical direction. To account for the Coriolis force, an f-plane has been used. The free surface is taken into account using a sigma-coordinate transformation. The spatial discretization of the primitive equations is performed using a cell-centered finite volume method. In the horizontal plane an unstructured grid is used, while in the vertical direction the discretization is structured. The elements are prisms or bricks whose horizontal faces are triangles or quadrilateral elements, respectively. A Riemann solver is used for computation of the convective fluxes in vertical interfaces, which makes it possible to handle discontinuous solutions. For convective fluxes in horizontal interfaces, two schemes are available: a low order (based on upwinding) and a high order. The low-order scheme requires considerable less time than the high-order scheme. Use is made of the high-order scheme for the accurate simulation of the advection–diffusion simulations (see Section2). For the time integration a semi-implicit approach is used, where the horizontal terms are treated explicitly and the vertical terms implicitly [19]. The MIKE 21 FM (HD) model has been used for simulations of the tidal propagation in the Gulf of Patras, thus providing the boundary conditions both at the entrance of the Messolonghi–Aetoliko lagoon (in the NW part of the Gulf) and at the tidal inlets of the Papas lagoon (in the SW part of the Gulf). The model simulates unsteady two-dimensional flow in one layer of vertically homogeneous fluid, by having the equations for the conservation of mass and momentum integrated over the vertical [20]. We note that the entrances of both the Papas lagoon and the Messolonghi lagoon are at a safe distance from the Rio–Antirio straits, where the presence of stratification influences local hydrodynamics [21]. Thus, the depth-averaged simulations produce adequate boundary conditions for the three-dimensional simulations of flow in both lagoons. Finally, the advection and diffusion of the conservative tracer, applied in the Nidova and Papas lagoons, is simulated utilizing the CFD code MIKE 3 FM Transport Module (TR). This modeling system simulates the spreading and fate of dissolved or suspended substances in an aquatic environment under the influence of the fluid transport and the associated diffusion processes. The hydrodynamic basis for the Transport Module (TR) is calculated with the Hydrodynamic Module (HD) [22].

2.3. Computational Domain and Grid Due to a lack of free surface time series measurements at the entrance of the tidal inlets of the Nidova and the Papas lagoons, which would have been adequate data as boundary conditions for flow simulations, the only alternative is the computation of such data. The only locations that are suitable for boundaries of numerical simulations and where, at the same time, the harmonic constituents of the tide are available, are both ends of the Gulf of Patras, one of which is close to the southern opening of the Messolonghi lagoon and the tidal inlets of the Papas lagoon [23]. It would have been numerically inefficient to perform fully three-dimensional simulations in a domain comprising of an area as large and deep as the Gulf of Patras (135 m maximum depth) together with the lagoonal systems, which includes extensive areas with depth less than 0.5 m, to focus on a small section of the entire Messolonghi–Aetoliko lagoon, namely the Nidova lagoon. Thus, it was decided to resort to two-dimensional, depth-averaged simulations in a domain similar to the one used by [24] covering the entire area of the Gulf of Patras to extract boundary conditions for the three-dimensional simulations Water 2018, 10, 237 5 of 16 in the Messolonghi–Aetoliko lagoon. Such two-dimensional simulations are adequate, in terms of tidal propagation,Water 2018, 10 even, x FOR in PEER summer REVIEW conditions when thermal stratification is set in the lagoon ecosystems.5 of 16

2.3.1.terms The of Nidova tidal propagation, Lagoon even in summer conditions when thermal stratification is set in the lagoon ecosystems. The numerical domain for the three-dimensional simulations covers the entire Messolonghi–Aetoliko2.3.1. The Nidova Lagoon lagoonal system and a small part of the adjacent open waters of the northwestern part of the Gulf of Patras (i.e., the coastal waters in front of Messolonghi lagoon). The numerical domain for the three‐dimensional simulations covers the entire Messolonghi– ThisAetoliko domain lagoonal was discretized system and using a small a part numerical of the adjacent grid consisting open waters of of athe three-zone northwestern triangular part of the mesh in theGulf horizontal of Patras (i.e., (Figure the 2coastal). In the waters ﬁrst in zone, front covering of Messolonghi the northwestern lagoon). This partdomain of thewas gulfdiscretized of Patras, the characteristicusing a numerical length grid is consisting up to 400 of m a offshore. three‐zone In triangular the second mesh zone, in the the horizontal characteristic (Figure length 2). In is the 200 m andfirst covers zone, the covering greater areathe northwestern of the Messolonghi–Aetoliko part of the gulf of Patras, lagoon the complex, characteristic upstream length and is up downstream to 400 of them areaoffshore. of interest, In the second and in zone, the third the characteristic zone the length length dimension is 200 m and varies covers from the 20greater to 50 area m and of the covers the transitionalMessolonghi–Aetoliko part between lagoon the complex, Messolonghi upstream and and Aetoliko downstream lagoons, of the where area of the interest, area ofand the in Nidovathe lagoonthird is zone embedded. the length dimension varies from 20 to 50 m and covers the transitional part between the Messolonghi and Aetoliko lagoons, where the area of the Nidova lagoon is embedded.

FigureFigure 2. Bathymetric 2. Bathymetric map map of of the the Messolonghi, Messolonghi, Aetoliko, and and Nidova Nidova lagoons, lagoons, with with isobaths isobaths shown shown everyevery 8 m. 8 Superimposed m. Superimposed is theis the unstructured unstructured triangular triangular mesh. mesh. The coordinate system system refers refers to to UTM UTM-34.‐ In the34. middle In the middle of the domainof the domain a ﬁner a finer mesh mesh covers covers the the wider wider area area of of the the Nidova Nidova lagoon. lagoon.

TheThe goal goal of theof the present present study study is is to to compare compare how the the residence residence time time of ofsemi semi-enclosed‐enclosed water water bodiesbodies (i.e., (i.e., lagoons) lagoons) depends depends upon upon the the details details of their geometry. geometry. Since Since the the evaluation evaluation of residence of residence times is based on simulations of numerical tracers’ transport, it was found necessary, in order to times is based on simulations of numerical tracers’ transport, it was found necessary, in order to increase the accuracy, to create a third (even smaller) domain (Figure 3), consisting of the entire increase the accuracy, to create a third (even smaller) domain (Figure3), consisting of the entire Nidova Nidova lagoon, the Aetoliko lagoon, and part of the surrounding Messolonghi lagoon area. It is lagoon,within the this Aetoliko truncated lagoon, domain and that part the of Nidova the surrounding waters are estimated Messolonghi to remain lagoon when area. exchanged It is within with this truncatedadjacent domain waters thatof the the Messolonghi Nidova waters and Aetoliko are estimated lagoons to under remain tidal when forcing, exchanged at least for with the time adjacent watersspan of of the interest. Messolonghi Again, the and free Aetoliko‐surface‐time lagoons‐series under boundary tidal conditions forcing, atfor least this truncated for the time domain span of interest.are to Again, be obtained the free-surface-time-series from flow simulations boundary in the immediately conditions larger for this domain truncated (Figure domain 2). In are the to be obtainedtruncated from domain, ﬂow simulations the numerical in the grid immediately consists of larger 10 equidistant domain (Figure layers2). in In the the vertical, truncated and domain, a the numericalhorizontally grid varied consists mesh lying of 10 between equidistant 10 and layers 20 m. in This the domain vertical, proved and aadequate horizontally for simulations varied mesh lyingcovering between at 10least and 40 20days, m. which, This domain as verified proved a posteriori, adequate greatly for exceeds simulations the water covering residence at least time 40 for days, which,the as Nidova veriﬁed lagoon. a posteriori, greatly exceeds the water residence time for the Nidova lagoon. Finally, to produce a grid on which the numerical simulations would require a reasonable Finally, to produce a grid on which the numerical simulations would require a reasonable amount amount of computer time, it was found necessary to merge in one opening all the openings of the of computer time, it was found necessary to merge in one opening all the openings of the series series of arches supporting the stone bridge located at the junction of the Nidova and Aetoliko

Water 2018, 10, 237 6 of 16 of archesWater 2018 supporting, 10, x FOR PEER the REVIEW stone bridge located at the junction of the Nidova and Aetoliko lagoons.6 of 16 TheWater reason 2018 for, 10, this x FOR approximation PEER REVIEW is that the span of the arches is barely a few meters, so discretization6 of 16 lagoons. The reason for this approximation is that the span of the arches is barely a few meters, so of all the arches would require a mesh of characteristic length on the order of 30 cm or so, which is not discretizationlagoons. The ofreason all the for arches this approximation would require is a thatmesh the of spancharacteristic of the arches length is onbarely the ordera few ofmeters, 30 cm so or practical. This practice gave rise to the discretization depicted in Figures2 and3. so,discretization which is not of practical. all the arches This practicewould require gave rise a mesh to the of discretizationcharacteristic lengthdepicted on inthe Figures order of 2 and30 cm 3. or so, which is not practical. This practice gave rise to the discretization depicted in Figures 2 and 3.

FigureFigure 3. Truncated3. Truncated domain domain for for the the wider wider area area of of the the Nidova Nidova lagoon, lagoon, covering covering the the Aetoliko Aetoliko lagoon lagoon and partandFigure of part the 3. Messolonghi of Truncated the Messolonghi domain lagoon. lagoon. for the wider area of the Nidova lagoon, covering the Aetoliko lagoon and part of the Messolonghi lagoon. 2.3.2.2.3.2. The The Papas Papas Lagoon Lagoon 2.3.2. The Papas Lagoon ConcerningConcerning the the Papas Papas lagoon, lagoon, a truncated a truncated computational computational domain domain was was formed formed covering covering the the entire Concerning the Papas lagoon, a truncated computational domain was formed covering the lagoonentire and lagoon the adjacentand the adjacent open waters open waters of the southwesternof the southwestern part ofpart Gulf of Gulf of Patras, of Patras, consisting consisting of threeof entire lagoon and the adjacent open waters of the southwestern part of Gulf of Patras, consisting of zonesthree in zones the horizontal in the horizontal (Figure (Figure4). 4). three zones in the horizontal (Figure 4).

FigureFigureFigure 4. 4.Truncated 4. Truncated Truncated domain domain domain for for for the thethe wider widerwider area areaarea ofof the Papas Papas lagoon, lagoon, coveringcovering covering part part part of of the of the the Gulf Gulf Gulf of of Patras. Patras. of Patras.

InIn theIn the the ﬁrst first first zone, zone, zone, grid grid grid triangles triangles triangles have havehave a aa characteristic characteristiccharacteristic length length of of upup up toto to 300300 300 mm moffshore, offshore, offshore, and and and cover cover cover the the the southwesternsouthwesternsouthwestern part part part of ofof the thethe gulf gulfgulf of ofof Patras, Patras,Patras, which which is included inin in thethe the simulationsimulation simulation domain.domain. domain. InIn the Inthe thesecond second second zone,zone,zone, the the the characteristic characteristic characteristic length length varies varies varies fromfrom from 20 to 20to 100 to m 100 and m covers and covers thethe greatergreater the area area greater of of the the area Papas Papas of lagoon, thelagoon, Papas lagoon,whichwhich which is is the the area isarea the of of area main main of interest interest main interest and,and, finally,finally, and, in ﬁnally, the third in zone, the third thethe cells’cells’ zone, dimensiondimension the cells’ varies varies dimension from from 5 5 variesto to from2020 5m m to and and 20 covers mcovers and the the covers tidal tidal inlets theinlets tidal ofof thethe inlets lagoonlagoon of the as well lagoon as the as transitional well as the partpart transitional betweenbetween the partthe open open between gulf’s gulf’s the waterswaters and and the the lagoon.lagoon. ThisThis truncatedtruncated domaindomain is designed so thatthat itsits peripheryperiphery isis veryvery nearlynearly an an

Water 2018, 10, 237 7 of 16 open gulf’s waters and the lagoon. This truncated domain is designed so that its periphery is very nearly an equitidal line, and, as in the case of Nidova, was made large enough so that waters initially inside the Papas lagoon and later exchanged with Gulf of Patras waters will remain inside this domain during the whole length of the simulations, as veriﬁed by the numerical tracer experiments. The grid consists of 10 equidistant layers in the vertical.

2.4. Boundary and Initial Conditions In all cases considered herein, the coastline has been defined as an impermeable, zero normal velocity boundary, while the bottom is a no-slip (via wall functions), impermeable boundary. For the first domain where the Nidova lagoon is located, the bottom roughness was set equal to 0.01 m and care was taken to ensure that the geometry of the bottom cell was compatible with the requirement of fully rough flow, assuming the minimum flow depth to be 0.4 m. In the transitional part, i.e., in the interior of Messolonghi lagoon, a higher bottom roughness was considered in order to represent the vegetated bottom of the shallow lagoon. At the southern end of the computational domain lies the Gulf of Patras: it is from this boundary that the tide enters the lagoons, namely OB1 (Figure1). To formulate an elevation time series for the location of this open boundary, results from the two-dimensional simulations of the Gulf of Patras were used in the simulations that follow. For the secondary truncated domain (Figure3), used for the experiments with the tracer, tidal boundary conditions were extracted from the previously conducted simulations of the intermediate domain (Figure2). Concerning the Papas lagoon, tidal elevation time series that resulted from the two-dimensional simulations of the Gulf of Patras were used as open boundary conditions in the simulations that follow (Figure4). Initial conditions were needed in all four regions: (a) the Aetoliko lagoon at the northern of the domain, (b) the Messolonghi lagoon in the central part, (c) the opening (OB1) at the northeastern part of the Gulf, and (d) the Papas lagoon. Mean temperature and salinity profiles were imposed as initial conditions throughout the Aetoliko basin, based on the field measurements at four stations covering the longitudinal axis of the lagoon in a NW–SE direction, measured in July 2010 [25], since these measurements showed little horizontal variation. Since this dataset included no measurements in the Messolonghi lagoon, field measurements performed by [26] in the same summer period, i.e., July 2006, were used. Finally, the required profiles for the Gulf of Patras were taken as in [21]. Concerning the Papas lagoon, the simulations were performed considering barotropic flow in the basin even for the summer months, when the Gulf’s waters (outside the Papas lagoon) were found to be stratified [27]. This seems justified because in the shallow waters of the Gulf, within the domain chosen, previous simulations show that the stratification is destroyed and the waters become nearly isothermal and these waters are of constant salinity. Further, according to measurements of [28], stratification does not seem to be important in the lagoon during the summer months. Therefore, the flow, both into the lagoon and in the near vicinity outside it, can be taken as homogeneous.

2.5. The Tracer In this section we present the method we applied to estimate the residence time of the Nidova and Papas lagoonal ecosystems. Various transport time scales have been used in the literature to quantify the renewal of waters in natural systems (e.g., [29]). The present work has been stimulated by research in coastal lagoons that suffer from recurring dystrophic crises, the inception of which has been observed to occur locally before spreading to the entire lagoon [18]. Therefore, it is desirable to aim at calculating a time scale characterizing the local transport rate rather than an integral time scale characterizing the overall renewal of the entire lagoon. For the Papas lagoon, the latter has been carefully calculated in the form of flushing time by [14], who based their calculations on water quality measurements in the lagoon. We note that even though they call their time scale a residence time, we have referred to it as a flushing time since herein we use the definition of [29] for flushing time as an integral scale, and retain the local character they give to the term residence time. Water 2018, 10, 237 8 of 16

More precisely, for the purposes of the calculation, we deﬁne as residence time the time needed for theWater concentration 2018, 10, x FOR PEER of a REVIEW conservative, passive tracer to fall to 1/e (~37%) of its initial value8 (seeof 16 for example [30,31]). By deﬁning the initial concentration of the conservative numerical tracer to be equal example [30,31]). By defining the initial concentration of the conservative numerical tracer to be equal to 1 inside and 0 outside the lagoon, we are thus able to calculate the residence time at each point to 1 inside and 0 outside the lagoon, we are thus able to calculate the residence time at each point insideinside the the lagoon lagoon by by following following the the evolution evolution of of thethe concentration of of the the tracer tracer as asdetermined determined by the by the advection–diffusionadvection–diffusion equation. equation. This This information information shouldshould be be useful useful in in the the analysis analysis of ofthe the very very complex complex problemproblem of the of the inception inception of of the the recurring recurring dystrophic dystrophic crises that that plague plague especially especially the the Papas Papas lagoon. lagoon. We note,We note, however, however, that that the the e-folding e‐folding value value is is a a mere mere convention and and that that in in different different applications applications the the use ofuse different of different cutoffs cutoffs may may be be required. required. This This is is especiallyespecially true true for for research research concerning concerning the the causes causes of of the dystrophicthe dystrophic crises, crises, a topic a topic not not well well understood understood atat thisthis time.

3. Results3. Results and and Discussion Discussion

3.1. Hydrodynamic3.1. Hydrodynamic Characteristics Characteristics of of the the Lagoon Lagoon Ecosystems Ecosystems BothBoth the Nidovathe Nidova and and the Papasthe Papas lagoon lagoon communicate communicate with with the Gulfthe Gulf of Patras: of Patras: the former the former is situated is in thesituated northwest, in the whereas northwest, the latterwhereas is in the the latter southwest is in the of the southwest Gulf (Figure of the1), Gulf and are(Figure therefore 1), and subject are to similartherefore tidal forcing, subject to in similar terms oftidal amplitude, forcing, in because terms of the amplitude, distance because of both the locations distance from of both the locations Rio–Antirio Straits,from where the Rio–Antirio the semidiurnal Straits, where tide entering the semidiurnal the Gulf tide of entering Patras fromthe Gulf the of Ionian Patras Sea from undergoes the Ionian the Sea undergoes the reflection [24], is nearly the same. In the following summary of the salient features reflection [24], is nearly the same. In the following summary of the salient features of the hydrodynamic of the hydrodynamic forcing of the lagoons, we confine our attention to the purely tidal flow, forcing of the lagoons, we confine our attention to the purely tidal flow, ignoring wind-induced effects, ignoring wind‐induced effects, since this is the most severe situation that arises, in terms of water sincerenewal, this is the in both most lagoons. severe situation that arises, in terms of water renewal, in both lagoons. An instanceAn instance of the of velocitythe velocity field field induced induced by flood by flood tide intide the in Messolonghi–Aetoliko the Messolonghi–Aetoliko lagoonal lagoonal system is depictedsystem is in depicted Figure5 ,in where Figure it 5, can where be observed it can be observed that surface that velocities surface velocities range between range between 5 and 125 and cm/s, except12 incm/s, locations except where in locations the depth where is very the shallow.depth is Thevery high shallow. velocities The arehigh especially velocities pronounced are especially at the sandpronounced bars, i.e., in at sites the where sand tidalbars, inletsi.e., in are sites formed, where at tidal the entrance inlets are of formed, the Messolonghi at the entrance lagoon of (from the the GulfMessolonghi of Patras), and lagoon are crucial(from the for Gulf fish migrationof Patras), intoand theare lagooncrucial ecosystem.for fish migration into the lagoon ecosystem.

FigureFigure 5. The 5. The surface surface flow flow field field during during flood flood tide tide intointo the Messolonghi–Aetoliko Messolonghi–Aetoliko lagoonal lagoonal complex. complex. At theAt right the right upper upper corner, corner, detail detail of theof the wider wider area area of of Nidova Nidova lagoon lagoon is is shown, shown, and numerical stations stations t7, t8, andt7, t8, t9 and are marked.t9 are marked.

TheThe very very shallow shallow tidal tidal ﬂow flow in in the the Messolonghi Messolonghi and Nidova Nidova lagoons lagoons is iscontrolled controlled by byhigh high bottom bottom friction.friction. This This is documented is documented in in Figure Figure6, 6, where where it it is is shown shown that, as as we we proceed proceed from from the the Gulf Gulf of Patras of Patras towards the Aetoliko lagoon through the Messolonghi lagoon, there is a decrease in the amplitude of towards the Aetoliko lagoon through the Messolonghi lagoon, there is a decrease in the amplitude of the tide and a delay. The latter becomes manifest as a phase difference between the time series at the

Water 2018, 10, 237 9 of 16

theWater tide 2018 and, 10 a, x delay. FOR PEER The REVIEW latter becomes manifest as a phase difference between the time series9 of at 16 the entrance of the Messolonghi lagoon (which is also the entrance of the underwater trench that leads to theentrance Southern of the entrance Messolonghi of Nidova) lagoon (which and at is the also stone the bridges,entrance of which the underwater delineate the trench northern that leads end of theto Messolonghi the Southern lagoon entrance but of alsoNidova) of the and Nidova at the stone lagoon bridges, (with which the interpolation delineate the of northern the Aetoliko end of island). the Thus,Messolonghi the Gulf oflagoon Patras but tide also reaches of the theNidova northern lagoon end (with of the the Nidova interpolation lagoon of via the the Aetoliko Aetoliko island). lagoon, theThus, surface the of Gulf which of Patras undergoes tide reaches oscillations the northern in unison, end becauseof the Nidova of its lagoon relatively via largethe Aetoliko depth (from lagoon, 12 m in the surface southern of partwhich up undergoes to 30–35 m oscillations in the northern in unison, part). because This differential of its relatively path large the tidedepth of (from the Gulf 12 of Patrasm in has the tosouthern take in part order up to to reach 30–35 them in two the ends northern of the part). Nidova This differential lagoon results path in the the tide development of the Gulf of a differentialof Patras has amplitude to take in andorder a to phase reach lag the and two therefore ends of the a pressureNidova lagoon gradient results along in the the development Nidova lagoon of a differential amplitude and a phase lag and therefore a pressure gradient along the Nidova lagoon (Figure7). This seems to be the key factor that causes the Nidova lagoon to function as a flow-through (Figure 7). This seems to be the key factor that causes the Nidova lagoon to function as a flow‐through lagoon, with a concomitantly short time of water renewal, as we shall see in the following. lagoon, with a concomitantly short time of water renewal, as we shall see in the following. This analysis was tested by performing a simulation in which we closed the tidal inlet that This analysis was tested by performing a simulation in which we closed the tidal inlet that connectsconnects the the Nidova Nidova and and Aetoliko Aetoliko lagoons,lagoons, so as as to to block block the the flushing flushing phenomenon. phenomenon. The The result result was, was, anticipatinganticipating Section Section 3.2 3.2 below, that that the the residence residence time time for this for blocked this blocked Nidova Nidova lagoon lagoonincreased increased to 20 to 20days, days, as compared as compared to the to less the than less thanthree three days dayswhen when flushing flushing is allowed is allowed to occur. to occur.

FigureFigure 6. 6.( a()a) Time Time series series ofof tidaltidal elevationelevation at at selected selected points points along along the the longitudinal longitudinal axis axis of the of the Messolonghi–Aetoliko lagoons, covering a simulation period from neap to spring tides, (b,c) detail Messolonghi–Aetoliko lagoons, covering a simulation period from neap to spring tides, (b,c) detail where tidal amplitude decrease and phase lag are revealed during the propagation of the tide in the where tidal amplitude decrease and phase lag are revealed during the propagation of the tide in the lagoonal system. The sites of the points are marked in Figure 5. lagoonal system. The sites of the points are marked in Figure5.

Water 2018, 10, 237 10 of 16 Water 2018, 10, x FOR PEER REVIEW 10 of 16

FigureFigure 7. 7.Sea Sea surface surface formation formation during during thethe tidal propagation in in the the wider wider area area of of Nidova Nidova lagoon. lagoon.

If weIf we were were to to confine confine our our attention attention toto itsits geometry alone, alone, we we would would have have to toclassify classify Nidova, Nidova, withwith its twoits two tidal tidal inlets inlets as a as restricted a restricted lagoon lagoon and wouldand would have have expected, expected, accordingly, accordingly, its water its water renewal to berenewal rather to slow. be rather The fact slow. that The the fact two that inlets the oftwo the inlets lagoon of the are lagoon situated are on situated opposite on sidesopposite of its sides long of axis doesits not long by axis itself does dictate not by the itself functioning dictate the of functioning the lagoon asof the a flow-through lagoon as a flow system,‐through because, system, as we because, shall see, nearlyas we the shall same see, geometrical nearly the setting same existsgeometrical for the setting Papas lagoon,exists for but the there Papas the lagoon, hydrodynamics but there impose the a radicallyhydrodynamics different impose forcing. a radically This fact different has not forcing. been This reported fact has in thenot been literature reported before, in the and literature therefore needsbefore, closer and examination therefore needs as to closer the exactexamination circumstances as to the in exact which circumstances it occurs. It in seems, which however, it occurs. toIt be a variationseems, however, of the famous, to be a invariation the history of the of famous, science, in precedent the history of of the science, quasi-periodic precedent currents of the quasi created‐ byperiodic the differential currents arrival created at by the the Strait differential of Euripus arrival (between at the Strait mainland of Euripus Greece (between and the mainland island Greece of Evvoia (orand Euboea) the island of the of tide Evvoia moving (or Euboea) around of Evvoia the tide [32 moving,33]. These around currents Evvoia have [32,33]. been These famous currents since have ancient been famous since ancient times because they were associated with the name of Aristotle, who, living times because they were associated with the name of Aristotle, who, living his last years in Evvoia, his last years in Evvoia, became fascinated with them, though he only had partial success in became fascinated with them, though he only had partial success in explaining the phenomenon [34,35]. explaining the phenomenon [34,35]. The specific values for the tidal circulation in the Nidova lagoon are as follows. The incoming The specific values for the tidal circulation in the Nidova lagoon are as follows. The incoming 3 water,water, i.e., i.e., the the exchange exchange flowrate flowrate (Figure 8),8), was was computed computed to torange range between between 8 m3 8/s m(neap/s tides) (neap and tides) 3 3 and24 24m3/s m (spring/s (spring tide), with tide), an with intermediate an intermediate value of ~11 value m3/s (e.g. of ~11 mean m tidal/s (e.g.,range). mean Maximum tidal flow range). Maximumvelocities flow of tidal velocities currents of of tidal0.5 m/s currents and 0.4 of m/s 0.5 occur m/s in and the 0.4dredged m/s trench occur during in the the dredged flood and trench duringebb phases the flood of the and tidal ebb action, phases respectively. of the tidal Water action, velocities respectively. were found Water to diminish velocities rapidly were foundin the to diminishsubmerged rapidly open in channel, the submerged with values open of 0.20–0.30 channel, m/s with at the values free surface, of 0.20–0.30 while m/snear the at the bottom free these surface, whilevalues near were the bottomdecreased these to values0.05–0.1 were m/s. decreased In contrast, to 0.05–0.1at the opposite m/s. In side contrast, of the at lagoon, the opposite i.e., in sidethe of theneighborhood lagoon, i.e., in of the the neighborhood arc stone bridges, of thea water arc stoneflow velocity bridges, of a approximately water flow velocity 0.2 m/s of developed. approximately To 0.2summarize, m/s developed. the numerical To summarize, predictions the numericalshow that predictionsthe Nidova lagoon show that is being the Nidova flushed lagoon through is the being flushedsouth throughdredged thetrench, south transferring dredged tidal trench, waters transferring from the tidalgreater waters Messolonghi from the lagoon greater to the Messolonghi deeper lagoonAetoliko to the lagoon deeper in the Aetoliko north and lagoon back in to the the north Gulf of and Patras. back to the Gulf of Patras.

Water 2018, 10, 237 11 of 16 Water 2018, 10, x FOR PEER REVIEW 11 of 16 Water 2018, 10, x FOR PEER REVIEW 11 of 16

FigureFigure 8. 8.The The hydraulic hydraulic exchange exchange flowrate flowrate between the the Nidova Nidova lagoon lagoon and and the the surrounding surrounding waters waters (i.e.,(i.e.,Figure Aetoliko Aetoliko 8. The lagoon lagoonhydraulic – – tidal tidal exchange inlet inlet 1, 1, Messolonghiflowrate Messolonghi between lagoon the – –Nidova tidal tidal inlet inlet lagoon 2). 2). and the surrounding waters (i.e., Aetoliko lagoon – tidal inlet 1, Messolonghi lagoon – tidal inlet 2). InIn contrast contrast to to the the Nidova Nidova lagoon, lagoon, thethe Papas lagoon lagoon is is subject subject to to a astraightforward straightforward tidal tidal forcing. forcing. It hasIt has threeIn three contrast tidal tidal inlets: to inlets: the twoNidova two in in the thelagoon, eastern eastern the sidePapas and lagoon one one in inis the subject the northern northern to a straightforwardside side of of the the lagoon, lagoon, tidal and forcing. and all of all of themthemIt has are arethree exposed exposed tidal immediatelyinlets: immediately two in tothe to the theeastern semidiurnalsemidiurnal side and tide tideone ofin of thethe the Gulfnorthern Gulf of of Patras. Patras. side of The the The distances lagoon, distances and between between all of them are exposed immediately to the semidiurnal tide of the Gulf of Patras. The distances between themthem are are small small so so that that both both the the amplitude amplitude and the the phase phase of of the the tide tide is ispractically practically the the same same in all in three. all three. them are small so that both the amplitude and the phase of the tide is practically the same in all three. AnAn instance instance of of the the velocity velocity field field induced induced by floodflood tide tide in in the the lagoonal lagoonal system system is depicted is depicted in Figure in Figure 9, 9, An instance of the velocity field induced by flood tide in the lagoonal system is depicted in Figure 9, wherewhere it canit can be be observed observed that that surface surface velocities velocities rangerange between 0.5 0.5 and and 20 20 cm/s, cm/s, except except in inlocations locations where theit can flow be isobserved strongly that affected surface by velocitiesthe presence range of betweenthe inlets. 0.5 The and high 20 cm/s,velocities except are in especially locations where the flow is strongly affected by the presence of the inlets. The high velocities are especially pronouncedwhere the flow at the is threestrongly inlets affected and in by front the of presence these, since of the the inlets. tidal currents The high through velocities the arenarrow especially inlets pronounced at the three inlets and in front of these, since the tidal currents through the narrow inlets flowingpronounced into atthe the wide three lagoon inlets formand in a fronttidal ofjet, these, often since called the a tidalmushroom currents jet, through as it generates the narrow a vortex inlets flowing into the wide lagoon form a tidal jet, often called a mushroom jet, as it generates a vortex pair.flowing When into the the tide wide reverses lagoon (ebb form flow), a tidal the jet,pattern often of called the flow a mushroom resembles jet,a radial as it flowgenerates to a sink a vortex [36]. pair.Thepair. When hydraulic When the the tide exchange tide reverses reverses flowrate (ebb (ebb flow), betweenflow), thethe the pattern lagoon of of andthe the flowthe flow Gulf’s resembles resembles open a waters, radial a radial flowvia flow the to a tothree sink a sink tidal[36]. [ 36 ]. Theinlets,The hydraulic hydraulic is given exchange exchange in Figure flowrate flowrate 10. It can between between be seen thethe that lagoon the exchangeand and the the Gulf’s Gulf’s flowrate open open for waters, waters,the three via via the inlets the three three ranges tidal tidal inlets,betweeninlets, is givenis 4–6given m3/s in in Figure (neapFigure 10tides) 10.. ItIt and cancan 7–15 bebe seenseen m3/s that (spring the the tide),exchange exchange with flowratean flowrate intermediate for for the the threevalue three inletsof inlets5–10 ranges m3/s ranges between(e.g.between mean 4–6 4–6 m3/stidal m3/s range). (neap (neap tides) tides) and and 7–15 7–15 m3/s m3/s (spring tide), tide), with with an an intermediate intermediate value value of of 5–10 5–10 m3/s m3/s (e.g.,(e.g. mean mean tidal tidal range). range).

Figure 9. Cyclonic and anticyclonic gyres that form in the vicinity of tidal inlets in Papas lagoon FigureduringFigure 9. Cyclonicthe9. Cyclonic flood andtide. and anticyclonic anticyclonic gyres gyres that that form form in the in the vicinity vicinity of tidal of tidal inlets inlets in Papas in Papas lagoon lagoon during theduring ﬂood tide.the flood tide.

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FigureFigure 10. 10.The The hydraulic hydraulic exchange exchange ﬂowrateflowrate between the the Papas Papas lagoon lagoon and and the the Gulf Gulf of ofPatras. Patras. Figure 10. The hydraulic exchange flowrate between the Papas lagoon and the Gulf of Patras. 3.2. Residence Time of the Lagoons 3.2.3.2. Residence Residence Time Time of of the the Lagoons Lagoons 3.2.1.3.2.1. The The Nidova Nidova Lagoon Lagoon 3.2.1. The Nidova Lagoon Based on the above description of the tidal hydrodynamics of the Nidova basin, it is clear that BasedBased on on the the above above description description ofof thethe tidaltidal hydrodynamics of of the the Nidova Nidova basin, basin, it is it clear is clear that that the renewal mechanism of its waters differs substantially from the mechanism based on the mere thethe renewal renewal mechanism mechanism of of its its waters waters differsdiffers substantially from from the the mechanism mechanism based based on onthe the mere mere introduction of a volume of water equal to the tidal prism at the first half of the tidal cycle, introductionintroduction of aof volume a volume of water of water equal equal to the to tidal the prism tidal atprism the ﬁrstat the half first of the half tidal of cycle,the tidal recirculation cycle, recirculation and mixing of that volume within the lagoon, and subsequent exit of an almost equal andrecirculation mixing of that and volumemixing of within that volume the lagoon, within and the subsequent lagoon, and exit subsequent of an almost exit of equal an almost amount equal in the amount in the second half of the tidal cycle. This is because the water introduced from the southern secondamount half in of the the second tidal cycle. half of This the istidal because cycle. theThis water is because introduced the water from introduced the southern from tidal the southern inlet moves tidal inlet moves northwards and in part exits from the northern inlet into the Aetoliko lagoon, where tidal inlet moves northwards and in part exits from the northern inlet into the Aetoliko lagoon, where northwardsit mixes with and the in partAetoliko exits lagoon from the waters northern before inlet proceeding into the to Aetoliko the second lagoon, half of where the cycle. it mixes with the it mixes with the Aetoliko lagoon waters before proceeding to the second half of the cycle. AetolikoTo lagoon produce waters a value before for proceedingthe residence to time the secondscale, the half procedure of the cycle. described in Section 2.5 was To produce a value for the residence time scale, the procedure described in Section 2.5 was followed.To produce The result a value is summarized for the residence in Figure time 11, scale, from which the procedure it follows describedthat renewal in is Section achieved 2.5 in was followed. The result is summarized in Figure 11, from which it follows that renewal is achieved in followed.less than The three result days. is summarized in Figure 11, from which it follows that renewal is achieved in less thanless three than days. three days.

Figure 11. Spatial distribution of the residence time of the conservative tracer for the Nidova lagoon. FigureFigure 11. 11.Spatial Spatial distribution distribution of of the the residenceresidence time of of the the conservative conservative tracer tracer for for the the Nidova Nidova lagoon. lagoon. Values below 0.5 refer to 0 initial concentration. ValuesValues below below 0.5 0.5 refer refer to to 0 initial0 initial concentration. concentration.

Water 2018, 10, 237 13 of 16

It should be stressed again that this specific value depends strongly on the definition of the Water 2018, 10, x FOR PEER REVIEW 13 of 16 threshold under which the tracer’s value is considered small, so that the timescale value should be used withIt great should care be and stressed in conjunction again that this with specific the desired value application.depends strongly A further on the note definition of caution of the is in orderthreshold for the specific under sitewhich we the are tracer’s analyzing. value From is considered the above small, description, so that the it followstimescale that value waters should that be exit the Nidovaused with lagoon great mix care with and thein conjunction Aetoliko lagoon with the waters desired before application. re-entering A further in Nidova. note of caution Thus, the is in time scaleorder determined for the isspecific meaningful site we asare a analyzing. short-term From scale. the This above is becausedescription, we it base follows our that calculation waters that on the decreaseexit the of aNidova substance lagoon introduced mix with the once Aetoliko into the lagoon Nidova waters lagoon. before re If,‐entering however, in Nidova. substances Thus, such the as agriculturaltime scale fertilizers determined are is being meaningful introduced as a short intermittently‐term scale. This into is the because Aetoliko we base lagoon, our calculation the result mighton be a morethe decrease or less of well a substance mixed water introduced volume once of into a substantial the Nidova contaminant lagoon. If, however, that would substances be recirculated such as withinagricultural the Aetoliko–Nidova–Messolonghi fertilizers are being introduced lagoonal intermittently system into within the eachAetoliko tidal lagoon, cycle. the This result might might be the be a more or less well mixed water volume of a substantial contaminant that would be recirculated reason why, in spite of its impressively low residence time, recurring thick algae blooms have been within the Aetoliko–Nidova–Messolonghi lagoonal system within each tidal cycle. This might be the observed to develop during the last few years in the Nidova lagoon. reason why, in spite of its impressively low residence time, recurring thick algae blooms have been Theobserved note ofto develop caution during concerning the last the few definition years in the of theNidova residence lagoon. time using the standard e-folding value becomesThe note concrete of caution in concerning the following the definition simulated of the scenario. residence time The using effect the on standard residence e‐folding time of removingvalue the becomes embankment concrete separatingin the following the Nidovasimulated lagoon scenario. from The the effect Messolonghi on residence lagoon time of was removing examined numerically.the embankment From a purely separating hydrodynamic the Nidova point lagoon of view,from removingthe Messolonghi the embankment lagoon was enhanced examined the circulation,numerically. making From possible a purely the hydrodynamic development point of a gyreof view, encompassing removing the both embankment the Messolonghi enhanced and the the Nidovacirculation, lagoons (Figuremaking 12possible). The the residence development time, however, of a gyre encompassing was not significantly both the changed, Messolonghi still and remaining the belowNidova three days. lagoons (Figure 12). The residence time, however, was not significantly changed, still remaining below three days.

FigureFigure 12. Spatial 12. Spatial distribution distribution of theof the concentration concentration of of the the conservativeconservative tracer tracer for for the the Nidova Nidova lagoon, lagoon, after theafter embankment’s the embankment’s removal, removal, under under the the development development of of anan anti-cyclonicanti‐cyclonic gyre. gyre.

The aboveThe above analysis analysis rests rests on on a very a very important important condition condition that should should be be underlined. underlined. The The dredged dredged trench,trench, connecting connecting the southern the southern end ofend the of Nidova the Nidova lagoon lagoon with with the Messolonghi the Messolonghi lagoon, lagoon, should should remain clearremain of transported clear of transported material so material as to ensure so as thatto ensure the Gulf that ofthe Patras–Messolonghi–Nidova–Aetoliko Gulf of Patras–Messolonghi–Nidova– systemAetoliko remains system a ﬂow-through remains a flow system.‐through system.

3.2.2.3.2.2. The PapasThe Papas Lagoon Lagoon The numerical results showed that the residence time in the water body exhibits a strong spatial The numerical results showed that the residence time in the water body exhibits a strong spatial variation. In the region located in front of the inlets, rapid mixing occurs and these areas have the variation.shortest In theresidence region time located (~5 days). in front The of southern, the inlets, somewhat rapid mixing isolated occurs shallow and region these and areas also have the the shortestdeeper residence central–western time (~5 region, days). which The southern,is relatively somewhat far from the isolated inlets, shallowseems to region remain and at a alsonear the deeperstagnation central–western state for significant region, which time intervals, is relatively having far a residence from the time inlets, of more seems than to 40 remain days (Figure at a near

Water 2018, 10, 237 14 of 16 stagnation state for signiﬁcant time intervals, having a residence time of more than 40 days (Figure 13). TheWater hydrodynamic 2018, 10, x FOR gyresPEER REVIEW due to tidal action cause a conservative tracer to be trapped between14 of 16 the two openings in the eastern side of the lagoon. In the middle area of the eastern openings, a rather 13). The hydrodynamic gyres due to tidal action cause a conservative tracer to be trapped between unexpectedly high residence time appears. This area seems to be at a near stagnation state, having a the two openings in the eastern side of the lagoon. In the middle area of the eastern openings, a rather residenceunexpectedly time of high approximately residence time 25–30 appears. days. This It is wortharea seems noting to be that at ita isnear in thisstagnation area, i.e., state, in having the vicinity a of tidalresidence inlets, time that of the approximately dystrophic 25–30 crisis days. occurred It is worth in June noting 2012 that [18 ],it showingis in this area, that i.e., the in high the vicinity residence timeof in tidal this inlets, area is that not the incompatible dystrophic crisis with occurred the local in initiation June 2012 of [18], dystrophic showing phenomena. that the high residence timeFinally, in this it isarea worth is not noting incompatible that the with northern the local tidal initiation inlet and of dystrophic the lower ofphenomena. the two eastern inlets are geometricallyFinally, in it nearly is worth opposite noting positions.that the northern This lagoon, tidal inlet however, and the does lower not of functionthe two eastern as a ﬂow-through inlets are lagoongeometrically because the in tidalnearly hydrodynamics opposite positions. do not This favor lagoon, it. In however, other words, does not the function tide arrives as a flow simultaneously‐through at alllagoon the inlets, because with the no tidal substantial hydrodynamics difference do in amplitude.not favor it. This In isother the reasonwords, whythe thetide opening arrives of thesimultaneously middle inlet in at 1992 all the [18 inlets,] made with only no asubstantial limited contribution difference in toamplitude. the renewal This ofis the reason waters why of the Papasthe lagoon. opening of the middle inlet in 1992 [18] made only a limited contribution to the renewal of the waters of the Papas lagoon.

FigureFigure 13. 13.Spatial Spatial distribution distribution of of the the residence residence time time of the of passive the passive tracer for tracer the Papas for the lagoon. Papas Values lagoon. Valuesbelow below 5 outside 5 outside the lagoon the lagoon refer to refer 0 initial to 0 initialconcentration. concentration.

4. Conclusions4. Conclusions Restricted lagoons suffer from long residence times, which result because of the limited tidal Restricted lagoons suffer from long residence times, which result because of the limited tidal hydraulic exchange between the lagoon and the adjacent open water body (the ocean). The present hydraulic exchange between the lagoon and the adjacent open water body (the ocean). The present study documented, however, that this state is not solely a result of the geometry of the lagoon, but studyalso documented, of the intricacies however, of thatthe thistidal state hydrodynamics, is not solely amaking result of credible the geometry the term of the “hydrodynamic lagoon, but also of thegeometry”. intricacies This of term the tidal is meant hydrodynamics, to signify that making if the geometry credible is the in termthe right “hydrodynamic relation with geometry”.the tidal Thisforcing term isapplied meant at todifferent signify tidal that inlets if the of the geometry lagoon, the is inresult the may right be relationthe creation with of a the flow tidal‐through forcing appliedsystem, at different which flushes tidal inletsthe lagoon of the waters lagoon, considerably the result maymore beefficiently the creation that the of aslow flow-through process of tidal system, whichprism flushes exchange the lagoonand mixing waters in successive considerably tidal cycles. more efficientlyAn example that of the the former slow is process the Nidova of tidal lagoon, prism exchangeand the and Papas mixing lagoon in successiveof the latter: tidal both cycles. are situated An example in Western of the Greece former and is forced the Nidova by the same lagoon, tide and the Papasof the Gulf lagoon of Patras. of the latter:The creation both are of strong situated currents in Western because Greece of the and differential forced by arrival the same of the tide tide of at the Gulfdifferent of Patras. locations The creation is not as of exotic strong as currents it might because seem since of the it has differential also been arrival known of to the happen tide at in different open locationswaters, is notas in as the exotic well as‐known it might Evripos seem sincestraits. it hasThis also advantage, been known in terms to happen of flushing in open rate, waters, should as in the well-knowntherefore be taken Evripos into straits. account This whenever advantage, possible in when terms deciding of flushing the opening rate, should of an therefore additional be tidal taken inlet in a lagoon in order to enhance its flushing rate. into account whenever possible when deciding the opening of an additional tidal inlet in a lagoon in orderAcknowledgments: to enhance its flushing Useful discussions rate. with Professors Yannis Cladas, of the Technological Educational Institute of Western Greece, and Constantin Koutsikopoulos, of the University of Patras, are gratefully

Water 2018, 10, 237 15 of 16

Acknowledgments: Useful discussions with Professors Yannis Cladas, of the Technological Educational Institute of Western Greece, and Constantin Koutsikopoulos, of the University of Patras, are gratefully acknowledged. Publication costs were provided by the Hydraulic Engineering Laboratory, Department of Civil Engineering, University of Patras. Author Contributions: Nikolaos Th. Fourniotis and Georgios M. Horsch conceived and designed the numerical experiments, carried out the analysis and interpretation of the results, and wrote the paper; Nikolaos Th. Fourniotis and Georgios A. Leftheriotis performed the numerical simulations and analyzed the numerical results. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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