Environmental State of a Harbor in Terms of Waters Renewal. A Case Study for a Fishery Harbor in Thessaloniki Gulf

The waters renewal of the fishery harbor of Nea Krini is presented here. The harbor is located at the east Thessaloniki Gulf (NE Thermaikos Gulf, Greece). The main research point is focused on the environmental state of the harbor which is under construction. Under that point of view, the description of a two-dimensional, depth average, hydrodynamic model follows, in order to simulate the wind generated circulation of waters, initially on the greater area of Thermaikos Gulf and then on the coastal basin of the fishing harbor. The renewal of waters in the harbor’s basin is subsequently studied. Tidal effects on the waters’ renewal are also studied. The calculation of the concentration of Biochemically Oxygen Demand (BOD) in the fishing harbor for the average time of waters’ renewal is then examined for three different cases, concerning the existence and operation of openings on the body of the groins. Finally, the analysis of the results shows a good environmental state of the harbor. It is obvious that the use of numerical models for different scenarios of engineering and design approaches can lead to the prognosis of hydrodynamic and environmental sate of a harbor’s basin so that the best possible technical design can be adopted.


Introduction
In recent years, numerical models are used more and more in order to contri-unpleasant and negative environmental effects. For example, sediment transport which causes a dynamic change of the coastline, coastal erosion or deposition (Monioudi et al., 2017;Karambas, 2014) stagnant waters in a harbor (Winterwerp, 2005) or the environmental state and the seawater quality of a harbor (Savvidis et al., 2017;Savvidis & Keramaris, 2021) are some of the most characteristic cases which are well studied through the use of mathematical models and more specifically hydrodynamic models, sediment transport models, water quality or ecological models. renewal of the waters) is defined as the time required for the replacement of the whole water of the marina basin by clean water (Kalitzi & Memos, 2008). It is well understood that the time required to achieve such a process is directly related to the external dynamics that move the waters of the basin and the topographic characteristics of the specific aquatic environment.
As far as the hydrodynamic circulation and the time of waters renewal in ports and coastal areas are concerned, a lot of works were done at a research level. This time, was calculated for a wide range of ports and harbors worldwide but also in several Greek harbors, marinas and fishing shelters and ranges from time periods less than a day to ten days or even more. Some relevant examples include the characteristic case of Cabreras' harbor in Spain, where waters' renewal time is achieved in 6 days (Orfila et al., 2005) while for the case of the inner basin of Boston's Harbor (United States of America) the time needed for waters' flushing is achieved between 2 to 10 days (Chan Hilton et al., 1998). Finally, the time needed for the waters of the Port of Thessaloniki (Northern Greece) to be renewed is of the order of one day since the flushing time due to wind was estimated between 1 and 2 days and the flushing time due to tide was 11 days (Thessaloniki Port Authority, 1995). The renewal time for a fishing shelter on Libya, was found to be 5.48 days (Christopoulou, 2010), for a marina on the east coasts of Thermaikos Bay (NW Aegean Sea, Greece), in Northern Greece, 2.90 days (Koutitas et al., 1996) while for a marina in Mytilene (NE Aegean Sea, Greece) 4.90 days (Alifragis, 2009). Furthermore the renewal time for the waters of Harbor of Nea Moudania (NW Aegean Sea), was studied with mathematical models and field measurements and found to be 0.70 days (Savvidis et al., 2009). Finally, the time for the renewal of the waters of the harbor of Agios Nikolaos, Volimes (Zakynthos, Ionian Sea, Greece) was 0.80 days (Kougianos et al., 2018).
The above mentioned renewal times were calculated either by field measure-  (Mamtsadeli, 2020).
It is pointed out that these studies leading to the relevant results do not take into account the same external forces that generate the hydrodynamic circulation and water renewal, but mainly the predominant forces concerning the specific study area. Additionally, these times are obviously not comparable since (apart from the different external forces) they also refer to different topographic and bathymetric characteristics of the harbor basin i.e. surface areas and water volumes of the basin.
It is very important to note that the processes and mechanisms of renewal and  Fountoulis and Memos (Fountoulis & Memos, 2004) focused on the optimization of openings for water renewal in a harbor basin concerning that latter contradictive factor. Furthermore recent studies of waters' renewal and sedimentation of an ideal square harbor encapsulated in a coastal front with seawalls due to wind generated hydrodynamic circulation in the greater coastal area (Savvidis & Keramaris, 2021) focused on the inverse relation between the waters renewal and depositional phenomena.
A significant environmental index is the harbor's self-purification capacity. This parameter can be evaluated by the calculation of the Biochemically Oxygen Demand (BOD) which is defined as the quantity needed for the oxidation of an organic component of waste materials from microbes in aerobic conditions (Kougolos, 2005) and constitutes a significant parameter for the estimation of the organic pollution of surficial waters as well as waste waters. Savvidis and Keramaris (2021) and Savvidis et al. (2009)

Study Area
The fishing shelter of Nea Krini in Kalamaria is described here. The study area is placed along the east coasts of Thessaloniki Gulf, along the NE Thermaikos Gulf which is located at the NW Aegean Sea. A geographical map of the greater area of Thermaikos Gulf is shown in Figure 1 (Pell et al., 2003).
The water depths of the harbor's basin are generally shallow, reaching approximately 4.5 to 5 m, near the breakwater. The study and the relevant calculations were carried out using the important tool of mathematical models. As it is shown in Figure 2, according to the study of the project (Christopoulos et al.,   Figure 2).
• An inner mole-pier of Τ shape in the middle of the basin with the length of the perpendicular to the land, part of the pier (of bridge type) 70 m and the length of the parallel part 95 m (3 in Figure 2). • Seawalls and all the operational surfaces behind the walls (4 in Figure 2).
• Land zone (5 in Figure 2) which includes projects to serve the needs of the fishing shelter, such as: water supply network, sanitary facilities, fire protection network, electric lighting and special waste tanks.

The Mathematical Background
The present study was based on the development and application of a two-dimensional, mean in depth, hydrodynamic model, in order to simulate the circulation of water in the coastal environment and the renewal of waters in the basin of a marina or a fishing harbor. For this reason, the hydrodynamic model was initially applied to the greater basin in which the harbor is encapsulated.
The model simulations were applied for wind generated water circulation and for mean in the year (annual) weighted value of wind speed for all the directions of blowing winds. The equations governing the hydrodynamic circulation of the waters which can be found in Koutitas (1988) and also in Koutitas and Scarlatos (2015) are the well-known equations of momentum and mass conservation, given below: where h is the water depths i.e. the height of the water column, U & V are the mean in depth horizontal velocities of the sea currents, ζ the elevation of the sea surface, ν h the horizontal turbulent coefficient of momentum diffusion, ρ the density of the sea water and g the gravity acceleration, f the Coriolis parameter (10 −4 for the study area), τ sx and τ sy the wind shear stresses on the sea surface which are given by the following relationships: where ρ is the seawater's density (1025 kg/m 3 ), W x and W y the wind velocity components 10 m above the sea surface and C s is the surface friction coefficient with values of the order of 10 −6 (usually between 1 × 10 −6 and 3 × 10 −6 ) (Koutitas & Scarlatos, 2015;Koutitas, 1988), τ bx and τ by are the bottom shear stresses which are given by the following relationships: where ρ is the seawater's density (1025 kg/m 3 ), U and V the components of current velocity and C b the bottom friction coefficient of the order of 10 −2 (Koutitas & Scarlatos, 2015).
Alternatively the wind shear stresses on the sea surface can be given by the following relationships: where ρ a is the air's density (1.3 kg/m 3 ), W x and W y the wind velocity components as described above and K s is the surface friction coefficient with values of the order of 10 −3 (about 1.4 × 10 −3 ) (Beer, 1983).
The above differential equations are approximated by algebraic equations resulting from the application of the finite difference method, which are then encoded in the computer program using the FORTRAN programming language.
In more detail, the derivatives of these well-known equations of mass and momentum conservation are approximated using explicit schemes for the finite differences' method. Time derivatives were approximated with forward differences, while the other derivatives are approximated with central differences.
Concerning the mesh, a square staggered discretization grid (Arakawa C grid) was used, where U, V components are referred to the nodes' sides, while ζ is referred to the interior of each mesh as shown in Koutitas and Scarlatos (2015) ( Figure 3).
Subsequently, after the computation of the velocity data on the mesh sides, the following half sums are computed, which refer to the mesh center.
, , 1, Given that an explicit solution scheme is used, in order to provide the appropriate stability for the numerical solution the following Courant-Friedrichs-Lewy (CFL) criterion (Koutitas & Scarlatos, 2015) was applied: where c is the maximum phase velocity ( = m c gh and h m is the maximum depth of the study area) and g is the acceleration of the gravity.
Concerning the initial conditions for the hydrodynamic model, it should be noted that model runs always started from scratch, i.e., zero water velocities and elevations.
As far as the conditions on the land-coastal boundaries are determined by the assumption of zero flow and consequently by the zero velocity normal to the land boundary of the coasts. The tangential component of the velocity is left free   (Koutitas, 1988).
Concerning the open sea boundary conditions the Orlanski boundary condition was applied. The interested reader can find details in (Orlanski, 1976).
The present study consisted of the two following basic successive steps: 1) the application of a two-dimensional, depth averaged, hydrodynamic mod- This nesting approach is given in Figure 4.
In more detail, a coarser two-dimensional hydrodynamic model was primarily applied over the greater area of the Thessaloniki Gulf. Then, the computed sea current velocities, corresponding to the grid cell which encapsulates the harbor, were applied along the northwest or southeast open sea boundary of the computational domain of the harbor basin. For the case of N, NW, NE and W winds that generate the sea water circulation over the Gulf, the current velocities, resulted by the coarser model on the cell that encapsulates the harbor domain, were applied along the northwest open sea boundary of the harbor's basin (properly interpolated) since these currents seem to contribute to the waters renewal of the harbor. Accordingly, for the case of S, SE, SW and E winds that generate the water circulation over the Gulf, the computed current velocities by the coarser model were applied along the southeast boundary of the harbor's basin. It is noted that for the study of the hydrodynamics on the harbor's basin, the model domain of the harbor is rotated at an angle of 35˚. Thus, the wind over the area and the sea current velocities on the open sea boundaries are properly projected on the x and y axis. The above described nesting technique was successfully adopted and applied in past research studies (Savvidis & Koutitas, 2000;Savvidis et al., 2007;Papadimitriou et al., 2021).
The hydrodynamic study of the harbor waters can be supplemented by the renewal of the waters in the basin while at a next stage the concentration of BOD in the fishing harbor can be calculated for the average time of waters' renewal (corresponding to a long time period). According to this process the self-cleaning capacity of the fish harbor can be calculated and, then, alternative technical practices concerning the harbor's design can be tested.
Three different alternative scenarios, concerning the structural design of the harbor, were studied in detail ( Figure 5).
Case Α, constitutes the initial "reference" case, and refers to a compact construction, with no openings in the "body" of the moles or the central pier. Thus the only communication paths of the waters of the basin with the open sea are the two inlets of 40 m long each, between the outer edges of the moles-groins and the breakwater.
Case B results from a modification of the initial case with some openings on the external moles as well as on the internal central mole as well as on the internal central mole as well on the internal central mole. More specifically, case B is the one that better simulates the proposal of the existing, initial, study. In this case we have the construction with an opening of 5 m at the base -root of each one of the two external moles, and 5 openings of 10 meters in the inner central mole-pier. The central pier is now made of a bridge type with the construction of a deck that rests on pedestals. In this way there is communication of the waters of the basin with the open sea from the new openings in the root of the external moles. In addition, however, there is communication between the waters of the two internal basins.
Finally case C refers to a modification of the initial case with even more openings on the external moles than those of case B. In more detail, in the third case, a hypothetical construction is studied, according to which, the openings at the base-root of the outer moles-groins are enlarged from 5 m to 10 m, while Y. Savvidis, S. Mamtsadeli  = Ω wind RT Q where Ω is the water volume of the study basin (m 3 ), Q the waters' renewal flow rate (m 3 /s) due to wind generated currents which results from the half of the sum of the entering and the leaving flow rates Q + and Q − respectively, and T is the waters' renewal time of the basin of the harbor (in seconds or days). The flows rates Q + and Q − (resulting almost equal in steady state conditions) were computed from the currents' velocity data using the following relationships: The weighted averages of water renewal in each of the three cases A, B and C are given as follows: Accordingly the values RT Bwind and RT Cwind were computed for case B and case C.
2) Renewal time due to tidal effect Although the renewal time due to tidal effects could be computed by a relevant numerical model for tidal circulation, the well-known method of tidal prism was adopted since it was considered as a simple and reliable calculating procedure which is also can be found in previous published works (Savvidis et al., 2009 The renewal time of the harbor RT tide due to the tide and the tidal renewal flow rate Q tide were computed by the tidal prism (from the elevation data of the sea surface due to tide). RT tide and Q tide are related through the following equation: = Ω tide tide RT Q where Ω is the water volume of the study basin (m 3 ).
The water volume which is exchanged between the harbor's basin and the open sea in a tidal period constitutes the "tidal prism". The volume of the tidal prism is where S is the area of the sea surface of the harbor and α is the amplitude of the tide (half of the tidal height) and consequently the renewal time of the harbor due to the tidal signal is given by the following relationship: where T tide is the tidal period The ultimate mean renewal time RΤ due to tide and wind is finally given by the following equation: The computation of the renewal time of harbor waters does not give concrete information about the environmental state of the waters, which however can be drawn from the estimation of self-purification capacity of the harbor waters through assessing the BOD concentrations of the waters. This latter parameter is described in the following paragraph.

3) Self-purification capacity of the harbor waters
The computation of the waters' renewal time allows for the subsequent calculation of the harbor's self-purification capacity. In more detail, the harbor's self-purification capacity, is computed from the mean renewal time T (here RT) of the harbor's waters, and the harbors waters' volume Ω, and the polluting load q that corresponds to sewage waters of a maximum number of the people on all the vessels moored in the harbor at the same time (i.e. q is the entering flow discharge) and the concentration C o of BOD of untreated sewage (220 -400 mg/lit, here 400 mg/l) and the biodegradation coefficient λ which for urban sewage is of the order of 0.1 per day (Tchobanoglous & Burton, 1991). A maximum value C max of BOD in the basin, of the order of 5 mg/lit is considered as acceptable.  (Koutitas et al., 1996;Savvidis et al., 2017):

Results
As Applying the hydrodynamic model described in Section 2, for the study of wind generated circulation forced by the most frequent NW winds with mean speed of 3.5 m/s the following water circulation patterns were resulted for the sea currents of the Thermaikos Gulf ( Figure 6) as well as for the sea currents of the harbor basin (Figures 7-9) for each one of the three cases, A, B and C. It is    . The wind generated sea currents due to NW wind of 3.5 m/s for case B. In X and Y axes the discretization of the field in orthogonal segments is shown (number of grid points). The color scale corresponds to the current velocity speeds. Figure 9. The wind generated sea currents due to NW wind of 3.5 m/s for case C. In X and Y axes the discretization of the field in orthogonal segments is shown (number of grid points). The color scale corresponds to the current velocity speeds. noted here that all the different wind directions were considered in the present study; however only the pattern of sea currents generated by NW wind was given, as an indicative case as well as the most representative one. Besides it is well known that NW winds dominate over the area of Thermaikos Gulf (Hyder et al., 2002).
It should be noted that four rivers are inflowing on the west coasts of Thermaikos Gulf (Galikos, Axios, Loudias and Aliakmonas), as shown in Figure 1, however the influence of the river water discharges, is not important, and they are neglected in the present study. More specifically, there are several decades since now that these riverine inflows have been dramatically reduced (Savvidis & Koutitas, 2000;Hyder et al., 2002) In addition there is a small river (Anthemountas) inflowing on the coastal area south of the harbor's basin, (shown in Figure   1), but that flow is also of minor importance and most of the time with zero values. Furthermore, the water depths of the basin are generally quite shallow. Consequently the assumption of barotropic circulation on the basin of Thermaikos Gulf can be generally considered as realistic. Figure 6 shows that, under the influence of NW winds, two eddies are formed near the south boundary of Thermaikos Gulf. More specifically a clockwise circulation is developed just over the southern boundary forming a large eddy in the central part of the gulf; also an anticlockwise circulation is developed with a small eddy, limited in the west part. The two eddies near the south boundary, distributed almost equally over the south part of the basin, are also formed by the influence of NNW wind and can be found in international bibliography (Poulos et al., 2000;Ganoulis, 1994;Volakos et al., 1998).
Hydrodynamic wind generated water circulation due to NW wind of 3.5 m/s (Case Α).
The area of the water surface of the basin is 31,050 m 2 while the volume of the waters of the basin is 123038.5 m 3 . The area of the water surface of the basin is 31,925 m 2 while the volume of the waters of the basin is 125783.5 m 3 As shown in Figure 8, a large clockwise movement tends to be formed around the horizontal part of the central pier as in this case the holes allow the circulation of water between the smaller sub-basins. The sea currents are quite low (below 0.007 m/s). Similarly, in this case, the renewal of the waters takes place mainly through the northwestern openings while the outflow takes place mainly through the southeastern opening. The renewal of the harbor waters is enhanced by the Y. Savvidis, S. Mamtsadeli small openings at the base of the external piers, where in particular the entrance through the small opening at the base of the northwest (left) mole and the exit through the small opening at the base of the southeast (right) mole.
Hydrodynamic wind generated water circulation due to NW wind of 3.5 m/s (Case C).
The area of the water surface of the basin is 32,175 m 2 while the volume of the waters of the basin is 126,746 m 3 .
As shown in Figure 9, the pattern of the hydrodynamic circulation in case C, is similar to that of case B. The currents are very low and specifically lower than 0.0065 m/s. The water renewal takes place through the openings formed between the end of the outer moles and the breakwater. In particular, the inflow of waters takes place from the open sea on the left (northwest opening) while there water outflow which takes place mainly through the opening on the right (southeast opening. The water renewal is enhanced even more by the small openings at the base of the external moles.
Finally, the waters' renewal times due to wind generated circulation, computed by the model runs for all the wind directions, are given in Table 2. It is noted here, that in all case the values of current velocities are very low, because the currents are generated by weak winds. Moreovere, these velocities correspond to mean in depth current intensities.

Renewal Time of Waters of the Harbor's Basin Due to Wind
The weighted averages of waters renewal in each of the three cases A, B and C, according to Equation (12) are given in Table 3.
Taking into account the mean tidal hight of 0.25 m (i.e. tidal aplitude of α = 0.125 m) simple calulations can follow as given just below.
The volume V, of water exchanged between the harbor basin and the open sea in a tidal period i.e. the "tidal prism", is given by the Equation (18) Concequently, the waters renewal in each of the three cases A, B and C are given in Table 4. The above results show that renewal times due to astronomical tide in the region are 2.5 to 3 times higher than the renewal times due to winds blowing over the area. However, since these two different phenomena develop in parallel the combined effect of these two external factors to the renewal of the harbor waters needs to be determined. It is interesting to note that the mean tidal signal is a relatively fixed variable for an area (even if the study examines the high and low tides) and consequently the waters renewal due to tidal effect is calculated as a function of the topographical-geometrical characteristics of the harbor. On the other hand, the winds blowing over an area can vary significantly in both intensity and direction and consequently the waters renewal due to winds can vary quite a lot, since they respectively determine the sea currents that enter and leave the harbor basin. It is reminded here, that the winds and tides constitute the prevailing factors that generate hydrodynamic circulation and renewal of the waters of the harbor basin in the study area.

Renewal Time of Waters of the Harbor's Basin Due to Winds and Tide
The renewal times due to the combined effect of winds and tide is given to Table  5.  (20) and (21), the combined effect of wind and tide lead to the following results for the waters renewal time and the mean concentration of BOD in the harbors' basin: Case Α RT wind = 2.87 days and RT tide = 7.93 days which leads to a mean resultant renewal time of the harbor waters RT Α = 2.10 days or 50.4 hours. and a mean concentration of biochemacally oxygen demand ΒΟD Α = 1.13 mg/lt. Case B RT wind = 2.79 days and RT tide = 7.88 days and respectively. RT Β = 2.06 days or 49.44 hours and a mean concentration of biochemacally oxygen demand ΒΟD Β = 1.08 mg/lt. Case C RT wind = 2.71 days and RT tide = 7.87 days and respectively. RT C = 2.01 days or 48.24 hours and a mean concentration of biochemacally oxygen demand ΒΟD C = 1.05 mg/lt.

Summary and Conclusions
The present study shed light on the following points: • In all the three cases A and B the renewal times due to the combined effect of winds and tide are approx. 2 days. The renewal time due to the winds, prevailing over the study area, ranges from the order of 1 or 2 days for winds of north or south directions to 4 or 5 days for winds of west or east directions. The renewal time due to tide is nearly 8 days.
• In each one of the three cases the time renewal of the waters due to the wind under the specific wind conditions (with prevailing weak winds) are about 3 times lower than the renewal time due to tide.
• It is obvious that if moderate or strong winds are taken into account, the water renewal times are expected to be greatly reduced which of course lead to even better environmental conditions. • According to the wind climate of the study area the lower renewal times (and higher renewal rates respectively) are those due to N winds while the relevant lower renewal times correspond to E winds.
• As for the openings in the inner central pier, although they do not affect the ultimate renewal of the waters of the harbor basin as a whole, they obviously affect the waters renewal of the sub-basins. It is obvious from the water circulation that their construction is considered very important since it allows Y. Savvidis, S. Mamtsadeli the water to move between the two sub-basins on either side of the central pier.
• In each of the three cases that were studied, the BOD concentrations for 1000 people in the harbor are much lower than the maximum acceptable values in terms of the self-cleaning capacity of the harbor, i.e. 5 mg/l. From this point of view, the construction of the external moles without openings would not create significant differences or severe problems except in prolonged periods of calm conditions. Based on the statistical investigation, it seems that the case of calm conditions reaches 25%, which is not a negligible percentage. So the design of the moles with the openings that allows the water to move freely is rather positive.
Based on the above presented points, it seems that case B and case C are the best alternative solutions (with case C being more recommended) because of the exchange of water masses between sub-basins of the harbor since they allow the water circulation to develop in the harbor through the openings of the central pier.
The present study shows that the significant tool of the numerical models can help the engineers and researchers to study effectively and possibly modify and adapt a project so that a more friendly design to the environment can be ensured.