Print This Article

Mediterranean Marine Science

Vol. 3, 2002

Development of a two-layer mathematical model for the study of hydrodynamic circulation in the sea. Application to the Thermaikos gulf

DODOU M.G. Division of Hydraulics & Environmental Engineering, Dept. of Civil Eng. Aristotle University of Thessaloniki, GR 54006 Thessaloniki SAVVIDIS Y.G. Department of Fisheries and Aquaculture, Technological Educational Institute of Thessaloniki, N. Moudania, 63200 Chalkidiki KRESTENITIS Y.N. Division of Hydraulics and Environmental Engineering, Civil Engineering Department, Aristotle University of Thessaloniki, 54006 Thessaloniki KOUTITAS C.G. Division of Hydraulics and Environmental Engineering, Civil Engineering Department, Aristotle University of Thessaloniki, 54006 Thessaloniki https://doi.org/10.12681/mms.245

To cite this article:

DODOU, M.G., SAVVIDIS, Y.G., KRESTENITIS, Y.N., & KOUTITAS, C.G. (2002). Development of a two-layer mathematical model for the study of hydrodynamic circulation in the sea. Application to the Thermaikos gulf. Mediterranean Marine Science, 3(2), 5-26. doi:https://doi.org/10.12681/mms.245

http://epublishing.ekt.gr | e-Publisher: EKT | Downloaded at 03/10/2021 14:48:14 | Mediterranean Marine Science Vol. 3/2, 2002, 05-25

Development of a two-layer mathematical model for the study of hydrodynamic circulation in the sea. Application to the Thermaikos gulf

M.G.DODOU, Y.G.SAVVIDIS, Y.N.KRESTENITIS and C.G.KOUTITAS

Division of Hydraulics & Environmental Engineering, Dept. of Civil Eng. Aristotle University of Thessaloniki, GR 54006 Thessaloniki, Greece e-mail: [email protected]

Abstract

A two-layer hydrodynamic model for stratified flows has been developed and applied to the study of the sea water circulation in the Thermaikos Gulf (North Aegean Sea in the east Mediterranean Sea). The model was based on the finite differences method. The wind and Coriolis forces applied to a stratified basin (with initial density differences ¢Ú/Ú = 5ò) constituted the basic factors for the study of the circulation in the gulf, corresponding to the stratification conditions. The findings of the model, concerning the basic pattern of circulation in the gulf, were in accordance with in situ data collected in previous studies of the area. Furthermore, the application of the model allowed for the tracking and recognition of the regions of upwelling in the gulf, which were related to the prevailing wind conditions. For the integration of the research, the study was complemented with runs of a two dimensional – depth averaged- model which corresponded to non- stratified conditions. Comparisons and evaluation of the results of the simulations close the study.

Keywords: Mathematical models, Hydrodynamic circulation, Stratified flow, Upwelling, Wind curl.

Introduction 1988), KOURAFALOU et al. (1996, 1998), KRESTENITIS et al. (1997, 1998), SAVVIDIS The hydrodynamic circulation of the et al. (2000), DODOU (2001) as well as many seawater has been studied in detail during the other researchers have successfully developed and applied mathematical models for the last decades. The use of mathematical modeling simulation of the coastal circulation. Those works contributed significantly to the progress of those included two-dimensional and three-dimensional studies and various mathematical models were mathematical models. developed in order to simulate the hydrodynamic The selection and application of a two or circulation of the seawater masses due to three-dimensional mathematical model is based different forcing factors. on the particular conditions of the vertical CHRISTODOULOU et al. (1982), structure of the water mass and the level of the BLUMBERG et al. (1987), KOUTITAS (1987, detail of the study pursued. Thus, the water

Medit. Mar. Sci., 3/2, 2002, 05-25 5

http://epublishing.ekt.gr | e-Publisher: EKT | Downloaded at 03/10/2021 14:48:14 | circulation of a non-stratified shallow coastal under stratification conditions, including the sea can be adequately described and studied by special processes of upwelling events. the application of a two-dimensional model. Wind driven flows or tidal circulations are often Delimination of the Gulf described by the application of two-dimensional models. On the other hand, if the vertical The Thermaikos Gulf is located in the structure of the seawater masses is characterized northern part of the Aegean Sea, situated north by intense stratification, it is necessary to apply of the line of the Posidi- Platamonas capes, a three-dimensional mathematical model, so defining the eastern and western limits of that that the complicated physics of the flow can be boundary. Figure 1.1 illustrates the gulf and its described adequately. sub-regions according to Panayiotidis The use of a two-layer mathematical model (PANAYOTIDIS, 1997): a) the Bay of constitutes a significant alternative way of Thessaloniki, occupying the northern part of modeling the hydrodynamic circulation in the the Thermaikos Gulf, and extending sea, because it combines the simplified southwards to the line of Cape Micro Emvolo mathematical approach and computer efficiency – Galikos river mouth, b) the Gulf of provided by the two-dimensional, depth- Thessaloniki, which extends from the line of averaged models, with the advantages of the Cape Micro Emvolo – Galikos river mouth, to more detailed study of a multiple-layer stratified the line of Cape Epanomi – Cape Atherida and flow provided by the three-dimensional c) the outer Thermaikos Gulf extending south mathematical models. from the Thessaloniki Gulf reaching the Two-layered mathematical models are southern boundary line of Cape Posidi – Cape generally suitable for the simulation of stratified Platamonas. flows with a characteristic pycnocline, while an As far as the accurate geographical position interesting application of those models is the of the study area is concerned, it extends for simulation of upwelling and down welling events. about 80 km north of 39 .6Æ N and for about 75 Upwelling is the upward movement of the water km east of 22.6Æ E (KOURAFALOU et al., from the deeper layers of the sea to the surface 1998). The basin we studied extends from the and constitutes one of the most important shallow nearshore coastal areas (depths about processes in the coastal ocean. More specifically, 3 to 4 m) to the deep offshore sea with depths upwelling dynamics is considered to be a vital reaching to 100 m (Fig. 1.2). phenomenon for the fishery and life in the sea Axios, Loudias and Aliakmon (and Pinios in general because it is related to nutrient to the south, but just outside the computational regeneration in the surface layer. domain) are the main rivers, outflowing along Hydrodynamic circulation during the the west coasts of the Thermaikos Gulf. summer period in the Thermaikos Gulf (N. Greece) constitutes a representative example Materials and Methods of wind-generated, vertically stratified flow. Due to a systematic decrease of the river flow input Description of the two-dimensional, along the west coast of the Gulf, observed in integrated in depth, mathematical model of recent decades, horizontal density differences coastal circulation are not included among the driving factors in our simulations. The main objective of this work The general form of the mathematical was the development and application of a model of coastal circulation constitutes a mathematical model of a two-layered flow which simplification of Reynolds equations based on is proved to be a very practical tool for the the realistic assumption that the circulation of simulation of Thermaikos Gulf water circulation the water in the coastal field is nearly

6 Medit. Mar. Sci., 3/2, 2002, 05-25

http://epublishing.ekt.gr | e-Publisher: EKT | Downloaded at 03/10/2021 14:48:14 | Fig. 1.1: Delimination of Thermaikos Gulf, distinction of the area in sub-zones and indication of the main outflowing rivers.

Fig. 1.2: Bathymetry of Thermaikos Gulf (depths contours in meters and axes in nautical miles).

Medit. Mar. Sci., 3/2, 2002, 05-25 7

http://epublishing.ekt.gr | e-Publisher: EKT | Downloaded at 03/10/2021 14:48:14 | horizontal, given that the horizontal along y axis dimensions of the coastal circulation field ∂v ∂v ∂v ∂˙ +u +v =–g –fu+ exceed considerably, in terms of magnitude, ∂t ∂x ∂y ∂y the vertical dimension of the water's depth ∂ ∂v ∂ ∂v ∂ ∂v (KOUTITAS, 1988). The assumption of nearly + v + v + v (2.5) ∂x h ∂x ∂y h ∂y ∂z v ∂z horizontal flow implies not only: a) the consideration of neglected vertical velocity Mass conservation equation components, but also b) a hydrostatic pressure ∂u ∂z ∂w distribution in depth with the respective + + =0 (2.6) expression of the horizontal pressure gradients, ∂x ∂y ∂z

∂p ∂˙ ∂p ∂˙ where u(x,y,z,t), v(x,y,z,t) and w(x,y,z,t) are the =Úg , =Úg (2.1) ∂ ∂ ∂ ∂ velocity components along x, y and z axis x x y y respectively, ˙(x,y,t) is the elevation of the mean whereÚ is the mean seawater density, g the surface level from the stagnant level and vh, vv gravity acceleration, ˙ the elevation of the mean are the eddy viscosity coefficients in the surface level from the stagnant level, c) the horizontal and vertical dimensions as functions importance of the Coriolis forces influence of the hydrodynamic conditions. (with their horizontal components) on a slowly Boundary conditions imply a) the equation of the Reynolds stresses on the free surface to developing flow, the shear stress components Ùsx, Ùsy due to the wind velocity (free surface boundary fxc = 2ø v sin Ê, fyc = –2ø u sin Ê (2.2) condition), where ø = 0.7297 x 10-6 rad/sec the angular Ùsx Ùsy =KW W 2+W 2 , =KW W 2+W 2 (2.7) velocity of the earth’s rotation, Ê the latitude, Ú x x y Ú y x y and d) the turbulent character of the flow due to large Reynolds numbers, providing the where Wx, Wy are the wind velocity components at a distance of 10 m above the application of the classical Boussinesq sea surface and K is a dimensionless constant approximation for the description of Reynolds with a magnitude of 1÷3x10-6, b) the expression stresses, of shear stress components on the bed Ùbx, Ùby

∂u ∂v in terms of near bed velocities (bottom Ù =Úv ,Ù =Úv xz v ∂ yz v ∂ (2.3) boundary condition), z z Ùbx 2 2 Ùby 2 2 where u, v are the velocity components along =Cuu+v , =Cvu+v (2.8) Ú f Ú f x and y axis respectively and vv is the eddy viscosity coefficient in the vertical dimension. where Cf is a dimensionless constant with a The model consists of the equations of mass magnitude ranging from 10–3 to 10–2 and c) the and momentum conservation and the propagation of the radiated part of the surface appropriate boundary conditions. elevation ˙r from the inner basin to the open sea across the open sea boundary without back Momentum conservation equations reflection (Sommerfeld radiation condition), along x axis ∂˙ ∂˙ r +C r =0 (2.9) ∂u ∂u ∂u ∂˙ ∂ ∂ +u +v =–g +fv+ t n ∂t ∂t ∂y ∂x where n is the normal unit vector pointing ∂ ∂ ∂ ∂ ∂ ∂ u u u outward the basin, C is the gravity waves + vh + vh + vv (2.4) ∂x ∂x ∂y ∂y ∂z ∂z propagation velocity.

8 Medit. Mar. Sci., 3/2, 2002, 05-25

http://epublishing.ekt.gr | e-Publisher: EKT | Downloaded at 03/10/2021 14:48:14 | The mathematical model described above momentum dispersion coefficients Óh', where can be further simplified if a logarithmic Óh' > Óh. velocity distribution over the entire flow depth is assumed, in order to allow the expression of Description of the two-layer mathematical the equations (2.4), (2.5) and (2.6) in terms of model of coastal circulation the depth-averaged velocities, through In the case of vertical stratification of integration along the flow depth h: density, successive models of depth average Momentum conservation equations flow are applied for each separate fluid layer. Provided measurements prove the existence ∂U ∂U ∂U +U +v = of a pycnocline, the fluid can be treated as a ∂t ∂x ∂y two-layered one, by applying the equations of ∂˙ Ù Ù equilibrium and mass conservation for each =–g + sx – bx +fV+v ∇ 2U (2.10) ∂x Úh Úh h h layer separately. The unknown variables of the differential equations are the average depths ho, hu of upper and lower layer and the ∂V ∂V ∂V +U +V = respective depth average velocity components ∂t ∂x ∂y Uo, Vo, Uu, Vu (Fig. 2.2 ). ∂˙ Ù Ù =–g + sx – bx –fU+v ∇ 2V (2.11) An interesting point in a two-layered flow ∂y Úh Úh h h model is the development of shear stresses in the interface of the two layers related to the Mass conservation equation relative velocity of the two successive layers.

∂˙ ∂ ∂ The model consists of the equations of mass + Uh + Vh =0 (2.12) ∂t ∂x ∂y and momentum conservation and the appropriate boundary conditions. Taking into account that real velocity profiles u, v in the case of wind-generated circulation UPPER LAYER deviate considerably from the logarithmic Mass conservation equation distribution, and in order to improve the non- linear acceleration terms approximation, the ∂ coefficients of the horizontal momentum ho ∂ ∂ + Uoho Voho =0 diffusion Óh are replaced with the horizontal ∂t ∂x ∂y (2.13)

Fig. 2.2: A two layered stratified flow field structure with basic variable symbols, i.e. ho, hu for average depths of upper and lower layer, uo, vo, uu, vu for the respective depth average velocity components, Úo, Úu for average upper and lower layer densities, Ùb, Ùi for bottom and interface shear stress respectively, zb bed distances from a reference axis (KOUTITAS et al., 1994).

Medit. Mar. Sci., 3/2, 2002, 05-25 9

http://epublishing.ekt.gr | e-Publisher: EKT | Downloaded at 03/10/2021 14:48:14 | Momentum conservation equations along y-axis: along x-axis ∂V ∂V ∂V u +U u +V u = ∂t u ∂x u ∂y ∂ ∂ ∂ Uo Uo Uo ∂ ∂ +U +V = ¢Ú ho ∂ o ∂ o ∂ =–g h +h +z –g + t x y ∂y o u b Ú ∂y ∂ =–g h +h +z + Ù Ù ∂ o u b ix by 2 x + – +A∇ V –fU (2.18) Ú h Ú h h h u u Ù Ù u u u u sx ix ∇ 2 + – +Ah h Uo +fVo (2.14) where Úo and Úu are the average upper and Úoho Úoho ¢Ú Ú –Ú lower layer densities,= u o is the relative Ú Úu along y-axis density, zb is the bed distance from a reference axis and Ùsx, Ùsy, Ùix, Ùiy, Ùbx, Ùby the surface, ∂V ∂V ∂V interface and bed shear stresses along x and y o +U o +V o = axes. ∂ o ∂ o ∂ t x y Boundary conditions refer to the surface, ∂ interface and bed, concerning the successive =–g ho +hu +zb + ∂x atmosphere influence on the upper layer, Ù Ù upper layer influence on the lower layer and sy iy ∇ 2 + – +Ah h Vo -fUo (2.15) bed influence on the lower layer. Úoho Úoho Free surface boundary condition LOWER LAYER Ù Mass conservation equation sx =k W W2 +W2 , Ú s x x y o ∂ hu ∂ ∂ Ù + U h V h =0 (2.16) sy =k W W2 +W2 ∂ ∂ u u ∂ u u s y x y (2.19) t x y Úo

Boundary condition on the interface Momentum conservation equations Ùix 2 2 along x-axis =Uo –Uo ki Uo –Uu +Vo –Vo , Úo

∂U ∂U ∂U Ùiy 2 2 u u u =V–V k U –U +V –V +Uu +Vu = o o i o u o u (2.20) ∂t ∂x ∂y Úo ∂ ¢Ú ∂h =–g h +z –g o + ∂x u b Ú ∂x Bottom boundary condition Ù Ù Ù bx =k U U 2 +V2 , ix bx ∇ 2 b u u u + – +Ah h Uu +fVu (2.17) Úo Úuhu Úuhu Ùby 2 2 =kb Vu Uu +Vu (2.21) Úo

where ks, ki, kb are the friction coefficients for the surface, interface and bed respectively with

10 Medit. Mar. Sci., 3/2, 2002, 05-25

http://epublishing.ekt.gr | e-Publisher: EKT | Downloaded at 03/10/2021 14:48:14 | 0[ks] = 5.10-6, 0[ki] = 10-3, 0[kb] = 10-2, Ùsx, Ùsy, model the numerical solution is based on a Ùix, Ùiy, Ùbx, Ùby are the respective shear stresses spatially centered scheme of second order and Wx, Wy are the wind velocity components. explicit differences and a special ‘leap frog’ Boundary conditions are supplemented with differences scheme for the approximation of the open sea boundary condition describing temporal derivatives. the free radiation of perturbation from the The stability of the numerical solution for interior to the exterior infinite field: both models is obtained through the satisfaction of relations between temporal Open sea boundary condition discretization steps ¢t and spatial discretization steps ¢x or ¢y, i.e. the CFL (Courant –

Friedrichs – Lewy) criterion: ⋅ ⋅ ⋅ (2.22) V n h= h–hinitial C ¢x ¢t < 2 C (2.24) where n denotes the normal unit vector to the max exterior of the field and C the gravity waves propagation velocity: where Cmax =ghmax is the maximum phase velocity and hmax is the maximum depth C =gh+h o o u observed. ¢Ú h C = gh u u o (2.23) Results Ú ho +hu

∆he two mathematical models, described Numerical solution of the mathematical above, have been applied to simulate the two models different regimes of the water circulation in the Thermaikos Gulf observed during previous For the numerical solution of both models studies in the area. a rectangular Arakawa C staggered grid was The first regime considered was a nearly used where U, V components refer to the homogeneous water column in order to nodes sides, while ˙ refers to the interior of describe the case of a late autumn. During this each mesh (Fig. 2.1). period the plume of fresh water is usually small In the case of the first model the derivatives so that strong density gradients do not appear, are approximated with explicit schemes of neither does thermal stratification exist, as is finite differences: time derivatives with forward obvious from a typical density profile (Fig. 3.1) differences and the other derivatives with measured in November ’94 at the station TP22 central differences. In the case of the second (Fig. 3.2), in the framework of research

Fig. 2.1: The computational molecule for the horizontal and vertical velocity components U,V and the sea level ˙.

Medit. Mar. Sci., 3/2, 2002, 05-25 11

http://epublishing.ekt.gr | e-Publisher: EKT | Downloaded at 03/10/2021 14:48:14 | Fig. 3.1: Depth distribution of Ûı density, measured at station TP22 in November 1994.

Fig. 3.2: A chart of the bathymetry over the survey area showing moorings ThA, ThB (marked ı∞, ıµ) and survey stations TP01-34 (KRESTENITIS et al., 1997). coordinated by Proudman Oceanographic Estuaries’, since they are weak with an average Laboratory (P.O.L). In other words, the case tidal height of about 25 cm. of a barotropic, wind-generated circulation The second regime studied was a two-layer was examined, neglecting tidal currents stratified basin approximating the summer case through the cross section ‘M.Emvolo – Axios during which a surface mixed layer had formed

12 Medit. Mar. Sci., 3/2, 2002, 05-25

http://epublishing.ekt.gr | e-Publisher: EKT | Downloaded at 03/10/2021 14:48:14 | overlying a steep pycnocline, together with and are summarized in Table 1 thermal and saline components. In particular, (KARAMANOS et al., 1998), which implies this is the case of July '94 (Fig. 3.3), when the that during summer the total discharges of the plume expanded to the whole basin and there rivers are gradually minimized, giving the was a small halocline parallel to the deep explanation of halocline suppression. thermocline. During the study of the summer baroclinic ∆his consideration is also suitable for the circulation, a surface layer of a 15-20 m simulation of the case where the pycnocline thickness was adopted, as well as a steep coincides with the thermocline, which suggests pycnocline corresponding to a pycnometric that the plume of fresh water is small, resulting difference of about 5ò, in order to be in in haline homogeneity, as happened during agreement with density profiles in Figures 3.1, August '94 (Fig. 3.4). 3.3, 3.4, implying a temperature difference of Measurements of the river discharges more than 10ÆC between the two layers. flowing into the Gulf have recently taken place

Fig. 3.3: Depth distribution of Ûı density, measured at station TP22 in July 1994.

Fig. 3.4: Depth distribution of Ûı density, measured at station TP22 in August 1994.

Medit. Mar. Sci., 3/2, 2002, 05-25 13

http://epublishing.ekt.gr | e-Publisher: EKT | Downloaded at 03/10/2021 14:48:14 | For both cases a constant wind velocity of 7 m/sec was applied. The wind direction was Table 1 Mean monthly water discharge of Axios, changed linearly along the y-axis from NNW Loudias, Aliakmon for the period 1997-98 at the northern boundary to NWW at the (KARAMANOS et al., 1998). southern boundary of the basin, in order to approximate the curl of wind vectors such as RIVER WATER DISCHARGES (m3/sec) the one shown in Figure 3.5, which constitutes Month Axios Loudias Aliakmonas the prevailing pattern of wind conditions. January 174.21 34.87 79.15 The development of stratified flow has February 149.73 13.77 96.60 been further examined under the influence of March 155.39 11.71 32.00 constant NNW, NW and NWW winds, April 97.00 40.00 11.23 assuming a surface layer depth of 20 m in all May 85.08 34.76 37.15 cases, while the case considering variable wind June 11.58 10.53 9.86 direction was examined for two alternative July 0.54 10.69 9.91 surface layer depths:15 and 20 m respectively. August 1.36 15.88 16.85 The computation grid was made by 41×42 September 37.55 22.78 33.36 grid points with a horizontal resolution of ¢x October 108.44 16.62 24.84 = ¢y = 1852m, it includes the Thermaikos November (*) 165.84 27.01 29.00 Gulf as far as the cross section, ‘Platamonas- December 223.24 37.40 33.17 Possidi’. A time step of 25 sec was used in order to satisfy the CFL criterion. The simulation Total mean monthly water discharge ≈ 158.26 m3/sec was run until the establishment of a steady flow (*) interpolation between October and December condition. The model results are summarized in Table 2.

Fig. 3.5: Surface wind pattern forecast for 31.10.01 [POSEIDON System, http://www.poseidon.ncmr.gr].

14 Medit. Mar. Sci., 3/2, 2002, 05-25

http://epublishing.ekt.gr | e-Publisher: EKT | Downloaded at 03/10/2021 14:48:14 | Table 2 Summary of the different cases for which the two models were applied and the respective figures representing the results.

CASE A: Wind of 7 m/sec intensity and linearly variable direction from NNW at the northern boundary to NWW at the southern boundary of the field CASE A1: No stratified flow Fig. 3.6 CASE A2: Stratified flow with a pycnocline at 20 m depth Fig. 3.7a, 3.7b, 3.7c, 3.8d CASE A3: Stratified flow with a pycnocline at 15 m depth Fig. 3.8a, 3.8b CASE B: Wind of 7 m/sec intensity and constant NNW direction Stratified flow with a pycnocline at 20 m depth Fig. 3.9a, 3.9b CASE C: Wind of 7 m/sec intensity and constant NW direction Stratified flow with a pycnocline at 20 m depth Fig. 3.10a, 3.10b CASE D: Wind of 7 m/sec intensity and constant NWW direction Stratified flow with a pycnocline at 20 m depth Fig. 3.11a, 3.11b

Discussion again to the western coasts. Then, the currents follow the west coastline moving towards the The application of both models using a western side of the south boundary and leave realistic topography of the Thermaikos Gulf the gulf, continuing their transport to the open has raised the following interesting issues sea of the Sporades Basin (Figs 3.7d). A very (DODOU, 2001): important issue arising from the simulation is ñ The circulation pattern is significantly the observation that a section of the inflowing influenced by the way that wind direction varies water masses enters the gulf from the eastern in the whole domain. The basic difference coasts and follows the basic trajectory of the between the case of a variable wind direction north anticyclone. Then, these water masses (Figs 3.7c,b, 3.8c,d) and the three other cases come up to the surface of the upwelling region, with constant wind (Figs 3.9a,b, 3.10a,b, refreshing the surface waters with cold, bottom 3.11a,b) is focused on the circulation pattern waters, enriched with nutrients originating of the upper layer, which tends to be from the north Aegean Sea (and more anticyclonic for constant wind and cyclonic for specifically from the Black Sea). In this way, variable wind, as far as wind direction is the results of the model simulations concerned (Ekman’s spiral effect). (concerning the hydrodynamic circulation in ñ An upwelling process takes place in some the gulf) are in line with the general circulation sub-regions of the coastal domain of the pattern presented by LYKOUSIS et al. (1981) Thermaikos Gulf, depending on the prevailing (Fig. 4.1). This general pattern of water inflow wind conditions, as well as the density and circulation in the Gulf constitutes a very gradients. In the lower layer of the eastern part strong point for the prognostic capability of of the south open sea boundary, a characteristic the model. inflow of seawater masses is observed, initially ñ Another important point regarding the moving along the eastern coastline. As this simulation, concerning the upwelling movement takes place a section of the water phenomenon, is related to the fact that the masses moves to the (opposite) western side most favorable wind for upwelling events, in of the gulf. The remainder of the inflow masses the case of shallow waters, is that normal to continues its transport northerly -to the the coastline blowing toward the open sea, due boundary of an upwelling region- where it turns to its collinearity with the Ekman’s transport

Medit. Mar. Sci., 3/2, 2002, 05-25 15

http://epublishing.ekt.gr | e-Publisher: EKT | Downloaded at 03/10/2021 14:48:14 | Fig. 3.6: Velocity pattern of non-stratified circulation under the influence of linearly variable wind from N¡W at the northern boundary to NWW at the southern boundary (CASE A1). The axes are in nautical miles and the velocities in m/sec.

Fig. 3.7a: Contours of the upper layer thickness under the influence of linearly variable wind from N¡W at the northern boundary to NWW at the southern boundary. The surface layer initial depth was 20m (CASE A2). The axes are in nautical miles and the thickness in meters.

16 Medit. Mar. Sci., 3/2, 2002, 05-25

http://epublishing.ekt.gr | e-Publisher: EKT | Downloaded at 03/10/2021 14:48:14 | Fig. 3.7b: Contours of the lower layer thickness under the influence of linearly variable wind from N¡W at the northern boundary to NWW at the southern boundary. The surface layer initial depth was 20m (CASE A2). The axes are in nautical miles and the thickness in meters.

Fig. 3.7c: Velocity pattern of the upper layer under the influence of linearly variable wind from N¡W at the northern boundary to NWW at the southern boundary. The surface layer initial depth was 20m (CASE A2). The axes are in nautical miles and the velocities in m/sec.

Medit. Mar. Sci., 3/2, 2002, 05-25 17

http://epublishing.ekt.gr | e-Publisher: EKT | Downloaded at 03/10/2021 14:48:14 | Fig. 3.7d: Velocity pattern of the lower layer under the influence of linearly variable wind from N¡W at the northern boundary to NWW at the southern boundary. The surface layer initial depth was 20m (CASE A2 ). The axes are in nautical miles and the velocities in m/sec.

Fig. 3.8a: Velocity pattern of the upper layer under the influence of linearly variable wind from N¡W at the northern boundary to NWW at the southern boundary. The surface layer initial depth was 15m (CASE A3). The axes are in nautical miles and the velocities in m/sec.

18 Medit. Mar. Sci., 3/2, 2002, 05-25

http://epublishing.ekt.gr | e-Publisher: EKT | Downloaded at 03/10/2021 14:48:14 | Fig. 3.8b: Velocity pattern of the lower layer under the influence of linearly variable wind from N¡W at the northern boundary to NWW at the southern boundary. The surface layer initial depth was 15m (CASE A3). The axes are in nautical miles and the velocities in m/sec.

Fig. 3.9a: Velocity pattern of the upper layer under the influence of constant NNW wind. The surface layer initial depth was 20m (CASE B). The axes are in nautical miles and the velocities in m/sec.

Medit. Mar. Sci., 3/2, 2002, 05-25 19

http://epublishing.ekt.gr | e-Publisher: EKT | Downloaded at 03/10/2021 14:48:14 | Fig. 3.9b: Velocity pattern of the lower layer under the influence of constant NNW wind. The surface layer initial depth was 20m (CASE B). The axes are in nautical miles and the velocities in m/sec.

Fig. 3.10a: Velocity pattern of the upper layer under the influence of constant NW wind. The surface layer initial depth was 20m (CASE C). The axes are in nautical miles and the velocities in m/sec.

20 Medit. Mar. Sci., 3/2, 2002, 05-25

http://epublishing.ekt.gr | e-Publisher: EKT | Downloaded at 03/10/2021 14:48:14 | Fig. 3.10b: Velocity pattern of the lower layer under the influence of constant NW wind. The surface layer initial depth was 20m (CASE C).The axes are in nautical miles and the velocities in m/sec.

Fig. 3.11a: Velocity pattern of the upper layer under the influence of constant NWW wind. The surface layer initial depth was 20m (CASE D). The axes are in nautical miles and the velocities in m/sec.

Medit. Mar. Sci., 3/2, 2002, 05-25 21

http://epublishing.ekt.gr | e-Publisher: EKT | Downloaded at 03/10/2021 14:48:14 | Fig. 3.11b: Velocity pattern of the lower layer under the influence of constant NWW wind. The surface layer initial depth was 20m (CASE D). The axes are in nautical miles and the velocities in m/sec.

Fig. 4.1: Schematic circulation pattern of Thermaikos Gulf proposed by LYKOUSIS et al., 1981.

22 Medit. Mar. Sci., 3/2, 2002, 05-25

http://epublishing.ekt.gr | e-Publisher: EKT | Downloaded at 03/10/2021 14:48:14 | direction. In this study, the prevailing NNW is strongly developed offshore of the western wind, along the northern coastal zones, is part of the north coastline. (Fig. 4.2). characterized by an important vertical The aforementioned observations support the theory of the zonation of the continental component to the western part of the northern shelf, concerning the different process of coastline, in this way generating significant upwelling dynamics (Fig. 4.3): transport of water mass towards the open sea. - Upwelling in the shallow coastal region It is also remarkable that before the generation (close to land) takes place when the wind blows of the upwelling process, a current of 0,45 m/sec towards the open sea (normal to the coastline).

Fig. 4.2: Velocity pattern of the upper layer under the influence of linearly variable wind from N¡W at the northern boundary to NWW at the southern boundary at time step 10 000 (2,7 hours). The surface layer initial depth was 20m.The axes are in nautical miles and the velocities in m/sec.

Fig. 4.3: Zonation of the coastal ocean into regions with different upwelling dynamics (TOMCZAK, 1996).

Medit. Mar. Sci., 3/2, 2002, 05-25 23

http://epublishing.ekt.gr | e-Publisher: EKT | Downloaded at 03/10/2021 14:48:14 | - Upwelling in the middle continental shelf References develops under the influence of winds blowing parallel to the coastline, with the land to the BALOPOULOS, ∂., CHRONIS, G., LYKOUSIS, left of their direction in the case of the northern V. & PAPAGEORGIOU, E., 1987. hemisphere, or to the right in the case of south Hydrodynamic and Sedimentological Processes hemisphere. in the North Aegean Sea: Thermaikos Plateau. - Furthermore, upwelling events can be Colloque International d’ Oceanologie, observed in the external zone of the continental ECOMEARGE, Perpignan, France. shelf, either due to ocean current variations or BLUMBERG, A.F. &MELLOR G.L., 1987. A due to tidal pumping (TOMCZAK, 1996). description of a three-dimensional coastal ñComparing the two cases for different circulation model. p.1-16. In: Three-dimensional thicknesses of the upper layer, 15 and 20 m, we Coastal Ocean Models, edited by Norman S. can conclude that the water circulation of the Heaps, Washington, American Geophysical upper layer as well as the lower layer presents Union. CHRISTODOULOU, G. & PROTOPAPAS, A., the same features, and the main difference 1982. Water circulation and dispersion in the bay refers exclusively to the intense expansion of of Elefsina. Technica Chronica, 2, No. 1-2 the upwelling region and the implicit decrease DODOU, M., 2001. Mathematical models of of the upper layer, which almost vanishes (Fig. stratified flows. Application for the study of 3.8a, b). circulation to Thermaikos Gulf during the summer ñThe pattern of winter circulation (no period, M. Sc. Thesis, Thessaloniki, AUTh, 180p stratified flow) which resulted from the (in Greek). application of a two - dimensional model is KARAMANOS, H. & POLYZONIS, E., 1998. The characterized by three anticyclones and a small adjacent land area and its potentiality for the fresh cyclone (located at the south-eastern end of water and sediment supply. «Dynamics of Matter the model domain), suggesting that the wind Transfer and Biogeochemical Cycles: Their curl influence is less determinant than the Modeling in Coastal Systems of the Mediterranean stratified flow case. (Fig. 3.6). An inefficiency Sea». A MAST-III ELOISE EU Project, Second of the model in describing water entrance into Annual Scientific Report, Volume II. the gulf through the south -eastern open KOURAFALOU, V., 1996. The fate of river boundary is also observed. discharge on the continental shelf 1. Modeling the ñSummarizing the development and river plume and the inner shelf coastal current. In: application of a two-layered hydrodynamic Journal of Geophysical Research, 101, No.C2: 3415- model presented in this paper helps to the 3434. better understanding of the physical KOURAFALOU, V., KRESTENITIS, Y. & mechanisms which govern the movements of BARBOPOULOS, K., 1998. Modelling the seasonal variability of the processes that affect the seawater masses in the case of stratified matter transfer on the Thermaikos Gulf. Part 1: waters where a characteristic pycnocline has land-sea interaction. «Dynamics of Matter Transfer developed in the water column. In the case of and Biogeochemical Cycles: Their Modelling in the Thermaikos Gulf, the simulation of the Coastal Systems of the Mediterranean Sea». A wind vector field as a curl with important NW MAST-III ELOISE EU Project, Second Annual components, applied to a stratified, two- Scientific Report, Volume II. layered seawater flow, provides an adequate KOUTITAS, C., 1987. ∆hree-Dimensional Models approximation of the gulf’s prevailing of Coastal Circulation: An Engineering Viewpoint, circulation pattern and leads to a realistic p.107-123. In: Three-dimensional Coastal Ocean description of the water refreshing Models, edited by Norman S. Heaps, Washington, mechanisms, i.e. the upwelling phenomenon. American Geophysical Union.

24 Medit. Mar. Sci., 3/2, 2002, 05-25

http://epublishing.ekt.gr | e-Publisher: EKT | Downloaded at 03/10/2021 14:48:14 | KOUTITAS, C., 1988. Mathematical models in PANAYIOTIDIS, P., 1997. The role of the benthic Coastal Engineering. London, Pentech Press primary production in the Land-Ocean Interaction Limited Zone of the system Thermaikos Gulf- North KOUTITAS, C., HASILTZOGLOU, N., Aegean Sea. «Dynamics of Matter Transfer and TRIANTAFILOU, G, KRESTENITIS, Y., 1994. Biogeochemical Cycles: Their Modelling in Development and application of an operational Coastal Systems of the Mediterranean Sea», A mathematical model of density currents. Reprint MAST-III ELOISE EU Project, First Annual of scientific yearbook in Polytechnic School, Scientific Report. Department of Architecture, 1991-1993. P.O.L. (Proudman Oceanographic Laborator), 1997. KRESTENITIS, Y.N., VALIOULIS π.∞., Processes in regions of freshwater influence – CHRISTOPOULOS S.P., & HAYDER, P. A., Profile. Final Report. 1997. The Rivers Influence on the Seasonal Coastal Circulation of the Thermaikos Gulf. In: SAVVIDIS, Y. & KOUTITAS, C., 2000. Simulation Proceedings of the Third International Conference of transport & fate of suspended matter along the on the Mediterranean Coastal Environment, coast of Agathoupolis (N. Greece). In: Proceedings MEDCOAST 97, Malta. of the 5th International Conference Protection and LYKOUSIS., V., COLLINS, M.B., & Restoration of the Environment, Thasos Greece. FERENTINOS, G., 1981. Modern Sedimentation TOMZACK, M., 1996, Shelf and Coastal Zone in the N. W. Aegean Sea. In: Marine Geology, 46: Lecture Notes, http://www.es.flinders.edu.au/ 111-130. /~mattom/ShelfCoast/index.html.

Medit. Mar. Sci., 3/2, 2002, 05-25 25