Tides in the Northern Adriatic Sea — the Gulf of Trieste

IL NUOVO CIMENTOVOL. 23 C, N. 4 Luglio-Agosto 2000 Tides in the northern Adriatic Sea — the Gulf of Trieste 1 2 V. MALACˇICˇ ( ) and D. VIEZZOLI ( ) (1) National Institute of Biology, Marine Biological Station Piran, Fornacˇe 41 6330 Piran, Slovenia (2) Istituto Nazionale di Oceanografia e Geofisica Sperimentale (OGS) Borgo Grotta Gigante 42/C, 34010 Sgonico, Trieste, Italy (ricevuto l’8 Aprile 1999; revisionato il 27 Marzo 2000; approvato l’11 Maggio 2000) Summary. — The effects of tides in the northern Adriatic Sea were examined using the 2D finite-difference model. The Eulerian residual velocity field of the calibrated model was checked for the mixing efficiency of tides in the northern Adriatic Sea. It is shown through the simulation of tides for the period of one half year that tides are too weak to mix the whole water column (at any time within this period), even in front of the promontories (e.g. the Po river outlet). The model resolution (556 m) allowed analysis of the tidal dynamics in smaller regions. In the Gulf of Trieste the model results are in satisfactory agreement with the current-meter observations for winter 1984-85 and spring 1985. It is shown that in the middle of the entrance to the gulf the sense of rotation of the tidal ellipse vector changes from a clockwise rotation at the southern part of the entrance to an anticlockwise rotation at the northern part of entrance. Tidal currents in the interior of the gulf rotate counterclockwise, while in small bays, and in front of them, the rotation is clockwise. PACS 92.10.Hm – Surface waves, tides, and sea level. 1. – Introduction Early studies on tidal dynamics of the Adriatic Sea began in the nineteenth century. Defant [1] showed that Mediterranean tides are strong in the northern part of the Adriatic Sea (the Gulf of Trieste). The tide there is of a mixed type, with the M2 constituent prevailing and K1 as the second most powerful one [2]. Taylor [3] described analytically the tidal dynamics of a rectangular semi-enclosed basin. His theory, however, does not apply to a domain around a co-oscillating gulf located at a side of the closed end of a basin (e.g., the Gulf of Trieste). The problem of the absorption of semidiurnal tidal waves at the head of the basin (the coast from Venice to Trieste) was studied in [4]. The absorption displaces the amphidromic point towards the western (Italian) coast. The early numerical models of the northern Adriatic Sea focused attention on the M2 and the K1 components [5] (2D model), and the M2 alone [6] (3D model). In both models different boundary conditions were utilised. G Società Italiana di Fisica 365 366 V. MALACˇICˇ and D. VIEZZOLI The TRIM 2D model (Tidal, Residual, Intertidal Mudflat) model was adapted for the simulation of tides in the Northern Adriatic Sea and in the Gulf of Trieste. The model was first applied to the tidal dynamics of San Francisco Bay in California [7], and recently also to the northern Adriatic Sea [8]. The model results for the Gulf of Trieste were summarized in [9]. This paper will show how tides are efficient at mixing the water column in the northern Adriatic Sea, how well the model results match the current-meter observations in the Gulf of Trieste, and what the model results are along the open-boundary line of the gulf. 2. – Numerical model The purpose of the model was to simulate accurately the tidal motion within the model sub-domain, which extends from about 20 km north of the open-boundary line towards the Gulf of Trieste. The open boundary line of the model, which is 124 km long, connects the past sea-level station Pesaro in Italy with the Kamenjak promontory in Croatia, the southernmost tip of the peninsula of Istria. Kamenjak is located near the past sea-level station Pula, as shown in fig. 1. The model topography was created 0 50 km MALAMOCCO VENEZIA LIDO 240 N 220 PORTO CORSINI 10 PO RIVER 200 20 180 GRADO ISONZO RIVER 160 B 20 140 A 10 TRIESTE 120 30 CAPE SAVUDRIJA 20 100 30 40 80 ROVINJ 60 20 40 50 20 PULA PESARO0 KAMENJAK 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 Fig. 1. – Model domain of the northern Adriatic Sea with its topography. The isobaths are in meters and the axes are in model units (1 unit = 555.6 m = 0.3 nautical miles). The inserted rectangle marks the model subdomain (the Gulf of Trieste). TIDES IN THE NORTHERN ADRIATIC SEA 367 from more than 6100 topographic data points and 3100 coastal data points, which were Kriging-interpolated. Each of the resulting square grid elements was 555.6 m wide. The 2D finite-difference model is of a semi-implicit type and is unconditionally stable. A detailed description of the model can be found in [10] and [7]. The model solves the vertically-averaged equations of motion: du ¯h g ¯r (t0 2t ) . 2fv42g 2 (D1h) 1y Du1 x x , H 1 ` dt ¯x 2r0 ¯x (D h) r0 (1) / 0 2 dv ¯h g ¯r (ty ty) ` 1fu42g 2 (D1h) 1y Dv1 , H 1 ´ dt ¯y 2r0 ¯y (D h) r0 together with the vertically integrated equation of continuity ¯h ¯[ (h1D) u] ¯[ (h1D) v] (2) 42 2 , ¯t ¯x ¯y where (u, v) is the vertically averaged (transport) velocity, h the sea-surface elevation 2 2 (SSE) above the mean-level, D the depth, f(41.04 Q 10 4 s 1) the Coriolis parameter, r the vertically averaged density, r 0 the reference density, y H the coefficient of 0 0 horizontal eddy viscosity, (t x , t y ) the wind-stress at the surface, and (t x , t y ) the bottom-friction stress. Density variations, horizontal diffusion of momentum, and wind-stress were all set to zero in tidal analysis. The system (1)-(2), which solves for the unknowns (u, v) and h, is nonlinear because of advection and bottom-friction terms. Bottom-friction stress is considered as a nonlinear function of transport velocity: t t y x 4 2 1 2 4 2 1 2 (3) CD u ku v , CD v ku v , r 0 r 0 where the drag coefficient CD , known in oceanography, is related to the Chezy-Manning coefficient CZ , used mainly in hydraulics [11]: g (4) C 4 . D 2 CZ The coefficient CD ranges from 0.002 to 0.003 for the bottom of the northern Adriatic Sea, which is composed of mud and mud/sand [11]. In shallow regions (DE4 m), however, CD is also a function of depth D. This dependence must be ascertained from the model results. For the determination of CZ the open-boundary conditions, which consist of the prescribed SSE along the line Pesaro-Pula, need to be defined first. They were deduced from Polli’s charts [2] using parabolic fits of amplitude and phase through the intersection points of cotidal and co-range lines with the open-boundary line [8]. From numerous runs of the model for the strongest semi-diurnal M2 constituents the following relationship 4 2 2 (5) CZ C0 [2 exp [ D/D0 ] ] , 4 1/2 21 4 where C0 40 m s and D0 2.5 m, has proven to give the best SSE amplitude damping and phase retardation of the tidal M2 wave in the port of Trieste. The friction 1/2 21 4 23 coefficient has a value of 62 m s (CD 2.55 Q 10 ) when D = 2 m and is almost depth 368 V. MALACˇICˇ and D. VIEZZOLI 4 1/2 21 4 23 D independent (CZ 80 m s , CD 1.53 Q 10 ) for D 12 m, when the variations with depth are smaller than 0.4%. After determination of CD , the open-boundary conditions were improved to obtain the best match with the sea-level observations in five ports (fig. 1): Rovinj, Trieste, Venezia-Lido, Malamocco and Porto Corsini [8]. After the calibration of parameters and fine-tuning of the open-boundary conditions, the model was run for the first 190 days of the year 1985, when currents were measured in the Gulf of Trieste. The model was forced with the superposition of seven tidal constituents at the open-boundary line. The hourly values of SSE and of the transport velocity components were extracted from the model output. Every fifth model cell in both axis directions was considered in the analysis with the harmonic least-square fit using the “singular value decomposition” algorithm [12]. The Rayleigh criteria was fully respected—the synodic period for the separation of S2 and K2 is 182.6 days [13]. The nodal factors were imposed on amplitudes and phases according to [14] by adopting the algorithm from [15]. A spin-up period of 31 days was applied to avoid initial transients completely. The model calibration was rather successful, since we have achieved the root-mean square error of amplitudes of SSE of all seven most important tidal constituents in five ports to be smaller than 1 cm (0.5 cm 6 0.5 cm). Nearly the same results were obtained for the vectorial difference between the model and observed values: 0.8 cm 6 0.7 cm. The error of phase lag was less than 57 (4.4764.27). Finer tuning would require a better determination of the observed values of harmonic constants. 3. – Tidal mixing in the northern Adriatic Sea Let us introduce a quantity P, which reflects the power of the stirring of tidal currents per unit of depth of the water column (D1h) (6) P4log , y N N3 z rCD u min where the density r41025 kg m23 was assumed.

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