Abstract
A three-layer quasi-geostrophic model was developed to examine the topographic eddies generated around the Eratosthenes Seamount in the southeastern Levantine basin, particularly the dipolar vortex structure, consisting of the anticyclonic Cyprus Eddy and a smaller-scale cyclone. The numerical experiments were carried out using the Contour Dynamics Method, imposing an eastward flow with different inclinations and intensities along the western boundary of the model domain to imitate the Mid-Mediterranean Jet. The dual nature of topographic eddies was previously reported to be generated frequently in a homogeneous ocean approximation, but in the current study, the consideration of baroclinicity primarily simulated a single vortex attributed to the Cyprus Eddy with the small-scale cyclone to be generated occasionally. Also, it was demonstrated that the direction and intensity of the imposed eastward flow along the western boundary of the model domain are the main factors in the formation of the cyclonic vortex. The modeling results showed a qualitative agreement with the geostrophic patterns derived from in-situ observations in the wider sea area of the Eratosthenes Seamount.
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Data availability
The datasets analyzed during the current study are available from the corresponding author on request.
References
Alhammoud BK, Béranger K, Mortier L, Crépon M, Dekeyser I (2005) Surface circulation of the Levantine Basin: comparison of model results with observations. Progr Oceanogr 66(2–4):299–320
Brenner S (1989) Structure and evolution of warm core eddies in the eastern Mediterranean Levantine Basin. J Geophys Res 94(C9):12.593-12.602
Brenner S (1993) Long-term evolution and dynamics of a persistent warm core eddy in the Eastern Mediterranean Sea. Deep-Sea Res II40:1193–1206
Brenner S, Rozentraub Z, Bishop J, Krom M (1991) The mixed–layer/thermocline cycle of a persistent warm core eddy in the eastern Mediterranean. Dyn Atmos Oceans 15(3–5):457–476
Egorova VM, Zyryanov VN, Sokolovskiy MA (2022) The hydrodynamic theory of the Cyprus Eddy. Ocean Dyn 72(1):1–20. https://doi.org/10.1007/s10236-021-01484-7
Filyushkin BN, Sokolovskiy MA, Kozhelupova NG, Vagina VM (2010) Dynamics of intrathermocline lenses. Doklady Earth Sci 434(part 2):1377–1380
Fusco G, Manzella GMR, Cruzado A, Gaĉic M, Gasparini GP, Kovaĉeviċ V, Millot C, Tziavos C, Velasquez ZR, Walne A, Zervakis V, Zodiatis G (2003) Variability of mesoscale features in the Mediterranean Sea fromXBT data analysis. Ann Geophys 21:21–32
Golnaraghi M and Robinson AR (1994) Dynamical studies of the Eastern Mediterranean circulation. In: Malanotte-Rizzoli P and Robinson AR (eds) Ocean processes in climate dynamics: global and mediterranean examples. NATO ASI Series, vol 419. Springer, Dordrecht https://doi.org/10.1007/978-94-011-0870-6_17
Groom S, Herut B, Brenner S, Zodiatis G, Psarra S, Kress N, Krom MD, Law CS, Drakopoulos P (2005) Satellite-derived spatial and temporal biological variability in the Cyprus Eddy. Deep-Sea Res II 52:2990–3010
Hamad N, Millot C, Taupier-Letage I (2006) The surface circulation in the eastern basin of the Mediterranean Sea. Sci Mar 70(3):457–503
Hayes DR, Dobricic S, Gildor H, Matsikaris A (2019) Operational assimilation of glider temperature and salinity for an improved description of the Cyprus eddy. Deep-Sea Res Part II 164:41–53
Hayes DR, Zodiatis G, Konnaris G, Hannides A, Solovyov D, and Testor P (2011) Glider transects in the Levantine Sea: characteristics of the warm core Cyprus eddy. OCEANS 2011 IEEE - Spain, 1–9 https://doi.org/10.1109/Oceans-Spain.2011.6003393
Hayes DR, Hannides A, Gergiou G, Testor P, Gildor H, and Zodiatis G (2014) Description of the long-lived subsurface mesoscale eddy south of Cyprus. 6th EGO meeting and final Symposium of the COST Action ES0904, Kiel, Germany ⟨hal-01139537⟩
Hecht A, Pinardi N, Robinson AR (1998) Currents, water masses, eddies, and jets in the Mediterranean Levantine Basin. J Phys Oceanogr 18(10):1320–1353
Holmboe J (1968) Instability of baroclinic three-layered models of the atmosphere. Geophys Publ 28:1–27
Huppert HE (1975) Some remarks on the initiation of inertial Taylor columns. J Fluid Mech 67:397–412
Huppert HE, Bryan K (1976) Topographically generated eddies. Deep Sea Res 23(8):655–679
Ikeda M (1983) Linear instability of a current flowing along a bottom slo** using a three-layer model. J Phys Oceanogr 13(2):208–223
Jacobs SJ (1964) On stratified flow over bottom topography. J Marine Res 22(3):223–235
Koshel KV, Ryzhov EA, Zyryanov VN (2014a) Toroidal vortices over isolated topography in geophysical flows. Fluid Dyn Res 46(3):031405
Koshel KV, Ryzhov EA, Zyryanov VN (2014b) A modification of the invariant imbedding methods for a singular boundary value problem. Commun Nonlinear Sci Numer Simulat 19:459–470
Kozlov VF (1968) The use of one-parameter models to the study of density thermohaline circulation in the ocean of finite depth. Izv USSR Acad Sci Atmos Ocean Phys 4(6):622–633
Kozlov VF (1983) The method of contour dynamics in model problems of the ocean topographic cyclogenesis. Izvestiya Atmos Ocean Phys 19(8):635–640
Kozlov VF, Sokolovskiy MA (1978) Stationary motion of a stratified fluid above a rough bottom (geostrophic approximation on the beta-plane). Oceanology 8(4):383–386
Kozlov VF, Makarov VG, Sokolovskiy MA (1986) Numerical model of the baroclinic instability of axially symmetric eddies in two-layer ocean. Izvestiya Atmos Ocean Phys 22(8):674–678
Kozlov VF (1984) Models of the topographic vortices in ocean. Nauka, Moscow (In Russian)
Krom MD, Woodward EMS, Herut B, Kress N, Carbo P, Mantoura RFC, Spyres G, Thingstad TF, Wassmann P, Wexels-Riser C, Kitidis V, Law CS, Zodiatis G (2005) Nutrient cycling in the southeast Levantine Basin of the eastern Mediterranean: results from a phosphorus starved system. Deep-Sea Res II 52:2879–2896
Kubryakov AI and Shapiro NB (1999) The study of a persistent warm core eddy in winter 1993 and the water mass formation in the Eastern Mediterranean Sea. In: Malanotte-Rizzoli P and Eremeev VN (eds) The Eastern Mediterranean as a laboratory basin for the assessment of contrasting ecosystems. – Springer, Dordrecht 19–31
Makarov VG (1991) A computational algorithm of the method of contour dynamics with changeable topology of the domains under Study. Model Mekh 5(22 №4):83–95
Mauri E, Sitz L, Gerin R, Poulain P-M, Hayes D, Gildor H (2019) On the variability of the circulation and water mass properties in the Eastern Levantine Sea between September 2016–August 2017. Water 11(9):1741. https://doi.org/10.3390/w11091741
Menna M, Poulain PM, Zodiatis G, Gertman I (2012) On the surface circulation of the Levantine sub-basin derived from Lagrangian drifters and satellite altimetry data. Deep-Sea Res I 65:46–58
Menna M, Gerin R, Notarstefano G, Mauri E, Bussani A, Pacciaroni M, Poulain PM (2021) On the circulation and thermohaline properties of the Eastern Mediterranean Sea. Front Mar Sci 8(671469):1–19. https://doi.org/10.3389/fmars.2021.671469
Menna M, Gačić M, Martellucci R, Notarstefano G, Fedele G, Mauri E, Gerin R, Poulain PM (2022) Climatic, decadal, and interannual variability in the upper layer of the Mediterranean Sea using remotely sensed and in-situ data. Remote Sens 14(6):1322. https://doi.org/10.3390/rs14061322
Monin AS, Neiman VG, Filyushkin BN (1970) Density stratifcation in the ocean. Dokl Akad Nauk USSR 191:1277–1279
Oulhen E, Reinaud JN, Carton X (2022) Formation of small-scale vortices in the core of a large merged vortex. Geophys Astrophys Fluid Dyn. https://doi.org/10.1080/03091929.2022.2074983
Ovchinnikov IM, Plakhin E, Moskalenko LV, Neglyad KV, Osadchiy AS, Fedoseyev AF, and Voytova KV (1976) Hydrology of the Mediterranean Sea. Gidrometeoizdat, Leningrad. 375 p (in Russian)
Ozer T, Gertman I, Kress N, Silverman J, Herut B (2017) Interannual thermohaline (1979–2014) and nutrient (2002–2014) dynamics in the Levantine surface and intermediate water masses, SE Mediterranean Sea. Global Planet Change 151:60–67
Özsoy E (1993) A synthesis of Levantine Basin circulation and hydrography, 1985–1990. Deep-Sea Res II 40(6):1075–1119
Özsoy E, Hecht A, Unluata U (1989) Circulation and hydrography of the Levantine Basin-Results of POEM coordinated experiments 1985–1986. Prog Oceanogr 22:125–170
Pinardi N, Masetti E (2000) Variability of the large scale general circulation of the Mediterranean Sea from observations and modelling: a review. Palaeogeogr Palaeoclimatol Palaeoecol 158(3–4):153–173
Pinardi N, Zavatarelli M, Adani M, Coppini G, Fratianni C, Oddo P, Simoncelli S, Tonani M, Lyubartsev V, Dobricic S (2015) Mediterranean Sea large-scale low-frequency ocean variability and water mass formation rates from 1987 to 2007: A retrospective analysis. Prog Oceanogr 132:318–332. https://doi.org/10.1016/j.pocean.2013.11.003
Pullin DL (1992) Contour dynamics methods. Annu Rev Fluid Mech 24:89–115
Reinaud JN (2022) Finite-core quasi-geostrophic circular vortex arrays with a central vortex. AIP Adv 12:025302. https://doi.org/10.1063/5.0081687
Robinson AR, Hecht A, Pinardi N, Bishop Y, Leslie WG, Rosentroub Z, Mariano AJ, Brenner S (1987) Small synoptic/mesoscale eddies: the energetic variability of the Eastern Levantine Basin. Nature 327(6118):131–134
Robinson AR, Malanotte-Rizzoli P, Hecht A, Michelato A, Roether W, Theocharis A, Ünlüata Ü, Pinardi N, Artegiani A, Bergamasco A, Bishop J, Brenner S, Christianidis S, Gacic M, Georgopoulos D, Golnaraghi M, Hausmann M, Junghaus HG, Lascaratos A, Latif MA, Leslie WG, Lozano CJ, Og T, Özso E, Papageorgiou E, Paschini E, Rozentroub Z, Sansone E, Scarazzato P, Schlitzer R, Spezie GC, Tziperman E, Zodiatis G, Athanassiadou L, Gerges M, Osman M (1992) General circulation of the Eastern Mediterranean. Earth Sci Rev 32:285–309
Ryzhov EA, Sokolovskiy MA (2016) Interaction of two-layer vortex pair with a submerged cylindrical obstacle in a two-layer rotating fluid. Phys Fluids 28:056602
Santeva EK, Bashmachnikov IL, Sokolovskiy MA (2021) On the stability of the Lofoten vortex in the Norwegian Sea. Oceanology 61(3):308–318
Schlitzer R (2023) Ocean data view, https://odv.awi.de
Schroeder K and Chiggiato J (2022) Oceanography of the Mediterranean Sea. Elsevier. ISBN: 978–0–12–823692–5.561
Schroeder K, Garcìa-Lafuente J, Josey SA, Artale V, Nardelli BB, Carrillo A, Gacic M, Gasparini GP, Herrmann M, Lionello P, Ludwig W, Millot C, Özsoy E, Pisacane G, Sánchez-Garrido JC, Sannino G, Santoleri R, Somot S, Struglia M, Stanev E, Taupier-Letage I, Tsimplis MN, Vargas-Yáñez M, Zervakis V, and Zodiatis G (2012) Circulation of the Mediterranean Sea and its variability. In: Climate of the Mediterranean Region. Lionello P (Ed), Elsevier, Amsterdam, 592 https://doi.org/10.1016/B978-0-12-416042-2.00003-3
Shteinbuch-Fridman B, Makarov V, Kizner Z (2017) Transitions and oscillatory regimes in two-layer geostrophic hetons and tripoles. J Fluid Mech 810:535–553
Simoncelli S, Fratianni C, Pinardi N, Grandi A, Drudi M, Oddo P (2014) Mediterranean Sea physical reanalysis (MEDREA 1987–2017) (Version 1) (Copernicus Monitoring Environment Marine Service (CMEMS))
Smeed DA (1988) Baroclinic instability of three-layer flows. Part I: Linear stability. J Fluid Mech 194:217–231
Sokolovskiy MA (1991) Modeling triple-layer vortical motions in the ocean by the Contour Dynamics Method. Izvestiya Atmos Ocean Phys 27(5):380–388
Sokolovskiy MA (1997a) Stability of an axisymmetric three-layer vortex. Izvestiya Atmos Ocean Phys 33(1):16–26
Sokolovskiy MA (1997b) Stability analysis of the axisymmetric three-layered vortex using contour dynamics method. Comput Fluid Dyn J 6(2):133–156
Sokolovskiy MA, Filyushkin BN (2015) Interaction between synoptic gyres and intrathermocline lenses. Oceanology 55(5):661–666
Sokolovskiy MA, Filyushkin BN, Carton XJ (2013) Dynamics of intrathermocline vortices in a gyre flow over a seamount chain. Ocean Dyn 63(7):741–760
Sokolovskiy MA, Carton XJ, Filyushkin BN, Yakovenko OI (2016) Interaction between a surface jet and subsurface vortices in a three-layer quasi-geostrophic model. Geophys Astrophys Fluid Dyn 110(3):201–223
Sokolovskiy MA, Carton XJ, Filyushkin BN (2020) Mathematical modeling of vortex interaction using a three-layer quasi-geostrophic model. Part 2: Finite-core-vortex approach and oceanographic application. Mathematics 8(8):1267. https://doi.org/10.3390/math8081267
Sokolovskiy MA, Verron J (2014) Dynamics of vortex structures in a stratified rotating fluid. Atmos and Oceanogr Sci Lib 47 Springer Swidzerland 382
Taylor GI (1923) Experiments on the motion of solid bodies in rotating fluids. Proc Roy Soc Lond 104:213–218
Waugh DW (1992) The efficiency of symmetric vortex merger. Phys Fluids A 4(8):1745–1758
Zabusky NJ, Hughes MH, Roberts KV (1979) Contour dynamics for Euler equations in two dimensions. J Comput Phys 30(1):96–106
Zodiatis G, Theodorou A, Demetropoulos A (1998) Hydrography and circulation south of Cyprus in late summer 1995 and in spring 1996. Oceanol Acta 21(3):447–458
Zodiatis G, Drakopoulos P, Brenner S, Groom S (2005a) Variability of the Cyprus warm core Eddy during the CYCLOPS project. Deep-Sea Res 52(2):2897–2910
Zodiatis G, Brenner S, Gertman I, Ozer T, Simoncelli S, Ioannou M, Savva S (2023) Twenty years of in-situ monitoring in the south-eastern Mediterranean Levantine Basin: basic elements of the thermohaline structure and of the mesoscale circulation during 1995–2015. Frontiers Marine Science. Clim Chang Impacts Mediterr Coast Transl Areas: Assessment, Projection, and Adaptation 9:1074504. https://doi.org/10.3389/fmars.2022.1074504
Zodiatis G, Drakopoulos P, Gertman I, Brenner S, Hayes D (2005b) The Atlantic Water Mesoscale Hydrodynamics in the Levantine Basin. In Strategies for understanding mesoscale processes, F. Briand (Ed), CIESM Monographs no. 37, Monaco
Zodiatis G, Gertman I, Poulain PM, and Menna M (2015) The general circulation in the SE Levantine. PERSEUS Conference Proceedings: Integrated Marine Research in the Mediterranean and Black Sea, Brussels, 231–232
Zyryanov VN (1995) Topographic eddies in sea currents dynamics. IWP RAS, Moscow (in Russian)
Zyryanov VN (2006) Topographic eddies in a stratified ocean. Reg Chaot Dyn 11(4):491–521
Zyryanov VN (2011) Secondary toroidal vortices above seamounts. J Marine Res 69(2–3):463–481
Zyryanov VN (2015) Experimental studies of vortex tori above bottom perturbations in homogeneous rotational fluid. Proc Geoenvir 2(2):46–54 (in Russian)
Zyryanov VN, Egorova VM (2022) Theoretical and laboratory modeling of topographic vortex bifurcation on vortex tori over two-stage axisymmetric elevation. Water Res 49(2):173–183
Zyryanov VN, Chebanova MK, Zyryanov DV (2022) Canyon vortices: Application of the theory of topographic vortices to the phenomenon of ice rings in Baikal. Water Res 49(2):163–172
Funding
The work of VME and MAS was carried out in the frame of the Program No. FMWZ-2022–0001 (State Registration No. 122041100222–7). VME and MAS were supported by the Russian Science Foundation (RSF project No. 22–27-00431), and MAS was supported also by Russian Foundation for Basic Research (RFBR project No. 20–05-00083).
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Egorova, V.M., Sokolovskiy, M.A. & Zodiatis, G. A three-layer model of hydrodynamic processes in the Cyprus Eddy system. Ocean Dynamics 74, 19–36 (2024). https://doi.org/10.1007/s10236-023-01584-6
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DOI: https://doi.org/10.1007/s10236-023-01584-6