The Establishment of the Tsugaru and the Alboran Gyres

Doron Nof Department of Oceanography and the Geophysical Fluid Dynamics Institute, The Florida State University, Tallahassee, Florida

Search for other papers by Doron Nof in
Current site
Google Scholar
PubMed
Close
and
Thierry Pichevin Service Hydrographique et Oceanographique de la Marine, Brest, France

Search for other papers by Thierry Pichevin in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

A new theory for the generation of the Tsugaru and Alboran gyres is proposed. The essence of the theory can be described as follows. Using the nonlinear reduced-gravity (shallow water) equations, it has been recently shown by Pichevin and Nof that a channel emptying light water into an otherwise resting ocean of denser water on an f plane produces a forever-growing gyre next to the channel mouth. The generation of the gyre is caused by the (otherwise imbalanced) flow force of the alongshore current downstream regardless of the initial current vorticity. [By changing the potential vorticity via friction, the fluid creates the required vorticity (on its own) in the cases where the incoming flow has a vorticity that cannot accommodate the gyre.]

It is shown here, analytically and numerically, that when the channel is oriented eastward (i.e., the channel is situated along a western boundary as is the case with the Tsugaru and Alboran gyres) the presence of β causes an arrest of the gyre’s growth. As a result, a steady state corresponding to a flow field resembling a snail is established. Here, the “shell” of the imaginary snail corresponds to the gyre and the elongated body of the snail corresponds to the downstream current. The establishment of the modeled steady gyre is inevitable, regardless of the upstream potential vorticity, and the gyre has a length scale involving both β and the Rossby radius.

The analytical solution to the inviscid nonlinear equations is constructed using a perturbation scheme in ε, the ratio of the Coriolis parameter variation across the current to the Coriolis parameter at the center. It shows that the gyre size is roughly 2Rd1/4 [where Rd is the Rossby radius (based on the downstream thickness H) and ε ≡ βRd/f0] implying that the Tsugaru and the Alboran gyres have a scale that is greater than the usual current scale (Rd). Numerical simulations, using the Bleck and Boudra model, are in excellent agreement with the theoretical prediction for the inviscid gyre size; they also show that the gyres are established regardless of the upstream potential vorticity. Both the analytical and the numerical results are in good agreement with the observations.

Corresponding author address: Prof. Doron Nof, Department of Oceanography (4320), The Florida State University, Tallahassee, FL 32306-4320.

Email: nof@ocean.fsu.edu

Abstract

A new theory for the generation of the Tsugaru and Alboran gyres is proposed. The essence of the theory can be described as follows. Using the nonlinear reduced-gravity (shallow water) equations, it has been recently shown by Pichevin and Nof that a channel emptying light water into an otherwise resting ocean of denser water on an f plane produces a forever-growing gyre next to the channel mouth. The generation of the gyre is caused by the (otherwise imbalanced) flow force of the alongshore current downstream regardless of the initial current vorticity. [By changing the potential vorticity via friction, the fluid creates the required vorticity (on its own) in the cases where the incoming flow has a vorticity that cannot accommodate the gyre.]

It is shown here, analytically and numerically, that when the channel is oriented eastward (i.e., the channel is situated along a western boundary as is the case with the Tsugaru and Alboran gyres) the presence of β causes an arrest of the gyre’s growth. As a result, a steady state corresponding to a flow field resembling a snail is established. Here, the “shell” of the imaginary snail corresponds to the gyre and the elongated body of the snail corresponds to the downstream current. The establishment of the modeled steady gyre is inevitable, regardless of the upstream potential vorticity, and the gyre has a length scale involving both β and the Rossby radius.

The analytical solution to the inviscid nonlinear equations is constructed using a perturbation scheme in ε, the ratio of the Coriolis parameter variation across the current to the Coriolis parameter at the center. It shows that the gyre size is roughly 2Rd1/4 [where Rd is the Rossby radius (based on the downstream thickness H) and ε ≡ βRd/f0] implying that the Tsugaru and the Alboran gyres have a scale that is greater than the usual current scale (Rd). Numerical simulations, using the Bleck and Boudra model, are in excellent agreement with the theoretical prediction for the inviscid gyre size; they also show that the gyres are established regardless of the upstream potential vorticity. Both the analytical and the numerical results are in good agreement with the observations.

Corresponding author address: Prof. Doron Nof, Department of Oceanography (4320), The Florida State University, Tallahassee, FL 32306-4320.

Email: nof@ocean.fsu.edu

Save
  • Batchelor, G. K., 1967: An Introduction to Fluid Dynamics. Cambridge University Press, 615 pp.

  • Bleck, R., and D. Boudra, 1986: Wind-driven spin-up in eddy-resolving ocean models formulated in isopycnic and isobaric coordinates. J. Geophys. Res.,91, 7611–7621.

  • Bormans, M., and C. Garrett, 1989: A simple criterion for gyre formation by the surface outflow from a strait, with application to the Alboran Sea. J. Geophys. Res.,94, 12 637–12 644.

  • Cherniawsky, J., and P. H. LeBlond, 1986: Rotating flows along indented coastlines. J. Fluid Mech.,169, 379–407.

  • Conlon, D. M., 1982: On the outflow modes of the Tsugaru warm current. La Mer,20, 60–64.

  • Flierl, G., 1979: A simple model of the structure of warm and cold-core rings. J. Geophys. Res.,84, 78–85.

  • Gliezon, P., G. Chabert D’Hieres, and D. Renouard, 1996: Experimental study of the Alboran Sea gyres. Oceanol. Acta,19, 499–511.

  • Heburn, G. W., and P. La Violette, 1990: Variations in the structure of the anticyclonic gyres found in the Alboran Sea. J. Geophys. Res.,95, 1599–1613.

  • Kawasaki, Y., and T. Sugimoto, 1984: Experimental studies on the formation and degeneration processses of the Tsugaru warm gyre. Ocean Hydrodynamics of the Japan and East China Sea, T. Ichiye, Ed., D. Reidel, 225–238.

  • Kennelly, M. A., R. H. Evans, and T. M. Joyce, 1985: Small-scale cyclones on the periphery of a Gulf Stream warm-core ring. J. Geophys. Res.,90, 8845–8857.

  • Killworth, P. D., 1983: On the motion of isolated lenses on a beta-plane. J. Phys. Oceanogr.,13, 368–376.

  • Kubokawa, A., 1991: On the behavior of outflows with low potential vorticity from a sea strait. Tellus,43A, 168–176.

  • Lacombe, H., and C. Tchernia, 1972: Caractères hydrologiques et circulation des eaux en Méditerranée. The Mediterranean Sea, D. J. Stanley, Ed., Dowden, Hutchinson, and Ross, 26–36.

  • Nof, D., 1978a: On geostrophic adjustment in sea straits and wide estuaries: Theory and laboratory experiments. Part I: One-layer system. J. Phys. Oceanogr.,8, 690–702.

  • ——, 1978b: On geostrophic adjustment in sea straits and wide estuaries: Theory and laboratory experiments. Part II: Two-layer system. J. Phys. Oceanogr.,8, 861–872.

  • ——, 1981: On the dynamics of equatorial outflows with application to the Amazon’s basin. J. Mar. Res.,39, 1–29.

  • ——, 1986: Geostrophic shock waves. J. Phys. Oceanogr.,16, 886–901.

  • ——, 1988: Outflows dynamics. Geophys. Astrophys. Fluid Dyn.,40, 165–193.

  • ——, 1993: Generation of ringlets. Tellus,45, 299–310.

  • ——, 1996: What controls the origin of the Indonesian throughflow? J. Geophys. Res.,101, 12 301–12 314.

  • Orlanski, I., 1976: A simple boundary condition for unbounded hyperbolic flows. J. Comput. Phys.,21, 251–269.

  • Perkins, H., T. Kinder, and P. La Violette, 1990: The Atlantic inflow in the western Alboran Sea. J. Phys. Oceanogr.,20, 242–263.

  • Pichevin, T., 1996: Curving and retroflecting currents: A new eddy generation process. Ph.D. thesis, University of Paris, 124 pp.

  • ——, and D. Nof, 1997: The momentum imbalance paradox. Tellus,49, 298–319.

  • Preller, R. H., 1986: A numerical model study of the Alboran Sea gyre. Progress in Oceanography, Vol. 16, Pergamon, 113–146.

  • Saint-Guily, B., 1957: Les méandres des veines de courant dans les océans. Bull. Inst. Océanogr.,1108, 1–11.

  • Speich, S., G. Madec, and M. Crépon, 1996: A strait outflow circulation process study: The case of the Alboran Sea. J. Phys. Oceanogr.,26, 320–340.

  • Viúdez, Á., 1997: An explanation for the curvature of the Atlantic jet past the Strait of Gibraltar. J. Phys. Oceanogr.,27, 1804–1810.

  • ——, and R. L. Haney, 1997: On the relative vorticity of the Atlantic jet in the Alboran Sea. J. Phys. Oceanogr.,27, 175–185.

  • ——, J. Tintoré, and R. L. Haney, 1996: Circulation in the Alboran Sea as determined by quasi-synoptic hydrographic observations. Part I: Three-dimensional structure of the two anticyclonic gyres. J. Phys. Oceanogr.,26, 684–705.

  • Werner, F. E., A. Cantos-Figuerola, and G. Parrilla, 1988: A sensitivity study of reduced-gravity channel flows with application to the Alboran Sea. J. Phys. Oceanogr.,18, 373–383.

  • Whitehead, J. A., and A. R. Miller, 1979: Laboratory simulation of the gyre in the Alboran Sea. J. Geophys. Res.,84, 3733–3742.

  • Yasuda, I., K. Okuda, M. Hirai, Y. Ogawa, H. Kudoh, S. Fukushima, and K. Mizuno, 1988: Short-term variations of the Tsugaru Warm Current in autumn. Bull. Tohuku Reg. Fish. Res. Lab.,50, 153–191.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 202 31 1
PDF Downloads 84 25 1