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Numerical simulation of coastal upwelling and inerfacial instability of a rotaion and stratified fluid

Published online by Cambridge University Press:  26 April 2006

Yan Zang  and
Robert L. Street
Yan Zang
Affiliation:
Environmental Fluid Mechanics Laboratory, Stanford University, CA 94305-4020, USA
Robert L. Street
Affiliation:
2Quantum Corporation, 500 McCarthy Blvd, Milpitas, CA 95035, USA
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Abstract

The evolution of the coastal upwelling and interfacial instability of a stratified and rotating fluid is studied numerically by using large-eddy simulation. Upwelling is generated near the sidewall of a rotating annulus by the shear at the top. The fluid initially consists of a stably stratified ‘two-layer’ structure with a narrow interface separating the two layers. The large-scale motion of the flow is simulated by solving the time-dependent non-hydrostaic incompressible Navier-Stockes and scalar transport equations while the small-scale motion is represented by a dynamic subgrid-scale model. The upwelling process contains both stable and unstable stratification. The vertical structure of upwelling consists of a persistent primary front, a trailing mixing zone on te shore side of the front, and a temporary secondary front which leads a top inversion layer. The longshore velocity profile has two maxima which occur at the edge of the sidewall boundary layer and at the density front. The upwelled density front is unstable to azimuthal perturbations and baroclinic waves develop and grow to large amplitude. Pairs of cyclonic and anticyclonic waves appear at the front which form ‘jet-streams’. The secondary front is unstable to azimuthal perturbations. Its instability, and the associated drop of the top inversion layer, take the form of radial bands which subsequently break up into isolated patches and eventually sink. The computed values of various upwelling time and length scales are compared to and are in good agreement with past experimental data.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 305 , 25 December 1995 , pp. 47 - 75
Copyright
© 1995 Cambridge University Press

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References

Allen, J. S. 1972a Upwelling of a stratified fluid in a rotating annulus:steady state. Part 1. Linear theory. J. Fluid Mech. 56, 429–445.Google Scholar
Allen, J. S. 1972b Upwelling of a stratified fluid in a rotating annulus:steady state. Part 2. Numerical solutions. J. Fluid Mech. 59, 337–368.Google Scholar
Allen, J. S. 1973Upwelling and coastal jets in a continuously stratified ocean. J. Phys. Oceanogr. 3, 245-257.
Caidwell, D. R., Atta, C. W. Van & Helland, K. N. 1972 A laboratory study of the turbulent Ekman layer. Geophys. Fluid Dyn. 3, 125–160.Google Scholar
Charney, J. G. 1955 The generation of oceanic currents by wind. J. Mar. Res 14, 477–498.Google Scholar
Chia, F. R., Griffiths, R. W. & Linden, P. F. 1982 Laboratory experiments on fronts. Part II. The formation of cyclonic eddies at upwelling fronts.Geophys. Astrophys. Fluid Dyn. 19, 189–206.
Colin, C. 1988 Coastal upwelling events in front of the Ivory Coast during the FOCAL program. Oceanologica ACTA 11, 125–137.Google Scholar
Eady, E. T. 1949 Long waves and cyclone waves.Tellus 1, 35–52.
Ekman, V. M. 1905 Ark. Mat. Astr. Fys. 2(11), 1–52.
Garvine, R. W. 1971 A simple model of coastal upwelling dynamics. J. Phys. Oceanogr. 1, 169–179.Google Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3, 1760–1765.
Gill, A. E. 1982 Atmosphere-Ocean Dynamics. Academic Press.
Greenspan, H. P. 1968 The Theory of Rotating Fluids Cambridge University Press.
Griffiths, R. W. & Linden, P. F. 1981 The stability of buoyancy driven coastal currents. Dyn. Atmos. Oceans 5, 281–306.Google Scholar
Griffiths, R. W. & Linden, P. F. 1982 Laboratory experiments on fronts. Part I. Density driven boundary currents.Geophys. Astrophys. Fluid. Dyn 19, 159–187.
Haidvogein, D. B. Beckman, A. & Hedstrom, K. S. 1991 Dynamical simulations of filament formation and evolution in the coastal transition zone.J. Geophys. Res. 96, 150147–15040.
Halpern, D. 1976 Structure of a coastal upwelling event observed off Oregon during July 1973. Deep-Sea Res 23, 495–508.Google Scholar
Hart, J. E. 1980 An experimental study of nonlinear baroclinic instability and mode selection in a large basin. Dyn. Atmos. Oceans 4, 115–135.Google Scholar
Hidaka, K. 1954 A contribution to the theory of upwelling and coastal currents.Trans. Am. Geophys. Union 35, 431–444.
Hide, R. 1971 Laboratory experiments of free thermal convection in a rotating fluid subject to a horizontal temperature gradient and their relation to the theory of the global atmospheric circulation. In The Global Circulation of the Atmosphere, pp. 196–221. R. Met. Soc. and Am. Met. Soc.
Hsueh, Y. & Kenney, R. N. 1972 Steady coastal upwelling in a continuously stratified ocean. J. Phys. Oceanogr 2, 27–33.Google Scholar
Huriburt, H. E. & Thompson, J. D. 1973 Coastal upwelling on a β plane. J. Phys. Oceanogr. 3, 16–32.Google Scholar
Huyer, A., Smith, R. L. & Paluszkiewicz, T. 1987 Coastal upwelling off Peru during normal and El Nino times, 1981–1984. J. Geophys. Res. 92, 14297–14307.Google Scholar
Ikeda, M., Mysak, L. A. & Emery, W. J. 1984 Observation and modeling of satellite-senced meanders and eddies off Vancouver Island. J. Phys. Oceanogr 14, 3–21.Google Scholar
Killworth, P. D., Paldor, N. & Stern, M. 1984 Wave propagation and growth on a surface front in a two-layer geostrophic current. J. Mar Res. 42, 761–785.Google Scholar
Linden, P. F. & Heust, G. J. F. VAN 1984 Two-layer spin up and frontogenesis. J. Fluid. Mech 143, 69–94.Google Scholar
Longuet-Higgins, M. S. 1965 On group velocity and energy flux in planetary wave motions, Deep-Sea Res. 11, 35–43.
Monismith, S. G. 1986 An experimental study of the upwelling response of stratified reservoirs to surface shear stress J. Fluid. Mech. 171, 407–439.
Mooers, C. N. K., Collins, C. A. & Smith, R. L. 1976 The dynamics structure of the frontal zone in the coastal upwelling region off Oregon.J. Phys. Oceanogr. 6, 3–21.
Mooers, C. N. K. & Robinson, A. R. 1984 Turbulent jets and eddies in the California current and inferred cross-shore transport.Science 223, 51–53.
Narimousa, S. & Maxworthy, T. 1985 Two-layer model of shear-driven coastal upwelling in the presence of bottom topography.J. Fluid. Mech. 159, 503–531.
Narimousa, S. & Maxworthy, T. 1987 Coastal upwelling on a sloping bottom: the formation of plumes, jets and pinched-off cyclones. J. Fluid Mech. 176, 169–190. (referred to herein as NM87).Google Scholar
Narimousa, S., Maxworthy, T. & Spedding, G. R. 1991 Experiments on the structure and dynamics of forced, quasi-two-dimensional turbulence. J. Fluid Mech 223, 113–133.Google Scholar
O'Brien, J. J. & Hurlburt, H. E. 1972 A numerical model of coastal upwelling. J. Phys. Oceanogr. 2, 14–26.Google Scholar
Pedlosky, J. 1974 Longshore currents, upwelling and bottom topography. J. Phys. Oceanogr. 4, 214–226.Google Scholar
Peffley, M. B. & O'Brien, J. J. 1976 A three-dimensional simulation of coastal upwelling off Oregon. J. Phys. Oceanogr. 6, 164–180.Google Scholar
Pelegri, J. L. & Richman, J. G. 1993 On the role of shear mixing during transient coastal upwelling. Continental Shelf Res. 13, 1363–1400.Google Scholar
Petrie, B., Topliss, B. J. & Wright, D. G. 1987 Coastal upwelling and eddy development off Nova Scotia. J. Geophys Res. 92, 12979–12991.Google Scholar
Phillips, N. A. 1954 Energy transformations and meridional circulations associated with simple baroclinic waves in a two-level, quasi-geostrohic model. Tellus 6, 273–286.Google Scholar
Preller, R. & O'Brien, J. J. 1980 The influence of bottom topography on upwelling off Peru. J. Phys. Oceanogr. 10, 1377–1398Google Scholar
Rienecker, M. M. & Mooers, C. N. K. 1987 Dynamical interpolation and forecast of the evolution of mesoscale feartures off Northern California. J. Phys. Oceanogr. 17, 1189–1213.Google Scholar
Roughgarden, J., Gines, S. & Possingham, H. 1988 Recruitment dynamics in complex life cycles. Science 241, 1460–1466.Google Scholar
Ryther, J. H. 1969 Photosynthesis and fish production in the sea. Science 116, 72–76.Google Scholar
Sanders, P. M. 1973 The instability of a baroclinic vortex. J. Phys. Oceanogr. 3, 61–65.Google Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations, I. The basic experiment. Mon. Weath. Rev. 91, 99–164.Google Scholar
Smith, R. L. 1968 Upwelling. Oceanogr. Mar. Biol. Ann. Rev.Allen 6, 11–47.Google Scholar
Smith, R. L. 1978 Poleward propagating perturbations in currents and sea level along the Peru coast. J. Geophys. Res. 83, 6083–6092.Google Scholar
Smith, R. L. Mooers, C. N. K. & Enfield, D. B. 1971 Mesoscale studies of the physical oceanography in two coastal upwelling regions: Oregon and Peru. In Fertility of the Sea vol. 2, pp. 513–535. Gorden and Breach.
Song, Y. & Haidvogel, D. 1994 A semi-implicit ocean circulation model using a generalized topography-following coordinate system. J. Comput. Phys. 115, 228–244.Google Scholar
Sverdrup, H. U. 1938 On the processes of upwelling. J. Mar. Res. 1, 155–164.Google Scholar
Yoshida, K. 1955 Coastal upwelling off the California coast. Rec. Oceanogr. Works Japan 2 (2), 1–13.Google Scholar
Yoshida, K. 1967 Circulation in the eastern tropical oceans with special reference to upwelling and undercurrents. Japan J. Geophys 4 (2), 1–75.Google Scholar
Zang, Y. 1993 On the development of tools for the simulation of geophysical flows. PhD dissertation, Dept. Mech. Engng, Stanford University.
Zang, Y., Street, R. L. & Koseff, J. R. 1993a Large eddy simulation of turbulent cavity flow using a dynamic subgrid-scale model. In Engineering Applications of Large Eddy Simulations (edS. A. Ragab & U. Piomelli). ASME FED vol. 162, pp. 121–126.
Zang, Y., Street, R. L. & Koseff, J. R. 1993b A dynamic mixed subgrid-scale model and its application to turbulent recirculating flows. Phys. Fluids A 5 3186–3196.Google Scholar
Zang, Y., Street, R. L. & Koseff, J. R. 1994 A non-staggered grid, fractional step method for timedependent incompressible Navier-Stokes equations in curvilinear coordinates. J. Comput. Phys. 114, 18–33.Google Scholar