Transients in the Nonlinear Adjustment to Geostrophy

  • James O’Donnell
Part of the NATO ASI Series book series (ASIC, volume 318)


The consequences of nonlinearity on the character of the waves generated during the adjustment to geostrophic equilibrium of a layer of incompressible fluid are investigated by comparing the results of a linear analysis to the approximate solution to the full nonlinear problem obtained numerically. The calculations show that when nonlinear advection and rotation are both important to the dynamics, the evolution of the flow is quite different from that found in the linear, rotating problem of Cahn and the nonlinear, nonrotating problem of Stoker. Solutions presented demonstrate that the adjustment is accomplished by the formation of a large amplitude jump in layer depth which propagates in the opposite direction to that of the initial discontinuity, i.e. towards high pressure. Comparison of this solution to that for the linear problem suggests that the jump is formed by the steepening of Poincare waves and that nonlinear effects have little influence on the rate of approach to the final geostrophic state.


Layer Depth Coastal Current Hydraulic Jump Buoyant Plume Nonlinear Advection 
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  1. Aure, J. and R. Saetre (1981) Wind effects on the Skagerrak outflow. In “The Norwegian Coastal Current”, R. Saetre and M. Mork edts. Univ. of Bergen.Google Scholar
  2. Bennett, A.F. and P.F. Cummins. (1988) Tracking fronts in solutions to the shallow water equations. J. Geophys. Res., 93, 1293–1301.CrossRefGoogle Scholar
  3. Boicourt, W.C., S.-Y. Chao, H.W. Ducklow, P.M. Gilbert, T.C. Malone, M.R. Roman, L.P. Sanford, J.A. Fuhrman, C. Garside and R.W. Garvine (1987) Physics and microbial ecology of a buoyant plume on the continental shelf. Eos, v68, n31, 666–668.Google Scholar
  4. Cahn, A. (1945) An investigation of the free oscillation of a simple current system. J. Meteorol., 2, 113–119.CrossRefGoogle Scholar
  5. Chao, S.-Y. (1988) River forced estuarine plumes. J. Phys. Oceanogr., 18, 72–88.CrossRefGoogle Scholar
  6. Dalziel, S.B. (1988) Two-layer hydraulics: maximal exchange flows. Ph.D. dissertation, Dept. of Applied Mathematics and Theoretical Physics, University of Cambridge. England.Google Scholar
  7. Garrett, C.J.R. and B. Toulany (1982) Sea level variability due to meteorological forcing in the northeast Gulf of St. Lawrence. J. Geophys. Res., 87, 1968–1978.CrossRefGoogle Scholar
  8. Garvine, R.W. (1987) Estuary plumes and fronts in shelf waters: A layer model. J. Phys. Oceanogr., 17, 1877–1896.CrossRefGoogle Scholar
  9. Gill, A.E. (1976) Adjustment under gravity in a rotating channel. J. Fluid Mech., 77, 603–621.CrossRefGoogle Scholar
  10. Gill, A.E. (1982) Ocean-Atmosphere Dynamics. Academic Press, New York, N.Y. 662pp.Google Scholar
  11. Houghton, D.D. (1969) Effects of rotation on the formation of hydraulic jumps. J. Geophys. Res., 74, 1351–1360.CrossRefGoogle Scholar
  12. O’Donnell, J. (1988) A numerical technique to incorporate frontal boundaries in two dimensional layer models of ocean dynamics. J. Phys. Oceanogr., 18, 1584–1600.CrossRefGoogle Scholar
  13. O’Donnell, J. and R.W. Garvine (1983) A time dependent, two-layer model of buoyant plume dynamics. Tellus, 35A, 73–80.CrossRefGoogle Scholar
  14. Rossby, C.-G. (1937) On the mutual adjustment of pressure and velocity distributions in certain current systems, 1. J. Mar. Res., 1, 15–28.Google Scholar
  15. Rossby, C.-G. (1938) On the mutual adjustment of pressure and velocity distributions in certain current systems, 2. J. Mar. Res., 2, 239–263.Google Scholar
  16. Stoker, J.J. (1957) Water Waves. Interscience, New York, N.Y., 567pp.Google Scholar
  17. Whitehead, J.A. (1986) Flows of a homogeneous rotating fluid through straits. Geophys. Astrophys. Fluid Dynamics, 36, 187–205.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • James O’Donnell
    • 1
  1. 1.Department of Marine SciencesThe University of ConnecticutGrotonUSA

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