• INTRODUCTION
  • STRATEGY
  • MODEL
  • RESULTS
  • THEORY
  • CONCLUSIONS
  • REFERENCES

    Restratification Theory

  • linear stability analysis

    The evolution of the integral properties of a column of ocean which, having become baroclinically unstable, subsequently goes on to exhibit finite amplitude instability (beginning the process of breaking-up into columns, restratifying the interior and carrying detatched fragments of the chimney away) depends on the interplay between surface buoyancy losses, B, and the lateral buoyancy flux by baroclinic eddies as follows

    where

    and

    the baroclinic eddy buoyancy flux.

    There are two limiting cases

  • The STEADY STATE case in which the tendency term in the above is assumed zero. Supposing buoyancy losses persist at the surface we can then solve for an EQUILIBRIUM DEPTH of the statistically steady state. At equilibrum baroclinic eddies will be importing buoyancy from the sides to offset buoyancy loss at the sea surface. This has been the subject of many recent research efforts for example Legg and Marshall 1993 , Brickman et al., 1995 , Marshall and Send 1995 and Visbeck et al., 1996 . Numerical and laboratory studies support the following dependence of h on B, r and f.

  • The RESTRATIFICATION case in which the right hand side of eqn.(2) is zero. Buoyancy loss from the surface has ceased and the eddies flux buoyancy in laterally from the ambient fluid, restratifying the homogenized patch. From eqn.(2) we can estimate a restratification time scale.

    It also follows that the rate of change of chimney buoyancy is set according to

    Plotting graphs of mean chimney buoyancy as a function of time (Fig.4(a)) enables us to determine the constant c_e empirically.

    The slopes of Figs.4 (b) and (c) suggest c_e=0.027. Returning to eqn.(3), this would imply a constant of proportionality of 4.8. Visbeck et al. (1995) find 3.9 plus or minus 0.9; Whitehead et al. (1995) find 4.6 plus or minus 0.5.



    Back to the top