Final technical report : contract N00014-81-C-0010 : 1 October 1980 - 30 September 1982
Whitehead, John A.
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Laboratory, theoretical and numerical research was conducted into the structure and stability of baroclinic non-linear currents in a rotating fluid. A rotating version of the dam-break problem in which a . density current is generated after a barrier has been removed was studied. The speed of the current and its width and depth were measured by Whitehead (1981) and more extensively by Stern, Whitehead, and Lien Hua (1982), who report the experiments and compare the results to theory. Properties of a limiting bore solution for rotation density currents predicted earlier by Stern are incorporated into the above theory to predict the speed of the nose of the current. Experiments are described in which the current width is measured to be in reasonable agreement with the theory. Theoretical studies of the stability of a free isolated baroclinic jet whose free surface in cross-section intersects the water surface at two points by Griffiths, Killworth and Stern (1982) was undertaken. The waves permit the release of both kinetic and potential energy. They can have rapid growth rates, thee-folding time for waves on a current with zero potential vorticity being close to one-half of a rotation period. Experiments with a current of buoyant fluid at the free surface of a lower layer were also conducted. The current was observed to be always unstable. Killworth and Stern (1982) showed that a coastal density current in a rotating system is unstable to downstream wave disturbances when the mean potential vorticity increases towards the (vertically-walled) coast and when the mean current vanishes there. Other new instability modes were also found which do not require the potential vorticity extremum of quasi-geostrophic theory. Paldor, in his Ph.D. thesis, used Rayleigh integral to prove that an unbounded geostrophic front of uniform potential vorticity is stable with respect to small perturbations of arbitrary wavelength. Stern and Paldor (1983) used extremum concepts to analyze large amplitude disturbances in a boundary layer shear flow with an inviscid and longwave theory. It was found that initially weak horizontal convergences were concentrated and amplified in time.