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.