Abstract:
Stimulated by new evidence from both "in situ" oceanic observations
and results from numerical modelling, a laboratory study of quasigeostrophic
flow and turbulence in a rotating homogeneous fluid has been undertaken.
Two dimensional turbulence driven by a uniform distribution of sources and
sinks which oscillate in time, can be fairly well reproduced in this context.
Inertial time scales are about ten times smaller than Ekman spinup
time, and typical Reynolds numbers read 2000. The observations emphasize
the spectral tendency of the energy containing eddies. The case of
no topography is first discussed. In steadily forced turbulence, it is
observed that the energy containing scale is significantly larger than
the forcing scale. In the decaying stage the red cascade is observed and
rates of interaction are measured. Theoretical arguments for both behaviors
are presented; the former concerning the forced turbulence case is
believed to be new.
The forcing is next applied over various large scale topographies,
modelling the geophysical beta effect. The polar beta plane geometry preserves
the above spectral characteristics but at the same time introduces
anisotropy into the flow pattern. A broad westward mean flow develops in
the north and is surrounded by a belt of cyclones lying on its southward
side. The calculated second-order Eulerian mean flows induced by steadily
and uniformly forced Rossby waves in a long zonal channel, exhibit much of
the same momentum distribution in the inertial regime. In contrast, the
"sliced cylinder" geometry which possesses no closed geostrophic contours
drastically modifies the above picture. Both mean flow production and a
large scale tendency for the eddies are inhibited. The geographical distribution of the eddy intensities and scales is now wildly inhomogeneous.
The second aspect of this work is a study of the interaction of Rossby
waves with mean flows. A zonally traveling, forced wave is generated near
the southern boundary of a polar beta plane. Due to energy radiation in
the free interior and (or) potential vorticity mixing by the finite amplitude waves, a westward zonal flow develops. The effect of the mean flow
upon the forced steady waves is to weaken the anticyclones and intensify
the cyclones. Pressure time series reveal a growth of harmonics and
general spectral broadening as the waves travel freely inwards, suggesting
active nonlinear interactions. An experimental test of Rhines' (1977) potential
vorticity mixing theory is also presented at free latitudes. The decay
period when the driving is suppressed shows that a net transfer from the
waves to the mean flow kinetic energy occurs. Connection with hydrodynamic
stability theory is discussed.
Interaction of Rossby waves with an externally generated westward mean
flow allows one to make a controlled study of the critical layer problem.
For small amplitude waves, the mean flow is accelerated in the entire region
between the forcing and the critical latitude which acts as a wall for mean
wave momentum. In nonlinear runs the steady profile of the westward flow
indicates that an accelerating force is acting everywhere, revealing the
increasing transmission of wave momentum through the critical layer. At
the same time, pressure measurements near the critical point show considerable
fine structure developing over a long time scale.
The third part deals with steady isolated source-sink flows in the
sliced cylinder geometry. The response of the fluid to a meridionally
oriented steady dipole extends exclusively westward of the forcing. The
viscously balanced solutions are discussed and relevance to oceanic abyssal
circulation is emphasized. With strong driving, the combination of
a cyclone to the north and an anticyclone to the south is absolutely
stable although the reverse configuration is not. A connection with a
certain class of free, steady, isolated, inertial solutions developed
recently by Stern (1976) is made.