Geoscience Reference
In-Depth Information
This tendency to form multiple, parallel wave trains and
zonal flows is reminiscent of the kind of flow regimes
obtained in thermally driven annulus experiments with
oppositely sloping end walls to generate a topographic
β
effect [e.g.,
Mason
, 1975;
Bastin and Read
, 1997, 1998;
Wordsworth et al.
, 2008]. As argued by
Read
[2011], how-
ever, in contrast to laboratory experiments with bound-
aries of variable end wall slope, the global Rhines length
scale (
Appleby, J. C. (1988), Selection of baroclinic waves,
Quart. J. R.
Meteor. Soc.
,
114
, 1173-1179.
Baines, P. G. (1976), The stability of planetary waves on a sphere,
J. Fluid Mech.
,
73
, 193-213.
Barry, L., G. C. Craig, and J. Thuburn (2002), Poleward
heat transport by the atmospheric heat engine,
Nature
,
415
,
774-777.
Basdevant, C., B. Legras, R. Sadourney, and M. Beland (1981),
A study of barotropic model flows: Intermittency, waves and
predictability,
J. Atmos. Sci.
,
38
, 2305-2326.
Bastin, M. E., and P. L. Read (1997), A laboratory study of
baroclinic waves and turbulence in an internally heated rotat-
ing fluid annulus with sloping endwalls,
J. Fluid Mech.
,
339
,
173-198.
Bastin, M. E., and P. L. Read (1998), Experiments on the struc-
ture of baroclinic waves and zonal jets in an internally heated,
rotating, cylinder of fluid,
Phys. Fluids
,
10
, 374-389.
Bell, M. J. (1989), Theoretical investigations prompted by exper-
iments with baroclinic fluids, Ph.D. thesis, Imperial College
London.
Bell, M. J., and A. A. White (1988), The stability of internal
baroclinic jets: Some analytical results,
J. Atmos. Sci.
,
45
,
2571-2590.
Bernadet, P., A. Butet, M. Deque, M. Ghil, and R. Pfeffer
(1990), Low-frequency oscillations in a rotating annulus with
topography,
J. Atmos. Sci.
,
47
, 3023-3043.
Boville, B. A. (1981), Amplitude vacillation on a
β
-plane,
J. Atmos. Sci.
,
38
, 609-618.
Bowden, M. (1961), An experimental investigation of heat trans-
fer in rotating fluids, Ph.D. thesis, Durham Univ., UK.
Bowden, M., and H. F. Eden (1965), Thermal convection in a
rotating fluid annulus: Temperature, heat flow and flow field
observations in the upper symmetric regime,
J. Atmos. Sci.
,
22
, 185-195.
Brachet, M. E., M. Meneguzzi, H. Politano, and P.-L. Sulem
(1988), The dynamics of freely-decaying two-dimensional tur-
bulence,
J. Fluid Mech.
,
194
, 333-349.
Brindley, J., and I. Moroz (1980), Lorenz attractor behaviour
in a continuously stratified baroclinic fluid,
Phys. Lett.
,
77A
,
441-444.
Buzyna, G., R. L. Pfeffer, and R. Kung (1978), Cyclic vari-
ations of the imposed temperature contrast in a thermally
driven rotating annulus of fluid,
J. Atmos. Sci.
,
35
, 859-
881.
Buzyna, G., R. L. Pfeffer, and R. Kung (1984), Transition
to geostrophic turbulence in a rotating differentially heated
annulus of fluid,
J. Fluid Mech.
,
145
, 377-403.
Castrejón-Pita, A. A., and P. L. Read (2007), Baroclinic waves
in an air-filled thermally driven rotating annulus,
Phys. Rev.
E
,
75
, 026,301.
Cazalbou, J.-B., P. Chassaing, G. Dufour, and X. Carbonneau
(2005), Two-equation modeling of turbulent rotating flows,
Phys. Fluids
,
17
, 055,110.
Charney, J. G., and M. E. Stern (1962), On the stability of inter-
nal baroclinic jets in a rotating atmosphere,
J. Atmos. Sci.
,
19
,
159-172.
Danabasoglu, G., and J. C. McWilliams (1995), Sensitivity of the
global ocean circulation to parameterizations of mesoscale
tracer transports,
J. Clim.
,
8
, 2967-2987.
(U
rms
a/(
2
))
1
/
2
) is not indepen-
dent of the thermal Rossby number in a planetary cir-
culation. It is largely set by the spherical
l ge
ometry and,
in simple cases, may scale roughly as
√
S
(though the
full situation may be more complicated than this; e.g., see
Jansen and Ferrari
[2012] for further discussion). Thus,
provided an analog of the planetary vorticity gradient is
present in the laboratory, there appear to be strong paral-
lels between the principal sequences of regime transitions
in both cylindrical annular laboratory experiments and
planetary atmospheres in spherical shells across much of
the parameter space. But many gaps in our understanding
of these parallels remain to be explored in detail.
However, the ability to run many experiments in the lab-
oratory in order to sample parameter space densely offers
the possibility of testing various theoretical scalings for
circulations that operate on a planetary scale in atmo-
spheres and oceans. Numerical models will continue to
struggle to match this, especially at high planetary rotation
rates where the range of dynamically significant scales of
motion demands the use of very high resolution models.
(U
rms
/β)
1
/
2
∼
∼
Acknowledgments.
Several aspects of this chapter
originated in a series of graduate lectures given at the
University of Oxford. It is a pleasure to thank the many
colleagues and collaborators with whom I have worked on
this problem for a number of years. Particular thanks are
due to Drs. R. Hide, P. Hignett, M. J. Bell, and A. A. White
of the UK Met. Office for their many insights and to
D. W. Johnson, R. M. Small, W.-G. Früh, P. D. Williams,
and A. A. Castrejón-Pita in connection with some of the
experimental work discussed herein. We are also grate-
ful to two anonymous referees whose comments greatly
assisted in improving the presentation of this chapter.
REFERENCES
Abbe, C. (1907), Projections of the globe appropriate for lab-
oratory methods of studying the general circulation of the
atmosphere,
B. Am. Math. Soc.
,
13
, 502-506.
Andrews, D. G., J. R. Holton, and C. B. Leovy (1987),
Middle
Atmosphere Dynamics
, Academic Press, Orlando, Fla.
Appleby, J. C. (1982), Comparative theoretical and experimental
studies of baroclinic waves in a two-layer system, Ph.D. thesis,
Univ. of Leeds.
