Geoscience Reference
In-Depth Information
These DNS results underscore the care that must be
taken when using laboratory-scale stratified turbulence as
a proxy for the atmospheric mesoscale and oceanic sub-
mesoscale. In particular, steep spectral slopes from exper-
iments with Re
b
∼
Babin, A., A. Mahalov, B. Nicolaenko, and Y. Zhou (1997),
On the asymptotic regimes and the strongly stratified limit of
rotating Boussinesq equations,
Theor. Comput. Fluid Dyn.
,
9
,
223-251.
Bartello, P. (2000), Potential vorticity, resonance and dis-
sipation in rotating convective turbulence, in
Geophysi-
cal and Astrophysical Convection
,editedbyR.H.Ker ,
P. Fox, and C.-H. Moeng, pp. 309-321, Gordon and Breach,
Amsterdam.
Bartello, P. (2010), Quasigeostrophic and stratified turbulence in
the atmosphere, in
IUTAN Symposium on Turbulence in the
Atmosphere and Oceans
, vol. IUTAM Bookseries 28, edited
by D. G. Dritschel, pp. 117-130, Springer, New York.
Bartello, P., and S. Tobias (2013), Sensitivity of stratified turbu-
lence to the buoyancy Reynolds number,
J. Fluid Mech.
,
725
,
1-22.
Billant, P., and J.-M. Chomaz (2000), Three-dimensional sta-
bility of a vertical columnar vortex pair in a stratified fluid,
J. Fluid Mech.
,
419
, 65-91.
Billant, P., and J.-M. Chomaz (2001), Self-similarity of strongly
stratified inviscid flows,
Phys. Fluids
,
13
, 1645-1651.
Brethouwer, G., P. Billant, E. Lindborg, and J.-M. Chomaz
(2007), Scaling analysis and simulation of strongly stratified
turbulent flows,
J. Fluid Mech.
,
585
, 343-368.
Charney, J. G. (1971), Geostrophic turbulence,
J.Atmos.Sci.
,
28
,
1087-1095.
Cho, .Y.N ,Y.Zhu,R.E.Newe ,B.E.Anderson,
J. D. Barrick, G. L. Gregory, G. W. Sachse, M. A. Carroll,
and G. M. Albercook (1999), Horizontal wavenumber spec-
tra of winds, temperature, and trace gases during the Pacific
Exploratory Missions: 1. Climatology,
J. Geophys. Res.
,
104
,
5697-5716.
Dewan, E. M. (1979), Stratospheric wave spectra resembling
turbulence,
Science
,
204
, 832-835.
Drazin, P. G. (1961), On the steady flow of a fluid of variable
density past an obstacle,
Tellus
,
13
, 239-251.
Durran, D. R. (2010),
Numerical Methods for Fluid Dynamics
:
With Applications to Geophysics, Springer, New York.
Embid, P. F., and A. J. Majda (1998), Low Froude number lim-
iting dynamics for stably stratified flow with small or finite
Rossby numbers,
Geophys. Astrophys. Fluid Dyn.
,
87
, 1-50.
Gage, K. S. (1979), Evidence for a
k
−
5
/
3
law inertial range
in mesoscale two-dimensional turbulence,
J. Atmos. Sci.
,
36
,
1950-1954.
Gage, K. S., and G. D. Nastrom (1986), Theoretical inter-
pretation of atmospheric wavenumber spectra of wind and
temperature observed by commercial aircraft during GASP,
J. Atmos. Sci.
,
43
, 729-740.
Godoy-Diana, R., J.-M. Chomaz, and P. Billant (2004), Vertical
length scale selection for pancake vortices in strongly stratified
viscous fluids.
J. Fluid Mech.
,
504
, 229-238.
Hebert, D. A., and S. M. de Bruyn Kops (2006a), Relationship
between vertical shear rate and kinetic energy dissipation rate
in stably stratified flows,
Geophys. Research Lett.
,
33
, L06602.
Hebert, D. A., and S. M. de Bruyn Kops (2006b), Predicting tur-
bulence in flows with strong stable stratification,
Phys. Fluids
,
18
, 066602.
Herring, J. R., and O. Métais (1989), Numerical experiments in
forced stably stratified turbulence,
J.FluidMech.
,
202
, 97-115.
O(
1
)
should not be extrapolated too
literally to geophysical scales. All else being equal, spec-
tra do get shallower as Re
b
increases, although it is still an
open question whether the limiting slope for Re
b
→∞
is
5
−
3
or something else. Nevertheless, it is quite encourag-
ing that these simulations are able to capture some basic
phenomena that are expected to hold at larger Re
b
.In
particular, the transfer of kinetic energy to small hori-
zontal scales by Kelvin-Helmholtz instabilities appears
to be quite robust, even for relatively modest values of
Re
b
, suggesting that the instabilities (if not the subse-
quent turbulent breakdown) are realizable in laboratory
experiments [
Augier et al.
, 2014].
A more serious concern about the geophysical applica-
bility of idealized laboratory experiments and numerical
simulations such as these is the question of how energy
gets into the large scales to begin with. Simulations and
experiments necessarily employ ad hoc methods to inject
energy at large scales, either through initial conditions
and/or forcing. But in the real atmosphere and ocean,
the large-scale motion is not stratified turbulence at all,
but rather quasi-geostrophic turbulence forced by radia-
tive heating, surface fluxes, and baroclinic instability. The
cascade through the atmospheric mesoscale and oceanic
sub-mesoscale that is envisioned by the stratified turbu-
lence hypothesis must be forced by the breakdown of
this larger-scale motion, for which the effects of rota-
tion cannot be ignored [e.g.,
Bartello
, 2010;
Molemaker
et al.
, 2010;
Vallgren et al.
, 2011]. The extent to which
the influence of this large-scale motion extends down into
the mesoscale/sub-mesoscale and beyond is still an open
question that requires further study.
Acknowledgments.
This work was supported by
a grant from the Natural Sciences and Engineering
Research Council of Canada. Computations were per-
formed on the GPC supercomputer at the SciNet HPC
Consortium [
Loken et al.
, 2010]. SciNet is funded by the
Canada Foundation for Innovation under the auspices of
Compute Canada, the Government of Ontario, Ontario
Research Fund, Research Excellence, and the University
of Toronto.
REFERENCES
Almalkie, S., and S. M. de Bruyn Kops (2012), Kinetic energy
dynamics in forced, homogeneous, and axisymmetric stably
stratified turbulence,
J. Turbul.
,
13
, N29.
Augier, P., P. Billant, M. E. Negretti, and J.-M. Chomaz
(2014), Experimental study of stratified turbulence forced
with columnar dipoles,
Phys. Fluids
,
26
, 046603.
