This study investigates the effect of nonlinear interactions of Rossby waves on large-scale zonal flow formation in two-dimensional turbulence on a rotating sphere. The coefficients of nonlinear interactions are first calculated. Then, the non-local, near-resonant, and non-local near-resonant interactions are investigated in detail. The results show that the formation of large-scale westward circumpolar zonal flows is directly caused by non-local energy transfer due to the three-wave near-resonant interactions of Rossby waves.
REFERENCES
1.
S.
Yoden
and
M.
Yamada
, “
A numerical experiment on two-dimensional decaying turbulence on a rotating sphere
,” J. Atmos. Sci.
50
, 631
–643
(1993
).2.
S.
Takehiro
,
M.
Yamada
, and
Y.-Y.
Hayashi
, “
Energy accumulation in easterly circumpolar jets generated by two-dimensional barotropic decaying turbulence on a rapidly rotating sphere
,” J. Atmos. Sci.
64
, 4084
–4097
(2006
).3.
T.
Nozawa
and
S.
Yoden
, “
Formation of zonal band structure in forced two-dimensional turbulence on a rotating sphere
,” Phys. Fluids
9
, 2081
–2093
(1997
).4.
K.
Obuse
,
S.
Takehiro
, and
M.
Yamada
, “
Long-time asymptotic states of forced two-dimensional barotropic incompressible flows on a rotating sphere
,” Phys. Fluids
22
, 156601
(2010
).5.
G.
Charney
and
P. G.
Drazin
, “
Propagation of planetary-scale disturbances from the lower into the upper atmosphere
,” J. Geophys. Res.
66
, 83
–110
, https://doi.org/10.1029/JZ066i001p00083 (1961
).6.
A.
Eliassen
and
E.
Palm
, “
On the transfer of energy in stationary mountain waves
,” Geofys. Publ.
22
(3
), 1
–23
(1961
).7.
D. G.
Andrews
and
M. E.
McIntyre
, “
Planetary waves in horizontal and vertical shear: The generalized Eliassen-Palm relation and the mean zonal acceleration
,” J. Atmos. Sci.
33
(11
), 2031
–2048
(1976
).8.
A. M.
Balk
and
S. V.
Nazarenko
, “
On the nonlocal turbulence of drift type waves
,” Phys. Lett. A
146
(4
), 217
–221
(1990
).9.
A. M.
Balk
,
V. E.
Zakharov
, and
S. V.
Nazarenko
, “
Nonlocal turbulence of drift waves
,” Sov. Phys. - JETP
71
(2
), 249
–260
(1990
).10.
L.
Smith
and
Y.
Lee
, “
On near resonances and symmetry breaking in forced rotating flows at moderate Rossby number
,” J. Fluid Mech.
535
, 111
–142
(2005
).11.
E.
Kartashova
, Nonlinear Resonance Analysis
(
Cambridge University Press
, 2010
).12.
V. E.
Zakharov
,
V. S.
L'vov
, and
G.
Falkovich
, Kolmogorov Spectra of Turbulence I: Wave Turbulence
(
Springer
, 1992
).13.
K.
Obuse
and
M.
Yamada
, “Large-scale zonal flow formation in unforced inviscid two-dimensional turbulence on a rotating sphere” (unpublished).14.
I.
Silberman
, “
Planetary waves in the atmosphere
,” J. Meteorol.
11
, 27
–34
(1954
).15.
G. M.
Reznik
,
L. I.
Piterbarg
, and
E. A.
Kartashova
, “
Nonlinear interactions of spherical Rossby modes
,” Dyn. Atoms. Oceans
18
, 235
–252
(1993
).16.
K.
Obuse
and
M.
Yamada
, “
Three-wave resonant interactions and zonal flows in two-dimensional Rossby–Haurwitz wave turbulence on a rotating sphere
,” Phys. Rev. Fluids
4
, 024601
(2019
).17.
M.
Yamada
and
T.
Yoneda
, “
Resonant interaction of Rossby waves in two-dimensional flow on a β plane
,” Phys. D
245
(17
), 1
–7
(2013
).18.
A.
Dutrifoy
and
M.
Yamada
, “High-rotation limit of two-dimensional Navier–Stokes flow on a rotating sphere” (unpublished).19.
K.
Obuse
and
M.
Yamada
, “
Energy transfer to resonant zonal Rossby modes in two-dimensional turbulence on a rotating sphere
,” J. Phys. Soc. Jpn.
89
, 064401
(2020
).20.
Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables
, edited by
M.
Abramowitz
and
I. A.
Stegun
(
Dover Books on Mathematics
, 1964
).21.
L.
Infeld
and
T. E.
Hull
, “
The factorization method
,” Rev. Mod. Phys.
23
, 21
(1951
).22.
H. A.
Rose
and
P. L.
Sulem
, “
Fully developed turbulence and statistical mechanics
,” J. Phys. Fr.
39
(5
), 441
–484
(1978
).23.
M.
Takaoka
,
N.
Yokoyama
, and
E.
Sasaki
, “
Local-flux vectores of conserved quantities in wavenumber space: Anisotropic structures in Charney-Hasegawa-Mima turbulence
,” Phys. Rev. Fluids
7
, L012601
(2022
).24.
S.
Takehiro
,
M.
Odaka
,
K.
Ishioka
,
M.
Ishiwatari
,
Y.-Y.
Hayashi
, and SPMODEL Development Group
, “
A series of hierarchical spectral models for geophysical fluid dynamics
,” Nagare Multimedia (2006
), see http://www.nagare.or.jp/mm/2006/spmodel/© 2024 Author(s). Published under an exclusive license by AIP Publishing.
2024
Author(s)
You do not currently have access to this content.
