We present numerical simulations of decaying two-dimensional (2D) and three-dimensional quasigeostrophic (3D QG) turbulence. The resulting vorticity fields are decomposed into three components: the vortex cores, the strain cells, and the background. In 2D, the vortex cores induce five times the energy as the background, while in 3D QG the background plays a more dominant role and induces the same amount of energy as the vortex cores, quantifying previous observations that 3D QG has a more active filamentary background. The probability density function of the total velocity field is nearly Gaussian in 3D QG but significantly less so in 2D. In both 2D and 3D QG, the velocities induced by the vortex cores and the strain cells are non-Gaussian. In both 2D and 3D QG turbulence, the enstrophy spectrum of the background is close to k1 predicted by inverse cascade theories.

1.
B.
Fornberg
, “
A numerical study of 2-D turbulence
,”
J. Comput. Phys.
25
,
1
(
1977
).
2.
J. C.
McWilliams
, “
The emergence of isolated and coherent vortices in turbulent flow
,”
J. Fluid Mech.
146
,
21
(
1984
).
3.
G. F.
Carnevale
,
J. C.
McWilliams
,
Y.
Pomeau
,
J. B.
Weiss
, and
W. R.
Young
, “
Evolution of vortex statistics in two-dimensional turbulence
,”
Phys. Rev. Lett.
66
,
2735
(
1991
).
4.
J. C.
McWilliams
,
J. B.
Weiss
, and
I.
Yavneh
, “
Anisotropy and coherent vortex structures in planetary turbulence
,”
Science
264
,
410
(
1994
).
5.
J. C.
McWilliams
, “
The vortices of geostrophic turbulence
,”
J. Fluid Mech.
219
,
387
(
1990
).
6.
J. C.
McWilliams
,
J. B.
Weiss
, and
I.
Yavneh
, “
The vortices of homogeneous geostropic turbulence
,”
J. Fluid Mech.
401
,
1
(
1999
).
7.
A.
Okubo
, “
Horizontal dispersion of floatable particles in the vicinity of velocity singularities such as convergences
,”
Deep-Sea Res.
17
,
445
(
1970
).
8.
J.
Weiss
, “
The dynamics of enstrophy transfer in two-dimensional hydrodynamics
,”
Physica D
48
,
273
(
1991
).
9.
D.
Elhmaïdi
,
A.
Provenzale
, and
A.
Babiano
, “
Elementary topology of two-dimensional turbulence from a Lagrangian viewpoint and single-particle dispersion
,”
J. Fluid Mech.
257
,
533
(
1993
).
10.
M.
Farge
,
N.
Kevlahan
,
V.
Perrier
, and
E.
Goirand
, “
Wavelets and turbulence
,”
Proc. IEEE
84
,
639
(
1996
).
11.
J. C.
McWilliams
, “
The vortices of two-dimensional turbulence
,”
J. Fluid Mech.
219
,
361
(
1990
).
12.
M.
Farge
and
T.
Philipovitch
, “
Coherent structure analysis and extraction using wavelets
,” in
Progress in Wavelet Analysis and Applications
, edited by
Y.
Meyer
and
S.
Roques
(
Editions Frontieres
,
Gif-sur-Yvette
,
1993
), p.
477
.
13.
A.
Siegel
and
J. B.
Weiss
, “
A wavelet-packet census algorithm for calculating vortex statistics
,”
Phys. Fluids
9
,
1988
(
1997
).
14.
M.
Farge
,
K.
Schneider
, and
N.
Kevlahan
, “
Non-Gaussianity and coherent vortex simulation for two-dimensional turbulence using an adaptive orthogonal wavelet basis
,”
Phys. Fluids
11
,
2187
(
1999
).
15.
J. E.
Ruppert-Felsot
,
O.
Praud
,
E.
Sharon
, and
H. L.
Swinney
, “
Extraction of coherent structures in a rotating turbulent flow experiment
,”
Phys. Rev. E
72
,
016311
(
2005
).
16.
C.
Pasquero
,
A.
Provenazale
, and
J. B.
Weiss
, “
Vortex statistics from eulerian and Lagrangian time series
,”
Phys. Rev. Lett.
89
,
284501
(
2002
).
17.
A.
Provenzale
, “
Transport by coherent barotropic vortices
,”
Annu. Rev. Fluid Mech.
31
,
55
(
1999
).
18.
J. C.
McWilliams
and
J. B.
Weiss
, “
Anisotropic geophysical vortices
,”
Chaos
4
,
305
(
1994
).
19.
A.
Bracco
,
J.
von Hardenberg
,
A.
Provenzale
,
J. B.
Weiss
, and
J. C.
McWilliams
, “
Dispersion and mixing in quasigeostrophic turbulence
,”
Phys. Rev. Lett.
92
,
084501
(
2004
).
20.
J. B.
Weiss
,
A.
Provenzalea
, and
J. C.
McWilliams
, “
Lagrangian dynamics in high-dimensional point-vortex systems
,”
Phys. Fluids
10
,
1929
(
1998
).
21.
A.
Bracco
,
J.
LaCasce
,
C.
Pasquero
, and
A.
Provenzale
, “
The velocity distribution of barotropic turbulence
,”
Phys. Fluids
12
,
2478
(
2000
).
22.
A.
Bracco
,
J. H.
LaCasce
, and
A.
Provenzale
, “
Velocity probability density functions for oceanic floats
,”
J. Phys. Oceanogr.
30
,
461
(
2000
).
23.
A.
Bracco
,
E. P.
Chassignet
,
Z. D.
Garraffo
, and
A.
Provenzale
, “
Lagrangian velocity distributions in a high-resolution numerical simulation of the North Atlantic
,”
J. Atmos. Ocean. Technol.
20
,
1212
(
2003
).
24.
J. G.
Charney
,
On the Scale of Atmospheric Motions
(
Geofysiske Publikasjoner
,
1948
), Vol.
17
, pp.
1
17
. Republished in
The Atmosphere, a Challenge: The Science of J. Gregory Charney
, edited by
R. S.
Lindzen
,
E. N.
Lorenz
, and
G. W.
Platzman
(
AMS
, Boston, MA,
1990
).
25.
R.
Salmon
,
Geophysical Fluid Dynamics
(
Oxford University Press
, New York,
1998
).
26.
J.
Jeong
and
F.
Hussain
, “
On the identification of a vortex
,”
J. Fluid Mech.
285
,
69
(
1995
).
27.
Y.
Dubief
and
F.
Delcayre
, “
On coherent vortex identification in turbulence
,”
J. Turbul.
1
,
111
(
2000
).
28.
F.
Paparella
,
A.
Babiano
,
C.
Basdevant
,
A.
Provenzale
, and
P.
Tanga
, “
A Lagrangian study of the Antarctic polar vortex
,”
J. Geophys. Res.
102
,
6765
(
1997
).
29.
P. R.
Spalart
,
R. D.
Moser
, and
M. M.
Rogers
, “
Spectral methods for the Navier-Stokes equations with one inifinite and two periodic directions
,”
J. Comput. Phys.
96
,
297
(
1991
).
30.
A. N.
Kolmogorov
, “
A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number
,”
J. Fluid Mech.
13
,
82
(
1962
).
31.
R. H.
Kraichnan
, “
Inertial ranges in two-dimensional turbulence
,”
Phys. Fluids
10
,
1417
(
1967
).
32.
J. G.
Charney
, “
Geostrophic turbulence
,”
J. Atmos. Sci.
28
,
1087
(
1971
).
33.
I.
Min
,
I.
Mezić
, and
A.
Leonard
, “
Lèvy stable distributions for velocity and velocity difference in systems of vortex elements
,”
Phys. Fluids
8
,
1169
(
1996
).
34.
D.
Sornette
,
Critical Phenomena in Natural Sciences
, 2nd ed. (
Springer
, New York,
2004
).
35.
A.
Griffa
,
K.
Owens
,
L.
Piterbarg
, and
B.
Rozovskii
, “
Estimates of turbulence parameters from Lagrangian data using a stochastic particle model
,”
N.Z.J. Mar. Freshwater Res.
53
,
371
(
1995
).
36.
P.
Falco
,
A.
Griffa
,
P.
Poulain
, and
E.
Zambianchi
, “
Transport properties in the Adriatic Sea as deduced from drifter data
,”
J. Phys. Oceanogr.
30
,
2055
(
2000
).
37.
M.
Veneziani
,
A.
Griffa
,
A. M.
Reynolds
, and
A. J.
Mariano
, “
Oceanic turbulence and stochastic models from subsurface Lagrangian data for the northwest Atlantic Ocean
,”
J. Phys. Oceanogr.
34
,
1884
(
2004
).
38.
A.
Griffa
,
L. I.
Piterbarg
, and
T.
Ozgokmen
, “
Predictability of Lagrangian particles trajectories: Effects of smoothing of the underlying Eulerian flow
,”
N.Z.J. Mar. Freshwater Res.
62
,
1
(
2004
).
39.
C.
Pasquero
,
A.
Provenzale
, and
A.
Babiano
, “
Parameterization of dispersion in two-dimensional turbulence
,”
J. Fluid Mech.
439
,
279
(
2001
).
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