TY - CONF

T1 - Universal Spectrum of Two-dimensional Turbulence On Rotating Sphere and Basic Features of Atmospheric Circulations On Giant Planets

AU - Galperin, B.

AU - Sukoriansky, S.

AU - Dikovskaya, N.

PY - 2002

Y1 - 2002

N2 - The Kolmogorov-Batchelor-Kraichnan (KBK) theory for isotropic
homogeneous two- dimensional (2D) turbulence in the energy range is
extended to small-scale forced 2D turbulence on the surface of a
rotating sphere. The energy spectrum in such flows develops considerable
anisotropy. The classical KBK scaling, E(n) propto epsilon(2/3}n({-5/3))
, is preserved for all but zonal directions in the spectral space,
while in the zonal direction, a steep spectrum E_Z(n) = C_Z (Omega/R)(2)
n(-5) had emerged [here, epsilon is the rate of energy injection at
small scales, Omega and R are the angular velocity and radius of the
sphere, respectively, n is the meridional wave number in spherical
geometry, and C_Z is O(1) constant]. Numer- ical simulations demonstrate
that this flow regime can be established in steady state due to the
action of a linear large scale drag. We argue that the conditions
favorable for the developing of this flow regime are typical of the
atmospheric circulation on all four giant planets of our Solar system
and show that indeed, the same steep spectra emerge from their observed
zonal velocity profiles. The results are used to explain some basic
characteristics of the large-scale circulations on the giant planets.
All numerical and observational data support the value of C_Z simeq 0.5
indicating that C_Z is a universal constant in the n(-5) zonal
spectrum.

AB - The Kolmogorov-Batchelor-Kraichnan (KBK) theory for isotropic
homogeneous two- dimensional (2D) turbulence in the energy range is
extended to small-scale forced 2D turbulence on the surface of a
rotating sphere. The energy spectrum in such flows develops considerable
anisotropy. The classical KBK scaling, E(n) propto epsilon(2/3}n({-5/3))
, is preserved for all but zonal directions in the spectral space,
while in the zonal direction, a steep spectrum E_Z(n) = C_Z (Omega/R)(2)
n(-5) had emerged [here, epsilon is the rate of energy injection at
small scales, Omega and R are the angular velocity and radius of the
sphere, respectively, n is the meridional wave number in spherical
geometry, and C_Z is O(1) constant]. Numer- ical simulations demonstrate
that this flow regime can be established in steady state due to the
action of a linear large scale drag. We argue that the conditions
favorable for the developing of this flow regime are typical of the
atmospheric circulation on all four giant planets of our Solar system
and show that indeed, the same steep spectra emerge from their observed
zonal velocity profiles. The results are used to explain some basic
characteristics of the large-scale circulations on the giant planets.
All numerical and observational data support the value of C_Z simeq 0.5
indicating that C_Z is a universal constant in the n(-5) zonal
spectrum.

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SP - 1118

ER -