-
2
-
-
36849111955
-
-
Phys. FluidsG.K. Batchelor, 12, 233 (1969);
-
(1969)
, vol.12
, pp. 233
-
-
Batchelor, G.K.1
-
5
-
-
85036159873
-
-
U. Frisch, Turbulence (Cambridge University Press, Cambridge, UK, 1995)
-
U. Frisch, Turbulence (Cambridge University Press, Cambridge, UK, 1995).
-
-
-
-
12
-
-
85036286515
-
-
DNS of Eq. (1) have been performed by means of a fully dealiased standard pseudospectral code on a doubly periodic square domain of size (Formula presented) with (Formula presented) grid points. Energy is injected into the system at a constant rate (Formula presented) by means of an isotropic Gaussian forcing f, concentrated on small scales (Formula presented) with correlation (Formula presented) 5. We also considered a Gaussian forcing in a restricted band of wave numbers. Viscous term in Eq. (1), as customary, has been replaced by a hyperviscous term (here of order eight). Time evolution is obtained by a second-order Runge-Kutta scheme, and integrations have been stopped when (Formula presented) is still well below the system size to avoid condensation and averages are made over several independent realizations
-
DNS of Eq. (1) have been performed by means of a fully dealiased standard pseudospectral code on a doubly periodic square domain of size (Formula presented) with (Formula presented) grid points. Energy is injected into the system at a constant rate (Formula presented) by means of an isotropic Gaussian forcing f, concentrated on small scales (Formula presented) with correlation (Formula presented) 5. We also considered a Gaussian forcing in a restricted band of wave numbers. Viscous term in Eq. (1), as customary, has been replaced by a hyperviscous term (here of order eight). Time evolution is obtained by a second-order Runge-Kutta scheme, and integrations have been stopped when (Formula presented) is still well below the system size to avoid condensation and averages are made over several independent realizations.
-
-
-
-
13
-
-
85036383841
-
-
A.S. Monin and A.M. Yaglom, Statistical Fluid Mechanics (MIT Press, Cambridge, MA, 1975), Vol. II
-
A.S. Monin and A.M. Yaglom, Statistical Fluid Mechanics (MIT Press, Cambridge, MA, 1975), Vol. II.
-
-
-
-
14
-
-
85036256783
-
-
T. Gotoh, ITP lectures noted of program on hydrodynamic turbulence, 2000, URL: http://online.itp.ucsb.edu/online/hydrot_c00/gotoh
-
T. Gotoh, ITP lectures noted of program on hydrodynamic turbulence, 2000, URL: http://online.itp.ucsb.edu/online/hydrot_c00/gotoh
-
-
-
-
15
-
-
85036233112
-
-
For (Formula presented), the quantity of interest is the conditional average (Formula presented). Due to rotational symmetry one has parity invariance, i.e., (Formula presented), which implies the invariance of (Formula presented) for (Formula presented). Taking into account that (Formula presented) (Formula presented) would be an odd function of V. Moreover, (Formula presented)
-
For (Formula presented), the quantity of interest is the conditional average (Formula presented). Due to rotational symmetry one has parity invariance, i.e., (Formula presented), which implies the invariance of (Formula presented) for (Formula presented). Taking into account that (Formula presented) (Formula presented) would be an odd function of V. Moreover, (Formula presented).
-
-
-
-
16
-
-
85036277600
-
-
order to guarantee the correct dimensionality, the Kolmogorov scaling (Formula presented) has been imposed in Eq. (3), i.e., we implicitly assumed the absence of intermittency, which should be consistent with the outcomes of the theory
-
In order to guarantee the correct dimensionality, the Kolmogorov scaling (Formula presented) has been imposed in Eq. (3), i.e., we implicitly assumed the absence of intermittency, which should be consistent with the outcomes of the theory.
-
-
-
-
18
-
-
85036251195
-
-
G. Boffetta, M. Cencini, and J. Davoudi (unpublished)
-
G. Boffetta, M. Cencini, and J. Davoudi (unpublished).
-
-
-
|