Cassini observations reveal a regime of zonostrophic macroturbulence on Jupiter

In December 2000, the Cassini fly-by near Jupiter delivered high-resolution images of Jupiter’s clouds over the entire planet in a band between 50°N and 50°S. Three daily-averaged two-dimensional velocity snapshots extracted from these images are used to perform spectral analysis of jovian atmospheric macroturbulence. A similar analysis is also performed on alternative data documented by Choi and Showman (Choi, D., Showman, A. [2011]. Icarus 216, 597–609), based on a different method of image processing. The inter-comparison of the products of both analyses ensures a better constraint of the spectral estimates. Both analyses reveal strong anisotropy of the kinetic energy spectrum. The zonal spectrum is very steep and most of the kinetic energy resides in slowly evolving, alternating zonal (west–east) jets, while the non-zonal, or residual spectrum obeys the Kolmogorov–Kraichnan law specific to two-dimensional turbulence in the range of the inverse energy cascade. The spectral data is used to estimate the inverse cascade rate ∊ and the zonostrophy index Rβ for the first time. Although both datasets yield somewhat different values of ∊, it is estimated to be in the range 0.5–1.0 × 10−5 m2 s−3. The ensuing values of Rβ ≳ 5 belong well in the range of zonostrophic turbulence whose threshold corresponds to Rβ ≃ 2.5. We infer that the large-scale circulation is maintained by an anisotropic inverse energy cascade. The removal of the Great Red Spot from both datasets has no significant effect upon either the spectra or the inverse cascade rate. The spectral data are used to compute the rate of the energy exchange, W, between the non-zonal structures and the large-scale zonal flow. It is found that instantaneous values of W may exceed ∊ by an order of magnitude. Previous numerical simulations with a barotropic model suggest that W and ∊ attain comparable values only after averaging of W over a sufficiently long time. Near-instantaneous values of W that have been routinely used to infer the rate of the kinetic energy supply to Jupiter’s zonal flow may therefore significantly overestimate ∊. This disparity between W and ∊ may resolve the long-standing conundrum of an unrealistically high rate of energy transfer to the zonal flow. The meridional diffusivity Kϕ in the regime of zonostrophic turbulence is given by an expression that depends on ∊. The value of Kϕ estimated from the spectra is compared against data from the dispersion of stratospheric gases and debris resulting from the Shoemaker-Levy 9 comet and Wesley asteroid impacts in 1994 and 2009 respectively. Not only is Kϕ found to be consistent with estimates for both impacts, but the eddy diffusivity found from observations appears to be scale-independent. This behaviour could be a consequence of the interaction between anisotropic turbulence and Rossby waves specific to the regime of zonostrophic macroturbulence

Large eddy simulation of two-dimensional isotropic turbulence

Large eddy simulation (LES) of forced, homogeneous, isotropic, two-dimensional (2D) turbulence in the energy transfer subrange is the subject of this paper. A difficulty specific to this LES and its subgrid scale (SGS) representation is in that the energy source resides in high wave number modes excluded in simulations. Therefore, the SGS scheme in this case should assume the function of the energy source. In addition, the controversial requirements to ensure direct enstrophy transfer and inverse energy transfer make the conventional scheme of positive and dissipative eddy viscosity inapplicable to 2D turbulence. It is shown that these requirements can be reconciled by utilizing a two-parametric viscosity introduced by Kraichnan (1976) that accounts for the energy and enstrophy exchange between the resolved and subgrid scale modes in a way consistent with the dynamics of 2D turbulence; it is negative on large scales, positive on small scales and complies with the basic conservation laws for energy and enstrophy. Different implementations of the two-parametric viscosity for LES of 2D turbulence were considered. It was found that if kept constant, this viscosity results in unstable numerical scheme. Therefore, another scheme was advanced in which the two-parametric viscosity depends on the flow field. In addition, to extend simulations beyond the limits imposed by the finiteness of computational domain, a large scale drag was introduced. The resulting LES exhibited remarkable and fast convergence to the solution obtained in the preceding direct numerical simulations (DNS) by Chekhlov et al. (1994) while the flow parameters were in good agreement with their DNS counterparts. Also, good agreement with the Kolmogorov theory was found. This LES could be continued virtually indefinitely. Then, a simplifiedComment: 34 pages plain tex + 18 postscript figures separately, uses auxilary djnlx.tex fil

Quasi-Normal Scale Elimination Theory of Turbulence

We present an analytical theory of turbulence based upon the procedure of successive elimination of small-scale modes that leads to gradual coarsening of the flow field and accumulation of eddy viscosity. The Reynolds number based upon the eddy viscosity remains O(1). The main results of the theory are analytical expressions for eddy viscosity and kinetic energy spectrum. Partial scale elimination yields a subgrid-scale representation for large eddy simulations while the elimination of all fluctuating scales is analogous to the Reynolds averaging

Anisotropic Turbulence and Internal Waves in Stably Stratified Flows (QNSE Theory)

The quasi-normal scale elimination (QNSE) theory is an analytical spectral theory of turbulence based upon successive elimination of small scales of motion and calculating ensuing corrections to the viscosity and diffusivity. The main results of the theory are analytical expressions for eddy viscosity, eddy diffusivity, and kinetic energy and temperature spectra. Partial scale elimination yields a subgrid-scale representation for large-eddy simulations, whereas the elimination of all fluctuating scales is analogous to the Reynolds averaging. The scale-dependent analysis enables one to put processes on different scales at the spotlight and elucidate their contributions to eddy viscosities and eddy diffusivities. In addition, the method traces the modification of the flow with increasing stratification and recovers growing anisotropy and the effect of the internal waves. The QNSE-based Reynolds-averaged models present a viable alternative to conventional Reynolds stress models. A QNSE model of this kind was tested in the numerical weather prediction system HIRLAM instead of the existing reference Reynolds stress model. The performance of the QNSE model was superior in all simulations where stable stratification was noticeable