Turbulence energy cascade

Meneveau, C. and J. Katz (2000). On the Lagrangian nature of the turbulence energy cascade. 

Applying a turbulent energy cascade model, Ertesvag and Magnussen [2000] derived expressions for nY and ft in terms of the turbulent kinetic energy k and the turbulence dissipation rate s ... 

The turbulent energy, extracted from the mean flow, passes through the energy cascade and is ultimately converted into internal energy by viscous dissipation. 

Leonard, A. (1974), On the energy cascade in large-eddy simulations of turbulent flows, Adv. Geophys. A., 18, 237. 

Leonard A (1974) Energy Cascade in Large-Eddy Simulations of Turbulent Fluid Flows. Adv Geophys 18A 237-248... 

The physical interpretation that the particles may introduce a inverse cascade of turbulence has been confirmed numerically by [44] who used direct numerical simulations of arrays of bubbles (12 by 12 and 18 by 18) in 2D low Reynolds number bubbly flows to investigate the relative motion of several bubbles. They found that the bubbles produced eddies much larger than the bubble size. Those eddies kept growing until they were of the same size as the computational domain for the small (12 by 12) array. (For the 18 by 18 array the computation was stopped while the eddies were still growing, and not reached the size of the computational domain). Later studies on the the inverse energy cascade structure of turbulence in bubbly flows and on turbulence structures induced by bubble buoyancy by [106, 107] confirmed the findings of [44]. 

Murai Y, Kitagawa A, Song X-Q, Ohta J, Yamamoto F (2000) Inverse Energy Cascade Structure of Turbulence in a Bubbly Flow (PIV measurement and results). JSME Int J Series B-Fluids and Thermal Engineering 43 (2) 188-196 Naot D, Rodi W (1982) Calculation of secondary currents in cannel flow. Proc Am Soc Civ Engrs 108 (HY8) 948-968... 

The description of turbulent mixing of passive scalars is based on an extension of the turbulence theory developed for the momentum transfer processes, described in sect 1.2.7. In particular, the energy cascade idea introduced by Richardson [76] and the Kolmogorov hypotheses [47] are adopted. 

This closely resembles the inertial range of the energy cascade process in homogeneous turbulence at high Reynolds numbers. Analogously, assuming... 

The atmosphere is a turbulent fluid. Nonlinear advections cause the motions on one scale to interact and affect other scales of motion. Through the nonlinear interactions, energy cascades from one scale to another. Because it is impossible to obtain an accurate description of the atmosphere s state at all scales, a perfect weather forecast is impossible the initial conditions for a time integration of the governing equations are never precisely known. 

Hossain, M. Inverse energy cascades in three dimensional turbulence. Phys. Fluids B. 3(2), 511-514 (1991)... 

It will now be demonstrated by presenting counterexamples that there is no direct correlation between the turbulence dissipation (which is directly tied to the energy cascade) and local fluctuations in the helicity. Consider the case of two-dimensional turbulence with the velocity field... 

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