Eddy cascade

Depending on the requirements, C-scan or a cascading display are used. These types of display facilitate tests for internal damage below the surface with low-frequency eddy currents in addition to high-frequency tests for surface cracks. 

At high Reynolds numbers, we can again expect the small scales of the scalar field to be nearly isotropic. In the classical picture of turbulent mixing, one speaks of scalar eddies produced at large scales, with a distinct directional orientation, that lose their directional preference as they cascade down to small scales where they are dissipated by molecular diffusion. 

The collection of eddies that appear for identical reasons is called eddy group in this section. When the cascade process of turbulent kinetic energy transfer is considered, it can be understood that the smallest eddy group, that is, the basic eddy group, is determined naturally for an individual fluid, according to its property of viscosity. 

The next stage in the cascade energy transfer from the external forcing over the horizontal scales is the formation of mesoscale eddies [35]. 

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

Figure 4.6 Budget of large-eddy simulation SGS kinetic energy normalized by friction velocity and canopy height energy cascade from resolved flow (solid line) viscous dissipation (long dash line) transfer of SGS energy to wakes (thin solid line) diffusion by resolved and SGS motions (short dash line). (From Shaw and Patton, 2003 [578]).

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

For steady-state simulations, considering the turbulence spectrum in terms of eddy size (length scale), the scales predicted by the k-e model is thus much larger than the particle size. The inclusion of turbulence production due to the bubbles relative motion is therefore based on the assumption of an inverse cascade of turbulence. 

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]. 

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