We conducted a spectral analysis of the turbulence kinetic energy (TKE) budget in a bubble plume using particle image velocimetry with fluorescent particles. Our findings confirmed the hypothesis of an inverse energy cascade in the bubble plume, where TKE is transferred from small to large eddies. This is attributed to direct injection of TKE by bubble passages across a wide range of scales, in contrast to canonical shear production of TKE in large scales. Turbulence dissipation was identified as the primary sink of the bubble-produced TKE and occurred at all scales. The decomposition of velocities using the critical length scale of inter-scale energy transfer allowed us to distinguish between large- and small-scale motions in the bubble plume. The large-scale turbulent fluctuations exhibited a skewed distribution and were likely associated with the return flow after bubble passage and the velocities induced by the bubble wake. The small-scale turbulent fluctuations followed a Gaussian distribution relatively well. The large-scale motions contributed to over half of the Reynolds stresses, while there were significant small-scale contributions to the normal stresses near the plume center but not to the shear stress. The large-scale motions in the vorticity field induced a street of vertically elongated vortex pairs, while the small-scale vortices exhibited similar sizes in both horizontal and vertical directions.
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Fully developed turbulence is a universal and scale-invariant chaotic state characterized by an energy cascade from large to small scales at which the cascade is eventually arrested by dissipation1–6. Here we show how to harness these seemingly structureless turbulent cascades to generate patterns. Pattern formation entails a process of wavelength selection, which can usually be traced to the linear instability of a homogeneous state7. By contrast, the mechanism we propose here is fully nonlinear. It is triggered by the non-dissipative arrest of turbulent cascades: energy piles up at an intermediate scale, which is neither the system size nor the smallest scales at which energy is usually dissipated. Using a combination of theory and large-scale simulations, we show that the tunable wavelength of these cascade-induced patterns can be set by a non-dissipative transport coefficient called odd viscosity, ubiquitous in chiral fluids ranging from bioactive to quantum systems8–12. Odd viscosity, which acts as a scale-dependent Coriolis-like force, leads to a two-dimensionalization of the flow at small scales, in contrast with rotating fluids in which a two-dimensionalization occurs at large scales4. Apart from odd viscosity fluids, we discuss how cascade-induced patterns can arise in natural systems, including atmospheric flows13–19, stellar plasma such as the solar wind20–22, or the pulverization and coagulation of objects or droplets in which mass rather than energy cascades23–25.
more » « less- PAR ID:
- 10507493
- Publisher / Repository:
- Springer Nature
- Date Published:
- Journal Name:
- Nature
- Volume:
- 627
- Issue:
- 8004
- ISSN:
- 0028-0836
- Page Range / eLocation ID:
- 515 to 521
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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