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Register a new userDual local and non-local cascades in 3D turbulent Beltrami flows
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We discuss the possibility of dual local and non-local cascades in a 3D turbulent Beltrami flow, with inverse energy cascade and direct helicity cascade, by analogy with 2D turbulence. We discuss the corresponding energy spectrum in both local and non-local case. Comparison with a high Reynolds number turbulent von Karman flow is provided and discussed.
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The nonlinear and nonlocal coupling of vorticity and strain-rate constitutes a major hindrance in understanding the self-amplification of velocity gradients in turbulent fluid flows. Utilizing highly-resolved direct numerical simulations of isotropic turbulence in periodic domains of up to $12288^3$ grid points, and Taylor-scale Reynolds number $R_lambda$ in the range $140-1300$, we investigate this non-locality by decomposing the strain-rate tensor into local and non-local contributions obtained through Biot-Savart integration of vorticity in a sphere of radius $R$. We find that vorticity is predominantly amplified by the non-local strain coming beyond a characteristic scale size, which varies as a simple power-law of vorticity magnitude. The underlying dynamics preferentially align vorticity with the most extensive eigenvector of non-local strain. The remaining local strain aligns vorticity with the intermediate eigenvector and does not contribute significantly to amplification; instead it surprisingly attenuates intense vorticity, leading to breakdown of the observed power-law and ultimately also the scale-invariance of vorticity amplification, with important implications for prevailing intermittency theories.
Helicity, as one of only two inviscid invariants in three-dimensional turbulence, plays an important role in the generation and evolution of turbulence. From the traditional viewpoint, there exists only one channel of helicity cascade similar to that of kinetic energy cascade. Through theoretical analysis, we find that there are two channels in helicity cascade process. The first channel mainly originates from vortex twisting process, and the second channel mainly originates from vortex stretching process. By analysing the data of direct numerical simulations of typical turbulent flows, we find that these two channels behave differently. The ensemble averages of helicity flux in different channels are equal in homogeneous and isotropic turbulence, while they are different in other type of turbulent flows. The second channel is more intermittent and acts more like a scalar, especially on small scales. Besides, we find a novel mechanism of hindered even inverse energy cascade, which could be attributed to the second-channel helicity flux with large amplitude.
In nature turbulent flows exist that are neither simply 2D nor 3D but boundary conditions, such as varying stratification, force them towards the one or the other. Here, we report the first evidence of the co-existence of 2D and 3D turbulence in an experimental flow driven by Faraday waves in water. We find that an inverse energy cascade at the fluid surface and a direct energy cascade in the 3D bulk flow underneath exist simultaneously. We base our analysis on temporally and spatially well-resolved velocity fields measured at horizontal and vertical planes. The findings suggest that the strongly turbulent 2D surface flow drives the 3D bulk flow through sporadic vertical jets as a source of momentum.
Local dissipation scales are a manifestation of the intermittent small-scale nature of turbulence. We report the first experimental evaluation of the distribution of local dissipation scales in turbulent pipe flows for a range of Reynolds numbers, 2.4x10^4<=Re_D<=7.0x10^4. Our measurements at the nearly isotropic pipe centerline and within the anisotropic logarithmic layer show excellent agreement with distributions that were previously calculated from numerical simulations of homogeneous isotropic box turbulence and with those predicted by theory. The reported results suggest a universality of the smallest-scale fluctuations around the classical Kolmogorov dissipation length.
Phoresis, the drift of particles induced by scalar gradients in a flow, can result in an effective compressibility, bringing together or repelling particles from each other. Here, we ask whether this effect can affect the transport of particles in a turbulent flow. To this end, we study how the dispersion of a cloud of phoretic particles is modified when injected in the flow, together with a blob of scalar, whose effect is to transiently bring particles together, or push them away from the center of the blob. The resulting phoretic effect can be quantified by a single dimensionless number. Phenomenological considerations lead to simple predictions for the mean separation between particles, which are consistent with results of direct numerical simulations. Using the numerical results presented here, as well as those from previous studies, we discuss quantitatively the experimental consequences of this work and the possible impact of such phoretic mechanisms in natural systems.
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