Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userIntermittency in the Joint Cascade of Energy and Helicity
67
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The statistics of the energy and helicity fluxes in isotropic turbulence are studied using high resolution direct numerical simulation. The scaling exponents of the energy flux agree with those of the transverse velocity structure functions through refined similarity hypothesis, consistent with Kraichnans prediction cite{Kr74}. The helicity flux is even more intermittent than the energy flux and its scaling exponents are closer to those of the passive scalar. Using Waleffes helical decomposition, we demonstrate that the existence of positive mean helicity flux inhibits the energy transfer in the negative helical modes, a non-passive effect.
rate research
Read More
Three-dimensional (3D) turbulence has both energy and helicity as inviscid constants of motion. In contrast to two-dimensional (2D) turbulence, where a second inviscid invariant--the enstrophy--blocks the energy cascade to small scales, in 3D there is a joint cascade of both energy and helicity simultaneously to small scales. The basic cancellation mechanism which permits a joint cascade of energy and helicity is illuminated by means of the helical decomposition of the velocity into positively and negatively polarized waves. This decomposition is employed in the present study both theoretically and also in a numerical simulation of homogeneous and isotropic 3D turbulence. It is shown that the transfer of energy to small scales produces a tremendous growth of helicity separately in the + and - helical modes at high wavenumbers, diverging in the limit of infinite Reynolds number. However, because of a tendency to restore reflection invariance at small scales, the net helicity from both modes remains finite in that limit. The net helicity flux is shown to be constant all the way up to the Kolmogorov wavenumber: there is no shorter inertial-range for helicity cascade than for energy cascade. The transfer of energy and helicity between + and - modes, which permits the joint cascade, is shown to be due to two distinct physical processes, advection and vortex stretching.
We show that oppositely directed fluxes of energy and magnetic helicity coexist in the inertial range in fully developed magnetohydrodynamic (MHD) turbulence with small-scale sources of magnetic helicity. Using a helical shell model of MHD turbulence, we study the high Reynolds number magnetohydrodynamic turbulence for helicity injection at a scale that is much smaller than the scale of energy injection. In a short range of scales larger than the forcing scale of magnetic helicity, a bottleneck-like effect appears, which results in a local reduction of the spectral slope. The slope changes in a domain with a high level of relative magnetic helicity, which determines that part of the magnetic energy related to the helical modes at a given scale. If the relative helicity approaches unity, the spectral slope tends to $-3/2$. We show that this energy pileup is caused by an inverse cascade of magnetic energy associated with the magnetic helicity. This negative energy flux is the contribution of the pure magnetic-to-magnetic energy transfer, which vanishes in the non-helical limit. In the context of astrophysical dynamos, our results indicate that a large-scale dynamo can be affected by the magnetic helicity generated at small scales. The kinetic helicity, in particular, is not involved in the process at all. An interesting finding is that an inverse cascade of magnetic energy can be provided by a small-scale source of magnetic helicity fluctuations without a mean injection of magnetic helicity.
We consider the turbulent energy dissipation from one-dimensional records in experiments using air and gaseous helium at cryogenic temperatures, and obtain the intermittency exponent via the two-point correlation function of the energy dissipation. The air data are obtained in a number of flows in a wind tunnel and the atmospheric boundary layer at a height of about 35 m above the ground. The helium data correspond to the centerline of a jet exhausting into a container. The air data on the intermittency exponent are consistent with each other and with a trend that increases with the Taylor microscale Reynolds number, R_lambda, of up to about 1000 and saturates thereafter. On the other hand, the helium data cluster around a constant value at nearly all R_lambda, this being about half of the asymptotic value for the air data. Some possible explanation is offered for this anomaly.
In this paper we discuss the dynamical features of intermittent fluctuations in homogeneous shear flow turbulence. In this flow the energy cascade is strongly modified by the production of turbulent kinetic energy related to the presence of vortical structures induced by the shear. By using direct numerical simulations, we show that the refined Kolmogorov similarity is broken and a new form of similarity is observed, in agreement to previous results obtained in turbulent boundary layers. As a consequence, the intermittency of velocity fluctuations increases with respect to homogeneous and isotropic turbulence. We find here that the statistical properties of the energy dissipation are practically unchanged with respect to homogeneous isotropic conditions, while the increased intermittency is entirely captured in terms of the new similarity law.
The Refined Kolmogorov Similarity Hypothesis is a valuable tool for the description of intermittency in isotropic conditions. For flows in presence of a substantial mean shear, the nature of intermittency changes since the process of energy transfer is affected by the turbulent kinetic energy production associated with the Reynolds stresses. In these conditions a new form of refined similarity law has been found able to describe the increased level of intermittency which characterizes shear dominated flows. Ideally a length scale associated with the mean shear separates the two ranges, i.e. the classical Kolmogorov-like inertial range, below, and the shear dominated range, above. However, the data analyzed in previous papers correspond to conditions where the two scaling regimes can only be observed individually. In the present letter we give evidence of the coexistence of the two regimes and support the conjecture that the statistical properties of the dissipation field are practically insensible to the mean shear. This allows for a theoretical prediction of the scaling exponents of structure functions in the shear dominated range based on the known intermittency corrections for isotropic flows. The prediction is found to closely match the available numerical and experimental data.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
