Decay of helicity in homogeneous turbulence

Levshin, A. O.; Chkhetiani, О. G.

doi:10.1134/s0021364013230070

Cited by 10 publications

(13 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The present theoretical predictions (4.3) for the decay exponent of helicity α H are compared to those of Levshin & Chkhetiani (2013) (LC13) in Table 3, obtained with considerations on integral invariants. To fill in Table 3, a very reasonable assumption is made, since initial conditions are not defined in LC13, so that there is no infrared slope σ.…”

Section: Appendix a Details On Non-local Expansionsmentioning

confidence: 89%

“…Recently, EDQNM has been intensively used to determine these theoretical decay exponents in different configurations, at high Reynolds numbers and after a large number of turnover times: the decay of kinetic integrated quantities in HIT (Meldi & Sagaut 2013), the extension to the decay of a passive scalar field in HIT (Briard et al 2015), and finally the decay of the velocity-scalar correlation in an isotropic turbulence with a mean scalar gradient (Briard et al 2016). The study of the helical case is therefore a natural extension and our predictions are compared to those of Levshin & Chkhetiani (2013) in Appendix B.…”

Section: About the Interest Of The Helicity Decaymentioning

confidence: 99%

“…Interestingly, the theoretical decay exponent of K H is equivalent to the one of the scalar variance in HIT with an infrared slope σ T = σ + 1 without any backscatter. Finally, our predictions for K H are compared to those of Levshin & Chkhetiani (2013) in Appendix B.…”

Section: The Decay Of Helicity K H (T)mentioning

confidence: 99%

“…The values of α H from LC13 are the same as the ones coming from (4.3) (−3/2, −8/5, −5/3 and −12/7), but there are not associated with the 8/5 −5/3 LC13 Table 2 −8/5 −5/3 −12/7 / (4.3) assessed by EDQNM -3/2 -8/5 -5/3 -12/7 Table 3. Comparison of the different theoretical decay exponents αH of helicity, obtained with classical CBC-like arguments, and by Levshin & Chkhetiani (2013) (LC13), as a function of the infrared slope σ of the kinetic energy spectrum E(k, t).…”

Section: Appendix a Details On Non-local Expansionsmentioning

confidence: 99%

“…Yet, the knowledge of the decay rate of integrated quantities, such as the inviscid invariants (kinetic energy and helicity), is crucial for the understanding and prediction of the turbulence dynamics in asymptotic regimes at large Reynolds numbers. Therefore, it could be interesting to have clear decay exponents for helicity: indeed, to our knowledge, there were no numerical papers providing decay exponents for helicity, except the theoretical one by Levshin & Chkhetiani (2013), which is not fully satisfactory as explained later on.…”

Section: Introductionmentioning

confidence: 97%

See 4 more Smart Citations

Dynamics of helicity in homogeneous skew-isotropic turbulence

Briard¹,

Gomez²

2017

J. Fluid Mech.

View full text Add to dashboard Cite

The dynamics of helicity in homogeneous skew-isotropic freely decaying turbulence is investigated, at very high Reynolds numbers, thanks to a classical eddy-damped quasi-normal Markovian (EDQNM) closure. In agreement with previous direct numerical simulations, a $k^{-5/3}$ inertial range is obtained for both the kinetic energy and helical spectra. In the early stage of the decay, when kinetic energy, initially only present at large scales cascades towards small scales, it is found that helicity slightly slows down the nonlinear transfers. Then, when the turbulence is fully developed, theoretical decay exponents are derived and assessed numerically for helicity. Furthermore, it is found that the presence of helicity does not modify the decay rate of the kinetic energy with respect to purely isotropic turbulence, except in Batchelor turbulence where the kinetic energy decays slightly more rapidly. In this case, non-local expansions are used to show analytically that the permanence of the large eddies hypothesis is verified for the helical spectrum, unlike the kinetic energy one. Moreover, the $4/3$ law for the two-point helical structure function is assessed numerically at very large Reynolds numbers. Afterwards, the evolution equation of the helicity dissipation rate is investigated analytically, which provides significant simplifications and leads notably to the definition of a helical derivative skewness and of a helical Taylor scale, which is numerically very close to the classical Taylor longitudinal scale at large Reynolds numbers. Finally, when both a mean scalar gradient and helicity are combined, the quadrature spectrum, linked to the antisymmetric part of the scalar flux, appears and scales like $k^{-7/3}$ and then like $k^{-5/3}$ in the inertial range.

show abstract

Section: Appendix a Details On Non-local Expansionsmentioning

confidence: 89%