Strongly localized events of energy, dissipation, enstrophy and enstrophy generation in turbulent flows

Bershadskii, A.; Kit, E.; Tsinober, A.; Vaisburd, H.

doi:10.1016/0169-5983(94)90023-x

Cited by 15 publications

(8 citation statements)

References 41 publications

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“…An analogous estimate was also established in [14] for large fluctuations of turbulence energy dissipation ε (at least for moderate values of Reynolds number, see also [17])…”

Section: Singularities On Causticssupporting

confidence: 65%

“…In the paper [14] self-similar behavior of subregions with large values of energy, energy dissipation and vorticity (enstrophy) were established based on experimental turbulence data. Namely, let us divide a region occupied by a turbulent flow into a set of subvolumes V i with characteristic scale r and define a local mean of some (positive) scalar field g(x)…”

Section: Singularities On Causticsmentioning

confidence: 99%

“…Therefore, for convenience, we will not write large in the corresponding places. It is well established that the probability density function (PDF) for turbulent energy has an exponential form for L/r 1 (at least for large enough values of energy; see, for example, [14] and references therein). This allows us to use the exponential asymptote of the energy PDF as a standard…”

Section: Singularities On Causticsmentioning

confidence: 99%

“…The multifractality of turbulent energy fluctuations was first studied in the paper [16]. In [14] the existence of a multifractal asymptote for turbulence energy fluctuations was shown; that is, the singular (power-law) estimate…”

Section: Singularities On Causticsmentioning

confidence: 99%

“…It should be noted that another multifractal asymptotic can also be realized for the energy dissipation field ( [14], [17]): D (ε)…”

Section: Singularities On Causticsmentioning

confidence: 99%

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Singularities in multifractal turbulence dissipation networks and their degeneration

Bershadskii¹,

Gibson²

1994

Physica A: Statistical Mechanics and its Applications

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We suggest that large-scale turbulence dissipation is concentrated along caustic networks (that appear due to vortex sheet instability in three-dimensional space), leading to an effective fractal dimension D eff = 5/3 of the network backbone and a turbulence intermittency exponent µ = 1/6. Actually, D ef f < 5/3 and µ > 1/6 due to singularities on these caustic networks. It is shown (using the theory of caustic singularities) that the strongest (however, stable on the backbone) singularities lead to D eff = 4/3 (an elastic backbone) and to µ = 1/3. Thus, there is a restriction of the network fractal variability: 4/3 < D eff < 5/3, and consequently: 1/6 < µ < 1/3.Degeneration of these networks into a system of smooth vortex filaments: D ef f = 1, leads to µ = 1/2. After degeneration, the strongest singularities of the dissipation field, ε, lose their power-law form, while the smoother field lnε takes it. It is shown (using the method of multifractal asymptotics) that the probability distribution of the dissipation changes its form from exponential-like to log-normal-like with this degeneration, and that the multifractal asymptote of the field lnε is related to the multifractal asymptote of the energy field.Finally, a phenomenon of acceleration of large-scale turbulent diffusion of passive scalar by the singularities is briefly discussed.All results are based on experimental data.

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“…An analogous estimate was also established in [14] for large fluctuations of turbulence energy dissipation ε (at least for moderate values of Reynolds number, see also [17])…”

Section: Singularities On Causticssupporting

confidence: 65%

Section: Singularities On Causticsmentioning

confidence: 99%

Section: Singularities On Causticsmentioning

confidence: 99%

Section: Singularities On Causticsmentioning

confidence: 99%

“…It should be noted that another multifractal asymptotic can also be realized for the energy dissipation field ( [14], [17]): D (ε)…”

Section: Singularities On Causticsmentioning

confidence: 99%

See 3 more Smart Citations