The dynamics of helical decaying turbulence

Polifke, Wolfgang; Shtilman, L.

doi:10.1063/1.857476

Cited by 48 publications

(41 citation statements)

References 18 publications

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“…The PDF of the helicity angle in Fig. 3 quickly changes into a distribution with peaks concentrated at cos θ = ±1 as reported in other turbulent flows [9,10]. The appearance of the in- FIG.…”

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confidence: 85%

Transient Vortex Events in the Initial Value Problem for Turbulence

Holm

Kerr

2002

Phys. Rev. Lett.

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A vorticity surge event that could be a paradigm for a wide class of bursting events in turbulence is studied to examine the role it plays in how the energy cascade is established. The identification of a new coherent mechanism is suggested by the discovery of locally transverse vortex configurations that are intrinsically helical. These appear simultaneously with strong, transient oscillations in the helicity wavenumber co-spectrum. At no time are non-helical, anti-parallel vorticity elements observed. The new mechanism complements the traditional expectation that the development of a peak of the maximum vorticity ω ∞(t) would be connected to nearly simultaneous growth of the dissipation, eventually leading to the formation of the energy cascade with signatures such as spectra approaching -5/3 and strongly Beltramized vortex tubes. Comparing how different large-eddy simulations treat the spectral transport of helicity demonstrates that the dynamics leading to the helical vortex configurations requires both nonlinear transport and dissipation. This finding emphasizes the importance of properly modeling both nonlinear transport and dissipation in large-eddy simulations. Although three-dimensional turbulence is characterized by intermittent events both in space and time, it is often envisaged as a homogeneous, statistically-steady tangle of vortex tubes accompanied by a steady transfer of energy through the spectrum to high wavenumbers and a k −5/3 energy spectrum. This statistically-steady description has been used to verify turbulence models through simulations of forced turbulence and decaying homogeneous, isotropic turbulence [1,2]. In these studies, it is sometimes argued that the initial nonequilibrium transients can be ignored as being non-universal. However, each intermittent burst of turbulence is itself a transient dynamical process involving individual vortex interactions whose ensemble average is responsible for the overall statistical properties. Our objective is to apply a coordinated set of diagnostics in both physical and wavenumber space for numerically detecting individual vortex surge events and their effects upon the subsequent dynamics.The numerical investigation of the decay of turbulence discussed here is designed to improve our understanding of individual intermittent events and continues a long tradition in numerical modeling of the initial value problems in computational fluid dynamics. Numerically, the question of transient phenomena in turbulence has been considered previously using a variety of initial conditions [3][4][5][6][7]. In this letter the evolution from smooth, random, initial conditions introduced in [5] to steady turbulent decay is considered using this coordinated set of diagnostics. These diagnostics show that this initial value problem for turbulence evolves through several complex states in a sequence of transitions. These include:• formation of vortex sheets that interact, encounter each other transversely and then begin to roll up into vortex tubes, • development of a...

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confidence: 85%

Transient Vortex Events in the Initial Value Problem for Turbulence

Holm

Kerr

2002

Phys. Rev. Lett.

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“…To elaborate this statement, consider interaction (4.12) and assume that |a k | and |a p | are 0(1) and |a~| ~0 and k>p. Differentiating the last equation and substituting the first two equations for ä* k and ä p gives ä~q+ co 2 It thus appears that a spectrum of only positive and slightly decreasing helicity may be a relatively stable configuration. Recently Polifke and Shtilman [39] have performed a numerical integration of the NavierStokes equations on a (64) 3 grid. They compared strongly helical with nonhelical flow and found that large initial helicity impedes the transfer of energy towards smaller scales.…”

Section: Two Hydrodynamic Scenariosmentioning

confidence: 99%

Self-Organization in Three-Dimensional Hydrodynamic Turbulence Self-Organization in Three-Dimensional Hydrodynamic Turbulence

Knorr

Lynov

Pécseli

1990

Zeitschrift Für Naturforschung A

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The three-dimensional incompressible Euler equations are expanded in eigenflows of the curl operator, which represent positive and negative helicity flows in a particularly simple and convenient way. Four different basic types of interactions between eigenflows are found. Two represent an "inverse cascade", the interaction familiar from the two-dimensional Euler equations, in which only modes of the same sign of the helicity interact. The other two interactions mix positive and negative helicity modes. Only these interactions can transport all of the available energy to higher wave numbers. Initial conditions, which lead to the appearance of structures and self-organization, are discussed.

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“…However, Kraichnan and Panda [12] showed that local helicity fluctuations are not enough to explain the observed reduction of nonlinearity, but that a certain preferential alignment of the wave vector and the Lamb vector is needed to explain the observed reduction of nonlinear interaction. Even though this study showed that local helicity fluctuations might not be the sole actor in the reduction of nonlinear transfer, helicity, at least in the average sense, plays a role in it [13].…”

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Influence of initial mean helicity on homogeneous turbulent shear flow

et al. 2011

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Helicity statistics are studied in homogeneous turbulent shear flow. Initial mean helicity is imposed on an isotropic turbulence field using a decomposition of the flow into complex-valued helical waves. The initial decay of the turbulent kinetic energy is weakened in the presence of strong mean helicity, consistent with an analytic analysis of the spectral tensor of velocity correlations. While exponential growth of the mean turbulent kinetic energy is obtained, the mean helicity decays. Probability distribution functions (PDFs) of helicity are skewed and show that the imposed mean helicity prevails throughout the simulations. A waveletbased scale-dependent analysis shows a trend to two dimensionalization for large scales of motion and a preference for helical motion at small scales. The magnitude of the skewness of the PDFs decreases for smaller scales. Joint PDFs indicate a strong correlation of the signs of both, helicity and superhelicity, for all cases. This correlation supports the conjecture that superhelicity dissipates helicity. Helicity statistics are studied in homogeneous turbulent shear flow. Initial mean helicity is imposed on an isotropic turbulence field using a decomposition of the flow into complex-valued helical waves. The initial decay of the turbulent kinetic energy is weakened in the presence of strong mean helicity, consistent with an analytic analysis of the spectral tensor of velocity correlations. While exponential growth of the mean turbulent kinetic energy is obtained, the mean helicity decays. Probability distribution functions (PDFs) of helicity are skewed and show that the imposed mean helicity prevails throughout the simulations. A wavelet-based scale-dependent analysis shows a trend to two dimensionalization for large scales of motion and a preference for helical motion at small scales. The magnitude of the skewness of the PDFs decreases for smaller scales. Joint PDFs indicate a strong correlation of the signs of both, helicity and superhelicity, for all cases. This correlation supports the conjecture that superhelicity dissipates helicity.

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The dynamics of helical decaying turbulence

Cited by 48 publications

References 18 publications

Transient Vortex Events in the Initial Value Problem for Turbulence

Transient Vortex Events in the Initial Value Problem for Turbulence

Self-Organization in Three-Dimensional Hydrodynamic Turbulence Self-Organization in Three-Dimensional Hydrodynamic Turbulence

Influence of initial mean helicity on homogeneous turbulent shear flow

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