Applicability of Kolmogorov's and Monin's 

equations of turbulence

Hill, R. J.

doi:10.1017/s0022112097007362

Cited by 82 publications

(103 citation statements)

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“…The most general forms of scale-by-scale energy budget for incompressible turbulent flows have been derived without making any assumption about the nature of the turbulence by Duchon & Robert (1999) without averaging and by Hill (1997), Hill (2001) and Hill (2002a) with averaging. Using the Reynolds decomposition (capital letters and ... indicate ensemble-and/or time-averaged quantities), the equation derived by Hill (1997), Hill (2001) and Hill (2002a) (which we refer to as KHMH equation) takes the form (see also Danaila et al 2012) ∂δu j ∂r i…”

Section: The Generalised Scale By Scale Energy Budgetmentioning

confidence: 99%

The turbulence cascade in the near wake of a square prism

2017

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We present a study of the turbulence cascade on the centreline of an inhomogeneous and anisotropic near field turbulent wake generated by a square prism at Re = 3900 using the Kármán-Howarth-Monin-Hill (KHMH) equation. This is the fully generalised scale-by-scale energy balance which, unlike the Kármán-Howarth equation, does not require homogeneity or isotropy assumptions. Our data are obtained from a direct numerical simulation (DNS) and therefore enable us to access all the processes involved in this energy balance. A significant range of length-scales exists where the orientation averaged non-linear interscale transfer rate is approximately constant and negative, indicating a forward turbulence cascade on average. This average cascade consists of coexisting forward and inverse cascade behaviours in different scale space orientations. With increasing distance from the prism but within the near field of the wake, the orientationaveraged non-linear interscale transfer rate tends to be approximately equal to minus the turbulence dissipation rate even though all the inhomogeneity-related energy processes in the scale-by-scale energy balance are significant, if not equally important. We also find well-defined near −5/3 energy spectra in the streamwise direction, in particular at a centreline position where the inverse cascade behaviour occurs for streamwise oriented length-scales.

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Section: The Generalised Scale By Scale Energy Budgetmentioning

confidence: 99%

The turbulence cascade in the near wake of a square prism

2017

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“…The pressure terms may be shown to vanish identically using homogeneity and incompressibility and assuming regularity as r → 0, as in the reflectionsymmetric, isotropic case [12,13]. The homogeneity condition S αγ,β (r) = S β,γα (−r) adds a further constraint, giving…”

Section: Howarth Equationmentioning

confidence: 99%

The reflection-antisymmetric counterpart of the Kármán–Howarth dynamical equation

Kurien

2003

Physica D: Nonlinear Phenomena

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We study the isotropic, helical component in homogeneous turbulence using statistical objects which have the correct symmetry and parity properties. Using these objects we derive an analogue of the Kármán-Howarth equation, that arises due to lack of mirror-reflection symmetry in isotropic flows. The main equation we obtain is consistent with the results of O. Chkhetiani [JETP, 63, 768, (1996)] and V.S. L'vov et al.[http://xxx.lanl.gov/abs/chao-dyn/9705016, (1997)] but is derived using only velocity correlations, with no direct consideration of the vorticity or helicity. This alternative formulation offers an advantage to both experimental and numerical measurements. We also postulate, under the assumption of self-similarity, the existence of a hierarchy of scaling ex-1 ponents for helical velocity correlation functions of arbitrary order, analogous to the Kolmogorov 1941 prediction for the scaling exponents of velocity structure function.

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“…Indeed, one can obtain Kolmogorov's 4/5 and 4/15 laws by integrating the second-order equations in the same manner, cf. Hill (1997).…”

Section: Resultsmentioning

confidence: 99%

Higher-order dissipation in the theory of homogeneous isotropic turbulence

et al. 2016

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The two-point theory of homogeneous isotropic turbulence is extended to source terms appearing in the equations for higher-order structure functions. For this, transport equations for these source terms are derived. We focus on the trace of the resulting equations, which is of particular interest because it is invariant and therefore independent of the coordinate system. In the trace of the even-order source term equation, we discover the higher-order moments of the dissipation distribution, and the individual even-order source term equations contain the higher-order moments of the longitudinal, transverse and mixed dissipation distribution functions. This shows for the first time that dissipation fluctuations, on which most of the phenomenological intermittency models are based, are contained in the Navier-Stokes equations. Noticeably, we also find the volume-averaged dissipation ε r used by Kolmogorov (J. Fluid Mech., vol. 13, 1962, pp. 82-85) in the resulting system of equations, because it is related to dissipation correlations.

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Applicability of Kolmogorov's and Monin's equations of turbulence

Cited by 82 publications

References 0 publications

The turbulence cascade in the near wake of a square prism

The turbulence cascade in the near wake of a square prism

The reflection-antisymmetric counterpart of the Kármán–Howarth dynamical equation

Higher-order dissipation in the theory of homogeneous isotropic turbulence

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